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9 points

·
21st Apr 2019

Range of a projectile is always maximum at 45 degrees. Anything above/below will be less than the maximum distance, and because 30 is 15 less than 45 the same range could be achieved at 15 more, or 60 degrees. This can help visualize: https://www.desmos.com/calculator/gjnco6mzjo

9 points

·
30th Dec 2018

If you're allowed to graph the expressions, then that's another way of finding the solutions.

But if you don't want to follow that approach (or aren't allowed to), then you have to analyze a whole bunch of different scenarios.

(1) (x+3) and (3x-1) are both positive

(2) (x+3) is positive and (3x-1) is negative

(3) (x+3) is negative and (3x-1) is positive

(4) (x+3) and (3x-1) are both negative

9 points

·
6th Jan 2020

Since PQRS is a Rhombus, PQR is congruent to PSR.

Also, PQR and PQR are isosceles.

And a triangle has interior angles that sum to 180.

This gets you, in particular, angle PRQ.

Then 33 + 68 + PRQ + x = 180.

7 points

·
2nd Aug 2011

For each guy ordering a pizza, we're going to assume that there is a 65% chance that this pizza has pepperoni in it. Let's call X the number of pizza w/ pepperoni ordered on this night. X follows a Binomial Distribution.

He'll run out of pepperoni if X>16.

We now have

P(X=20) = 20nCr1 * (0.65)^(20-0) * (1-0.65)^(0)

P(X=19) = 20nCr19 * (0.65)^(20-1) * (1-0.65)^(1)

And so on ... So P(X>16) = P(X=17) + ... + P(X=20) = 0.0443756

I'm not really good at probability, but if you have any question, don't hesitate !

7 points

·
12th Jun 2018

> How would you graph this absolute function?

With Desmos.

> y = | -(x+1)2 +2 | > > Is there a way to convert this into > > y = a|bx+c|+d?

No, because your first function is a second order polynomial while your second function is a first order polynomial, so you will have two kinks in you first function since (x+1)^2 changes directions by itself but only one kink in your second function as bx+c will always decrease or increase.

You can however by adding a second absolute function bracket bend the first order polynomial once more and approximate the first function: https://www.desmos.com/calculator/nj1jwuplv8

But you can never make it smooth just by adding constants. You need to have a second order polynomial somehow. You can however switch signs on the two terms.

6 points

·
10th Jun 2018

Surpised no-one has mentioned Anki. Anki is a free flashcard program designed to time reviews in such a way so you don't forget them. It has a web version and along with apps for most major operating systems. There are a bunch of shared decks for french and other languages.

6 points

·
23rd Jan 2011

Okay here's the link

the 0 = 5*0 is just there to explain that for an equation to be equal to zero, then one part of the equation must equal zero. Because you can't multiply and get a zero for an answer without one of the parts being zero.

Let me know if you still need help, I know I have bad handwriting.

5 points

·
11th Apr 2011

Just looked at your comment history to try to help generate a topic that might be relevant to your interests, since you'll probably do a better job if you care about the subject. It looked like you might play Minecraft, so one possibility would be the social benefits of gaming. The topic has adequate source material (researcher Jane McGonigal's book __Reality is Broken__ , here's her TED talk; also an article from Psychology Today) but is also nice because it pushes back against a better publicized narrative that blames gaming for a variety of social ills.

5 points

·
9th Jul 2012

If your school is anything like mine, it should offer a library resource for you to find articles. A lot of colleges offer online libraries as well so it isn't too difficult to find articles that you are looking for.

One of my professors recommended using this site for articles: http://www.jstor.org/

But when I googled "scholarly articles", Google provided: http://scholar.google.com/

5 points

·
8th Aug 2018

If we are talking about molecules instead of atoms, the body is only 20% proteins by mass. Here is what I found googling 'Human body composition by mass'

The exact amount varies depending on environmental factors, but Water is 60% to one sig fig.

5 points

·
23rd Dec 2012

Here's how to do a JOIN, I'll leave the rest to you. Might want to check out SQLzoo for some practice.

select * from csorder where orderdate in 'JUL, DEC' and orderdate = '2011' JOIN cscustomer ON (csorder.orderid = cscustomer.orderid) ...

5 points

·
12th Apr 2011

YouTube - Java Tutorials for Beginners

Java Basics - Input and Output

Google is your friend - You'll want to come back when you've got some slightly more specific questions.

3 points

·
4th Apr 2012

Okay. i can share my homework with you butyoushould familiarize yourself with the cubic spline in order to understand it and i can answer questionslater butsleep now I uploaded my homework with a fairly terse explanation of how tosolve for a parametric spline here

3 points

·
30th Jan 2013

Here you go buddy:

https://www.dropbox.com/sh/rrmtpnv230nx21t/xyToweWB69

This is my entire Ochem II course I compiled. I have the two textbooks I used along with the notes I typed out in Microsoft OneNote.

If you do happen to use my OneNotes then make sure you click on the right side for the different pages and formula sheets I made. My notes **are** missing stuff and may contain errors.

I'll be surprised if you're using the same textbooks as me. I included the ACS booklet, I do recommend you to study that in advance. Also, you can find the worked out problems of the ACS booklet somewhere in the link.

I do recommend to download the contents of the link, just in case I take it down by accident or if you lose the link.

I'm really proud of my Chapter 11 - Nucleophilic Sub. and Eliminations.one file. It covers it very well, it should be good enough for your exams or the ACS exam. So if you needed to you could just study off that instead of making your own notes or reading your text.

3 points

·
12th Nov 2012

Just by looking at the domains, all of those sites seem very sketchy. You need to do searches on academic sites. Try searching Google Scholar

3 points

·
7th Apr 2015

Yeah basically Sonny! Glad it might have helped a bit Eloosh, I did a little on this in uni but sounds like you are going more in depth than I had to (I looked up a bit extra on the side via Epigenetic Control of Gene Expression on Coursera). Obviously x inactivation is a whole chromosome being switched off while imprinting is usually specific genes. This link might help you too, especially where it mentions how imprinting was first discovered. Good luck!

3 points

·
24th Feb 2012

http://www.khanacademy.org/ is the best tutoring website I've been to ever. When I was in calculus, I looking for a website like this, but I didn't find it until after I dropped the class.

Also for step-by-step help in case you missed something and can't quite pick out what it is, I recommend http://www.wolframalpha.com/

3 points

·
17th May 2015

No one is going to do your homework for you, but I'll help you out by giving you some links to HTML and CSS tutorials.

3 points

·
9th Jun 2015

Talk to your teacher, ensure he/she did not make a typo.

The research I did via google tells me it does not quite mean severally but rather the take away I find is "inclusive" with the following synonyms showing up via a danish site: fraternal , collegial , loyal , trustworthy , compassionate , co-responsible

I believe that it refers to a more joint effort of sorts.

Typing ""Solidarisk" post world war II" into google shows a book that may or may not have much to do with this.

Further looking into a couple books with this term leads me to see the term "wage policy" coupled with the term.

" In actuality, the LO has gone so far that the so-called solidarity wage policy (solidarisk 16nepolitik)"

This line of research may provide a better line of reasoning. Note that the wage policy papers were written around 1970 which fits in with your timeline.

That is what google tells me at least.

3 points

·
25th Jun 2018

Hey, here I've plotted out the problem using Desmos, an online calculator.

Use the slider for X to consider different positions for P, Q is placed automatically. The circle around Q shows positions that are 2*sqrt(6) units away from Q. So you're looking for the position(s) where P is somewhere on that circle.

Algebraically, that means that:

(x*__P__* - x*__Q__* )^2 + (y*__P__* - y*__Q__* )^2 = 2*sqrt(6)

3 points

·
22nd Aug 2017

>I still don't understand what is M. I know it's **degree** but still

Nope. The value of m is what we call the slope, or gradient, of the line.

It's a measure of the line's steepness.

Move the slider around on this graph, and watch how changing the value of m changes how steep the line is.

3 points

·
22nd Aug 2017

For this particular problem I'd first sketch a graph of both 2|x| and |x-3|. You can see this here. You can see clearly which parts you're looking at,

there's an intersection where -2x = -(x-3) on the left,

and an intersection where +2x = -(x-3) on the right.

And the range we want to find is between -infinity and the left intersection, and between the right intersection and +infinity. So find the intersection points and you have your range.

Alternatively, you could find the intersection points by stating:

2|x| = |x-3| , then squaring.

4x^2 = (x-3)^2

3x^2 + 6x -9 = 0, then find the roots from there.

3 points

·
20th Aug 2017

Careful, the amplitude goes from the middle to the crest, not from positive crest to negative crest. It tells you that the wave oscillates between +1 and -1.

But yeah, the wavelength is pi, 3.14, because the second peak occurs at (pi,1).

A cos is just a sin that's shifted along the x axis by pi/2. This relates to the phase of the wave. This is a cos because it intercepts the y axis at its maximum, not 0.

The general equation of a cosine wave is:

y = A cos(2π (x-ϕ) / w) + c

Where we have the following:

A - amplitude of the oscillations

w - Wavelength of the wave

ϕ - Phase, though this is 0 in our case

c - A constant, the average that our wave oscillates around. This is 0 in our case too

What we have left is:

y = A cos(2π x/w)

Here's a little exercise I just whipped up on the incredibly useful graphing calculator desmos.com. Try messing around with the Amplitude and wavelength sliders until you can get the graph you need.

3 points

·
4th Nov 2012

OK, most of the stuff is very good indeed. Just watch out for a few things which come up quite a bit.

1) If an object (eg. a poll) is plural is generally needs an 's' (eg. polls)

2) If an object starts with a vowel, 'a' changes to 'an' (eg. a door, an egg)

3) Using colons and semi-colons is good but not so much! Use a maximum of one per sentence and then put a full stop and start the next sentence. Otherwise it is very difficult to read. (Point; evidence. Point; evidence. NOT Point; evidence; point; evidence; point ...)

4) Where you write "(Understanding Society 2012)" it is not necessary to write that every time you use the poll. Use it once and then just call it 'the poll'.

5) Other than that there are few mistakes and the standard of English is very good :) I have highlighted where I have changed things. If you don't understand something then just ask. Most of the changes are just to make it better English, not that the English is actually wrong.

https://www.dropbox.com/s/syehpxjpmdg18t5/Mid-term%20-%20Copia1.docx

3 points

·
1st May 2017

Looks like you're in safe hands with u/thePINKavenger, but bear in mind that it's against the rules to say how urgent your request is. I don't know how closely that rule is enforced, but I'd hate for your post to be taken down.

You can use a graphing calculator like Desmos to help you visualise your function here. I know that helped me understand projectile motion.

3 points

·
28th Feb 2015

Subtract 1 from each side

-e^(-6a)(6a + 1) = -0.2

Divide by (6a + 1)

-e^(-6a) = (-0.2)/(6a + 1)

Multiply both sides by -1

e^(-6a) = (0.2)/(6a + 1)

Take the natural log of both sides

-6a = ln(0.2) - ln(6a + 1)

After that, I get stuck. Although, it is possible to be solved numerically using Newtons Method or Interval Bisection. It can also be solved by graphing the LHS and the RHS and finding the point(s) of intersection.

Either of these methods yields the two answers a = -0.1534 or a = 0.4991

3 points

·
24th Feb 2015

This is a "weighted average" - to find your average x-value: take each location x value * weekly Quantity/ total quantity and add them all up.

x = 5*(15/90)+6*(20/90) + 3*(25/90) + 9*(30/90) = 6

- a normal average will put your location nearer A,B,C - but because D makes more clothes than the other locations, your point will need to be closer to D. graphing helps visualize this. see my link here: https://www.desmos.com/calculator/b2dn7wecwx

3 points

·
2nd Jun 2011

http://www.glenbrook225.org/south/departments/science/biology/APBiology283/Pages/Lectures.aspx

This site follows an AP biology book; go through the chapters. I used this for my AP Bio course this year, and it helped. Also:

http://www.khanacademy.org/#biology

Khan Academy is well known here on reddit, so I think that is obligatory. I also used it to review before my exam, and it provides an in depth review to certain processes.

3 points

·
17th Jul 2014

Soz, went for lunch.

So, Im assuming you have no programming knowledge whatsoever.

If you havent already done so, you're going to need to install Small Basic, You can download it from here http://smallbasic.com/

Also the introducing Small Basic pdf (Link Here) You should do the first 14 or so pages, it introduces you to programming in small basic (Who would have guessed) and is what your prepatory task is anyway.

(You can skip most of the larger blocks of text, just read the various lines of text that surround the screenshots of code)

**Task 1**

The first task is very simple, just copy the code straight from the IntroPDF and replace the formula to one that converts the other direction. You've done algebra in maths yes? (Oh and dont forget to change the text where it should say Celsius or Fahrenheit)

By now you should know how to use simple commands in SmallBasic, like getting it to let you enter a number and then doing something to that number.

**Task 3 (?)**

Now it wants you to add a simple IF statement.

In plain english.

If the number you entered is less than 100'C then the screen should say "Less than the boiling point of water"

If the number you entered is greater than 100'C then the screen should say "More than the boiling point of water"

The syntax for an IF statment in SmallBasic is

If (condition) Then action EndIf

In our case, our conditions are firstly; when the number entered is greater than 100, and secondly; when the number entered is less than 100.

Look at the clock example in the IntroPDF, your task here is exactly the same, except instead of checking if the time is before or after 12, its if the number is higher or lower than 100.

And our actions are going to be simply printing text on the screen. You already know how to do that from the previous task.

3 points

·
2nd Apr 2017

Get rid of "If you'd like me to be completely honest". It's very much implied you're being honest about your life story.

Take out "(AA for short)". That information is not necessary because it does not contribute anything to your story.

Should be "pitting my brother and me". Your mother pitted me against him, not I against him.

Should be "I found solace". One does not find solace like one finds a ring. You find a ring but you seek refuge, not seek a refuge.

The phrase "keeping my grades high enough" might rub the admissions committee the wrong way. Even though it's true that you devoted more of your time outside of class to extracurriculars because of your unique circumstances, you probably don't want to tell that to the ad com.

Remove the semicolon between "After five years of this, we moved to Florida to escape him when I was sixteen; between my sophomore and junior year of high school." In this case, a semicolon should separate two independent clauses. "between my sophomore and junior year of high school" is not an independent clause because it cannot stand by itself. Think of it this way, if someone came up to you and blurted out "between my sophomore and junior year of high school", would you have any idea what he/she/it was talking about?

Remove "on my own".

Grammatical errors are hard to find. I suggest doing a cursory check on http://www.hemingwayapp.com/ or grammarly.com. This is the very least you can do to revise a writing piece.

Best of luck.

3 points

·
18th Aug 2018

Like the other commenters are saying, Python is probably going to be your best bet. It's currently the 'real programming language' used most for math and statistics (unless you need crazy high performance, in which case you might use FORTRAN or C or something).

I'd recommend installing Python via Anaconda, which is a distribution of Python specifically for data science. You want version 3.6. The Matplotlib library (libraries provide premade code to make developing your programs easier) is good for drawing your graphs. I'm also a big fan of developing programs of using Jupyter Notebooks, which are a way of writing Python code and immediately seeing its output right there next to it. Jupyter comes with Anaconda. You could even do the whole project in Jupyter and do something like this to make it interactive.

The only caveat here is if the assignment requires you to turn in one single '.exe' file and have your teacher just be able to run it with no setup. Python is not very good at this. In this case, you might consider writing the program in C# and using Windows Forms for the interface, since I assume most schools run Windows.

3 points

·
3rd May 2018

What do you mean no? You can literally run the code I gave you: https://repl.it/repls/JoyfulBitterGoals and see that it gives you what you expect. I even made it print out the binary representation, which you can then put in https://www.h-schmidt.net/FloatConverter/IEEE754.html and see that the value stored in the float is exactly what you expect.

3 points

·
21st May 2021

Slight clarificaton: 0! = 1, and then for a positive integer n, n! = n*(n-1)!.

This is useful later, because then you can do things like 7!/7!0! and have it make sense instead of being undefined.

One way you can look at n! is the number of **permutations** or **ways to order** n elements.

If there are 0 elements, well, that's it. There's only one way to arrange them: nothingness.

If there is 1 element, that's also it: only one way to arrange it.

Anyhow, others have already explained what the answer they're looking for is (C) and why it's wrong (C is the number of pizzas with 4 different toppings...though it's also the number of pizzas with 3 different toppings).

<u>Anno's Mysterious Multiplying Jar</u> is a great introduction to factorials, but at a K-2 level. The artwork is gorgeous, though.

3 points

·
14th Apr 2015

Go to brave new worlds Wikipedia page to find some sources. Also, my reading of the book (it's one of my favorites) tells me that your thesis should be something about how in order for a person to be happy they need to ha e a purpose in life and be able to work to achieve it. The government could replace happiness from individuality by giving people drugs, but they had to reinforce a persons mission in life to maintain peace. (This is very similar to the noble lie in Republic by Plato)

3 points

·
20th Nov 2012

I've never read your book, but unless your instructor told you to do a one-paragraph-per-chapter essay, don't. They're terribly boring to read and are little more than a book report: First he says this. Then he says that. Then he says this. Repeat until asleep.

You mention that much of the book revolves around semantics. Taking your word for it that it's true, focus on that. Make a thesis that says something along the lines of "Sun Tzu's *Art of War* relies heavily on semantic wordplay to make obvious points." Then pick a few to maybe a half dozen examples you find in the book. Then analyze your examples.

For example, find a quotation from the book: "Sun Tzu argues that "quotation here." It is clear that his istention is that blah, blah, blah. What he elides however is that [your analysis here.]

Repeat for each example you find, saving your best, strongest analysis for last. (Or use it first, a matter of choice, really.)

Then write a conclusion stating that while *The Art of War* is a classic book, it is not as good as some might think because his arguments are not very strong, blah, blah, blah.

3 points

·
7th Nov 2011

This is indeed the 'assignment' operator and is the standard pseudo-code syntax used in "Introduction to Algorithms" by Cormen, Leiserson, and Rivest, which the __de facto__ standard algorithms text. You'll find this notation throughout CS courses taught with pen-and-paper. It's written this way for the following reasons:

- To unambiguously distinguish it from the equality operator (== in C and derivatives)
- To make it obvious that assignment happens from right to left. That is to say, first we evaluate the statement on the right side of the arrow, and then we store it in the variable whose name appears on the left.

It's obvious to those who have programmed for a while, but remember that algorithms is often the first or second class taken by CS students who may have little programming experience, so the notation is designed to be crystal clear.

2 points

·
8th Sep 2011

that is why the company only lets people go back to certain times. you can come up with an excuse for hte company in your story (maybe they dont want to alter certain events)? Or the technology is still new and they dont know how to pick any time, but are being a nice company (not murders) by releasing it early. Also to make your calculations easier use wolfram alpha. For example if I wanted to go back to the civial war 1861 and I left right now I would have to travel to July 31, 1861 (which is not september like we are in now) wolfram alpha

2 points

·
23rd Aug 2015

I think you can use L'hopital's rule on the first one and on the second bit of algebra manipulation, not done limit's for a while so could be totally wrong on this one.

My Working https://gyazo.com/90baa7b15c369c61709d85ad9b8efa69

2 points

·
23rd Aug 2015

The acceleration is given in metres per second and the velocity is given in kilometres per hour so first you should convert. The acceleration is the derivative of the velocity so you should integrate to find an equation for velocity, you are told it starts from rest so take that as c = 0. Then solve the integrated equation for the velocity in the correct units. Part b should then be a simple suvat equation based off the variables you worked out. My Working https://gyazo.com/e0cf6681f368ec9ee3c542c0f01c91ce

Edit - I'm an idiot its not suvat for part b as the acceleration is not constant, you would again have to integrate the velocity equation and solve when t = the answer from part a

2 points

·
12th Jun 2013

Try some of these videos by Khan Academy. They helped me immensely when I was in high school, and they have videos on pretty much every math topic.

2 points

·
16th Mar 2013

If you let h = 6 - r , you can write V = πr^(2)(6-r) = 6πr^(2) - πr^(3). Taking the derivative gives dV/dr = 12πr - 3πr^2. Maxima or minima occur when the derivative is 0, so setting dV/dr = 0 gives the extrema in terms of r, and plugging back in should give the right answer.

I believe you're calculating it in meters, so you get a result of 1/4 m, while the answer is supposed to be in cm. If you convert your units, you should get the right answer.

We can say the base has side length x and the sides have height h. We want V = x^(2)h = 4000cm^(3), and we basically want to minimize surface area. Since the box is open, hence has five sides, the surface area is the area of the bottom (x^(2)) plus the area of each of the sides (xh), i.e., A = x^2 + 4xh. Writing h in terms of x (from x^(2)h = 4000), you should be able to set it up as in the other problems and find x which minimizes A (that is, the value of x for which dA/dx = 0).

Here is Khan Academy's page on derivative applications; there's a whole section on optimization.

2 points

·
6th Dec 2016

Per this article, "There is debate" concerning the age "at which the ability to compare, including conservation and transitivity, develops." But you could check the research cited for that statement and other relevant materials for more detail and compare it with data on developmental milestones for numeracy:

Caddell, D. (1998). "Numeracy in the early years: What the research tells us. Dundee, Scotland: Learning and Teaching Scotland.

Stephan, M., & Clements, D. H. (2003). Linear and area measurement in prekindergarten to grade 2. In D. H. Clements & G. Bright (Eds.),

__Learning and teaching measurement__(2003 Yearbook, pp. 3–16). Reston, VA: National Council of Teachers of Mathematics.Wilson, P. S., & Rowland, R. (1993). Teaching measurement. In R. J. Jensen (Ed.), Research ideas for the classroom: Early childhood mathematics (pp. 171–194). Reston, VA: National Council of Teachers of Mathematics.

2 points

·
15th Apr 2015

Best pay dirt I found came from this essay (full text here) which includes English translations of contemporary responses to the war:

- Medick, Hans. "The Thirty Years' War as Experience and Memory: Contemporary Perceptions of a Macro-Historical Event."
__Enduring Loss in Early Modern Germany: Cross Disciplinary Perspectives__. Ed. Lynn Tatlock. Leiden: Brill Academic Publishers, 2010. 25-49.

Scholar Peter Wilson identifies the following texts as sources for contemporary histories of the war, translated into English. Perhaps your school or local library could help you acquire one.

- Benecke, Gerhard, ed.
__Germany in the Thirty Years War__. St Martin's Press, 1979. - Helfferich, Tryntje, ed.
__The Thirty Years War: A Documentary History__. Hackett Publishing, 2009. - Wilson, Peter H, ed.
__The Thirty Years War: A Sourcebook__. Palgrave Macmillan, 2010.

EBSCO or whatever database your school library uses should access

* Beller, E A. "Contemporary English Printed Sources for the Thirty Years War." __American Historical Review__ 32(1927).

2 points

·
26th Feb 2012

The rules must be memorized ad hoc: there are no tricks which can be used to derive those rules from the periodic table (except there are groups of things close to each other eg. Ca,Ba,Sr). I made a spreadsheet of the rules which helped me memorize them.

2 points

·
25th Mar 2012

Do some google searches for "Android Market Share" or "Smartphone Market Share"

Try to find the most recent figures. Here's one from the end of last year.

2 points

·
20th Aug 2015

you can use the equation ΔStotal = Rlnk where k is equilibrium constant and r = 8.314 to find the total entropy of the reaction. Once this is found you can use ΔStotal =ΔSsystem + ΔSsurrounding to find the enthalpy, as you have worked out the total entropy for the respective temperature and the entropy of the system can looked up in a text book.

My Working https://gyazo.com/0ee0253db53a6f1fd1f4276661bbf84d

2 points

·
3rd Dec 2011

This may be a little overkill...but it may help you think outside the box. ;) http://www.youtube.com/watch?v=_ve4M4UsJQo

And then there's eHow...

http://www.ehow.com/how_7765078_design-rube-goldberg-project.html

2 points

·
16th Oct 2019

Sorry I accidentally posted my comment before I was done.

What you are dealing with is equations of lines which are in the form of y=mx + b. m would be the slope and we can see that for every 1 increase in x, y will increase by m. The b variable is what I call the "offset" of the line. We can see that it is a constant (basically it doesn't change regardless of what x is), so all it does is increase y by itself.

Here's the firdt few points of the equation y = 2x:

(0,0) (1,2), (2,4)

Now let's look at the points of y = 2x + 3:

(0,3) (1,5) (2,7).

From the points we can see that the slope is the same, being that y is increasing by 2 each time, but the original point just started at 3 instead of 0. Thus we can say that the line has an offset of 3.

You'll probably learn to know the b as the y-intercept, or at what y value the line hits the y-axis. This is true, but I feel like it doesn't explain well what it actually does to the graph.

I would highly recommend trying out Desmos, which is an online graphing calculator. It allows you to visualize different functions in a very unset friendly way. Try entering the function y = mx + b and then click on the buttons that pop up under the equation to add a slider for both m and b. From there you can see your line equation and then use the slider to change the values of both m and b and see how your line transforms.

2 points

·
16th Oct 2019

If you have a line, the slope doesn't change whether or not you add a constant (a number). I think it's better illustrated in a graph here, you see that the two graphs are parallel (thus they have the same slope) regardless of the constant (the c-value in the graph I linked).

2 points

·
28th May 2013

Have you gone to the Wikipedia pages for each war and looked at the list of sources and external links?

You might also try http://scholar.google.com/

Are you looking for primary sources (documents from the time period) or secondary sources (second-hand accounts, nonfiction books analyzing the time period, etc.)?

2 points

·
16th May 2013

Did yo try looking at the Wikipedia article on him to see the sources that they used? You can follow links at the bottom of the Wiki article to sources.

Also, have you tried Google Scholar? http://scholar.google.com/scholar?hl=en&q=W.+B.+Yeats&btnG=&as_sdt=1%2C15&as_sdtp=

2 points

·
25th Apr 2013

Perhaps mention the many other types of video games that exist. The reason being, would the same proponents of the correlation in violence be as quick to say that an interest in RollerCoaster Tycoon makes someone more likely to be an architect or that playing the Sims makes one more likely to be a god?

Edit: For sources, try Google Scholar http://scholar.google.com/scholar?hl=en&q=video+game+violence

2 points

·
8th Mar 2013

on my 2nd search attempt: http://scholar.google.com/scholar?hl=en&as_sdt=0,6&q=lazy+habits

also try searching for "lazy school" and for terms like "education", "motivation" (or "lack of..."), etc.

2 points

·
24th Jan 2013

Your University should give you free access to some great scholarly journal/article entities that have very well established research on all/most of the listed topics. You can also use google scholar and just begin with a simple search on these. I did a quick search for titanium foam, and it is being used for bone tissue engineering. Also, The Journal of Materials Research(JMR) would be a great resource if your university gives you access to it.

High temperature polymers, biosensors, and battery materials are all fairly broad topics so if you're shooting for ease of research alone, those wouldn't be bad choices. But again, you may want to do a search on all of these and determine which interests you the most before jumping to the easiest to find information on.

Hopefully this was at least somewhat helpful and not too late.

2 points

·
17th Jan 2013

Google scholar is an excellent tool. Some papers will be on sites behind pay walls and your best bet for that would be a university library or at least the creds.

Here is A Short History of Lung Cancer Toxicological Sciences 2001 published free as a start.

2 points

·
23rd Sep 2012

I'm pretty sure all you have to do to find the maximum number of zeroes for a polynomial is to look at its degree, which in this case is 6.

http://www.khanacademy.org/ is a place people rave about for learning how to do things. It's a site where they have videos on a multitude of subjects such like math, economics, SAT prep, etc, even a precalculus section. They have sections on pretty much everything and if you do a little searching, you might be able to find help that's already there next time.

I hope that helped :)

2 points

·
10th Sep 2015

Sorry I removed my earlier comment, I just realized I was not allowed to post a full solution, only give hints. One of my earlier comments was removed because of this.

First of all, I recommend to name iteration variables something like $i. Try to keep your variable names as short as possible, too. Right now you've defined $Counter, but you're referring to $counter on line 12.

To output your results, use echo. You can include HTML there as well. Also make sure your indentation is correct at all times!

You seem to have understood the logic behind the problem (by using the modulus operator), so you're on the right track! Run the script and see if you get any errors, fix those and keep at it until you've got a working solution.

I also recommend that you use a for loop.

for($i = Starting_Number; $i <= Ending_Number; $i++) { //Check for fizz, buzz or fizzbuzz }

2 points

·
2nd Jun 2021

Hmm, how about practicing reading a book while listening to the audiobook at the same time? That will pace you so you read more slowly and carefully and might help you understand and remember what you're reading better and train your brain to read better.

If you want to try this for free, you can get free audiobooks of classics on LibriVox and the texts on Project Gutenberg. The readers on LibriVox can be variable, I can recommend John Van Stan, he's a very good reader and has read several of the Alexandre Dumas novels (The Three Musketeers and so on), which are really good fun and classic literature. You get get the texts here.

PS There's a phone app for LibriVox and you can download the audio files so you're not using data, if that helps.

2 points

·
17th Dec 2015

Just as a common sense sort of thing, no matter how good your plan is, something outside of it can mess it up. This is currently best-known in the saying 'No plan survives first contact with the enemy', which is a paraphrase of Helmuth von Moltke the Elder. https://en.wikiquote.org/wiki/Helmuth_von_Moltke_the_Elder

Now, in a common-sense way, I would say your teacher is correct. In a technical way, I would say that you are correct. It depends on the meaning of 'will'. If will implies that external events are certain to make things so that you have to change your plan to succeed, then the sentence is false. If will implies that external events are very probable to make things so that you have to change your plan to succeed, then the sentence is true.

2 points

·
5th Apr 2019

Do you mean something that looks like this?

If so, you can use the fact that both the left and right small sides are equal in length. That means it's also an isosceles triangle. That means it has the property that its other two angles are equal to each other.

2 points

·
31st Mar 2019

This is the mean value theorem.

I really wish it was called the "Average Slope" theorem.

Here's what it says: if the function is differentiable over an interval (a, b), and continuous over the interval [a, b], then somewhere between a and b, the derivative will have the same value as the line that connects the two endpoints.

We need the function to be continuous on [a, b], because we need to have the two endpoints: (a, f(a)) and (b, f(b)).

But it doesn't need to be differentiable at a and b themselves. That's what my link above shows. Even though my function has cusps at x = 2 and x = 5, we can still connect the points (2, f(2)) and (5, f(5)) with a straight line. And somewhere between those two points the derivative will take on the same value as the slope of that line.

It is not differentiable every between -6 and -2. So the theorem does not apply.

2 points

·
31st Jan 2019

We're gonna use that C has a minimum point at x=4

(I'm gonna say C = x^3 - 9x^2 + px to avoid confusion about which y I'm talking about. I'm also assuming you meant to write - 9x^2 , lemme know if I'm wrong on that! )

This minimum has dC/dx = 0 at x = 4, so let's differentiate C

dC/dx = 3x^2 - 18 x + p

When x = 4, dC/dx = 0, so just plug in those numbers to find that p = 24.

So far there's no integration, it probably comes up later in the question. Here's an online graphing calculator that I wish I'd had during my A-levels, it's super useful for questions like this.

2 points

·
5th Nov 2018

Here's something for the second part.

I've used desmos, the online graphing calculator, to graph the wave function of the electron in the Particle-In-A-Box system. Here's another source for that system.

Just in case you're confused, we use A sin(nπx/L) because:

- It's 0 at x=0 and x=L, like how a guitar string can't vibrate right at the ends
- Why not some other function that's 0 at each end? Sine waves specifically satisfy the Schrodinger equation, because its second derivative is proportional to the negative of the original sine.
- Why the π and L? Specifically to make it so n peaks-or-troughs fit between 0 and L
- Why the n? Because n can be any integer > 1 and the function still satisfies the Schrodinger equation
- What's A? The Schrodinger equation doesn't set this, we set it by requiring the wave function squared to have an integral of 1 in the box.

2 points

·
14th Dec 2012

If it were me, I would do a paper on microbial life found near vents in the ocean floor.

Extremophiles like that make for interesting reads.

Or.... Methane hydrate deposits in the ocean releasing methane into the atmosphere.

2 points

·
28th Nov 2012

2 points

·
4th Mar 2012

If you're not familiar with http://www.khanacademy.org/, check it out.

Scroll down to "Algebra: Exponents and Radicals" and watch the first several videos. It's a great resource for when you miss math class or you still don't really understand something.

2 points

·
12th Jun 2015

I don't know C++, so I attempted this in Python. It looks like this: http://ideone.com/plain/4Sr5xJ

I got (w, x, y, z ) to be (-10.5833333333, -6.41666666667, 28.3333333333, 52.5)

edit: I'm stupid, didn't read the question fully. (w, x, y, z) = (-11 ,-6 30, 55)

Code looks like this: http://ideone.com/plain/4Sr5xJ

2 points

·
24th Feb 2014

The book Force and Motion: An Illustrated Guide to Newton's Laws has an extended treatment of this problem, as a worked example.

Here is a PDF excerpt showing the worked example.

2 points

·
18th Sep 2014

Google is your best friend for things like this (unless you are ever required to find peer reviewed primary literature, then it's your worst enemy unless you're good at picking through Google Scholar). If you work on using their resources and learning how to search with important terms and limiting results, you can find pretty much anything you ever need.

For example: http://news.google.com/newspapers

This literally gives you a way to pile through newspaper archives. I found papers that would work for your prompt in about 5 minutes this way. I'm not going to link you anything specific because I think you'd benefit from learning to use Google as a tool. Also, don't limit yourself to it. There are many other good ways to find what you're looking for that aren't search engines.

2 points

·
18th Jul 2018

Book 8 is where he describes philosophers and philosophy. Looking at Gutenberg Project https://www.gutenberg.org/files/45304/45304-h/45304-h.htm#Page_305 he talks about philosophy literally being love of wisdom. And so since true wisdom leads to God, all true philosophers come to God. [Note: this is a bad, oversimplistic paraphrase.]

2 points

·
17th Dec 2011

There tend to be two major types of risk: market risk and company-specific risk (ignoring industry specific risk for now). A company with Beta = 1 will follow the market exactly. If the market goes up 1%, we expect the stock to go up 1%. Yahoo has a better definition here

It's not necessarily true that only "aggressive" companies have a beta of > 1, although it usually true of high tech companies. A higher beta means that, the greater the market movement, the greater the stock movement. Or, the stock is more sensitive (both up and down) to the moves of the market. A more well-established company, like Walmart or GE, would have a lower beta because, all else equal, the market trusts them more and is less likely to buy or sell based on minor news.

2 points

·
25th Aug 2018

> how would i know which function is the R and which is r?

That's where sketching a graph of the region comes in handy.

The line x+3 is farther away from the x-axis than the parabola x^(2)+1. So x+3 is the big radius, R.

2 points

·
11th Jul 2018

The trick is to use the fact that it's changing linearly between two values to change it to an equivalent constant average value. Use ideas of impulse to find and use the average air resistance force, and hence the average overall force.

2 points

·
11th Jul 2018

Hey! A quartic equation like:

x^4 + 2 x^3 + 5 x + 2

is a polynomial of order 4. The ones we're talking about will have 4 real zeros but that's not always the case. You can have a u shape quartic that doesn't touch the x axis at all, so no real zeros.

Let's use this example:

x^4 - 6x^3 - 11x^2 + 24x + 28

Which I've plotted here using Desmos. This has zeros at:

- x = -1
- x = 2
- x = -2
- x = 7

And so you can see that the curve is also described exactly by taking each of those zeros like so:

(x+1)(x+2)(x-2)(x-7)

That's 4 sets of brackets, each with (x-a) where a is a value of x where the function is zero. So we have x = +7, but (x-7).

So you get your equation for a quartic function by writing down all your factors and then multiplying it out. Give it a try!

2 points

·
3rd Apr 2018

Here's something I made to show that, if you set the mean, you're actually just choosing where to place the distribution along the number line. The shape of the distribution is already specified completely. The only shape parameter on the normal distribution is the standard deviation, which is set for us here.

So it should be possible to pick a mean such that 1% of the area of the bell curve is to the left of 5kg. Recalling that 95% of the area is within 2 standard deviations, and 99.7% is within 3, we should expect that this cutoff point is 2 point something standard deviations left of the mean.

That is, if the 5kg cutoff is 2.5 standard deviations out from the mean, then the mean must be:

5kg + 2.5 standard deviations = 5kg + 2.5*0.1 kg = 5.25kg

Here I've guessed the value of 2.5, you'd have to use a table to find a near-exact value.

2 points

·
19th Nov 2017

That's not true. This is not a true identity.

tan(x) / cos^(2)(x)

= (sin(x)/cos(x)) / cos^(2)(x)

= (sin(x)/cos(x)) * (1/cos^(2)(x))

= sin(x) / cos^(3)(x)

=/= sin(x)

2 points

·
8th Nov 2017

No problem! So as I said last time the function you are going to be integrating is z = 9 - x - y. You can tell you are going to integrate this since its the only function given with z. Solving for z will also get everything in terms of x and y which is what you want in a double integral. Now you can find your bounds by graphing the xy-plane. This gives you this triangle (region in the 1st quadrant). Now we have to write out the bounds of x and y, and there are two ways to do this. One way is by defining the region as x is between 0 and 9 and y is between the lines 2x+3y=18, and x+3y = 9, then solve both of these lines for y. You can then put these in an inequality which will be your bounds of integration. If you are not sure about any of this please tell me, I can try to write it out on paper and make it a little easier to follow.

2 points

·
8th Nov 2017

I solve these like so:

Graph/sketch the curves using paper or desmos.

Set them *equal* to each other and find intersection points by solving.

Use the graph to say in what range each function is larger. In your second example the cubic is higher than the quadratic in the range -1 < x < 0, and x>5.

2 points

·
25th Oct 2017

Think of a spring as an example for elastic potential energy it starts at zero, and as you pull it out, the PE increases until the farthest you can pull it. Now if you slowly release it back at the same speed you pulled it, the PE decreases back to zero at the same rate at which you pulled it. (This graph)[https://www.desmos.com/calculator/r2ccmnwyve] should help you visualize it. You start to pull, then at x = 3 you reach max elastic potential energy, then you begin to release the spring at the same rate you pulled it until PE is back to zero.

2 points

·
6th Oct 2017

Do you know the difference between a minimum and a maximum?

Both have f'(x) = 0, but a maximum has f''(x) < 0 and a minimum has f''(x) > 0.

On intuiting the equation given locations of critical points: A polynomial of degree n with have up to n-1 critical points. That means f'(x) is of one degree less that f(x).

Also, Desmos is a really good graphing thing online, it's a useful learning tool.

2 points

·
23rd Dec 2014

Neither extremely knowledgeable nor a professional, but I can give some advice where to start.

The Soviet education system was more or less built by the communists after the Civil war. You will want to approach it in some way and how it worked, what it achieved and why it was designed to be so. Then you'll have to find how the system changed under Stalin and as far as I know, not by a whole much. Wikipedia, as useless of a source it is, does give a basic idea on the topic. Armed with that, you can probably look for legit sources you can use in an essay or if you're lazy, read wikipedia's sources.

This is a nice read on the system in the Leninist years.

http://www.britannica.com/EBchecked/topic/179408/education/47688/1917-30

A nice look on the Stalinist years and what changed.

As to what happened in the Soviet union during 1929-1945, read up Wikipedia. You'll generally be interested in WWII, Stalinist propoganda, cult of personality, GULAGs, industrialization and collectivization. It's a fairly fascinating read if you're interested in history.

2 points

·
12th Mar 2011

For future reference you can use Wolfram Alpha for these problems. Wolfram

2 points

·
7th Oct 2015

I googled the first part of the first equation and got this. It looks like it depends on the ratios of the reactants. When the ratio is equal to or less than 1:1 the reaction favours the top scenario.

2 points

·
8th Dec 2011

I took 18 credits last semester. I'm taking 21 credits and working as a TA next semester so I understand your worries. I just ordered all of my books off of Amazon and plan to outline the chapters for conceptual classes or learn the basic formulas for math classes. Understanding the big picture going into the class will ensure that you know the reasoning behind trends if you need to interpret graphs/diagrams or can find reasonable answers to math-based questions.

Other tips: 1. Use Excel to make a spreadsheet which details blocks of time for classes, studying, exercising and sleeping. Depending on how fast you pick up new material, you should schedule .5 to 2 hours of studying per credit hour per week. If you stick to a basic schedule, you'll be fine. 2. Tell your family and friends that you need extra support from them next semester and patience if you can't interact with them as often as you'd like. Also tell your profs so they'll be understanding if you happen to miss a deadline. 3. Try to avoid working off-campus or wasting time commuting to various places. If you have any long commutes, bring notecards or podcasts of your classes (if you're lucky enough to have those) so you're not just sitting around. 4. If you're taking any basic math classes i.e. Calculus I, Statistics, etc. get a head start on the lectures at http://www.khanacademy.org/.

Good luck! Be good to yourself and be sure to spend some time each week unwinding i.e. yoga, massage, walking someplace pretty. :D

2 points

·
28th Oct 2011

http://www.khanacademy.org/video/introduction-to-gravity?playlist=Physics

That covers your specific problem. Which has nothing to do with circular motion whatsoever.

http://www.khanacademy.org/#physics That covers the problem of a "teacher who doesn't teach" Tips for this subreddit:

Don't be rude to the people who try to help you.

The more English you know, the more respect you get. I am assuming you are a non native speaker. Assuming that the error is on the part of the person who tried to help you and provided a clear and simple explanation is rude. See 1.

A "what do I plug in where" mentality can last you for a bit, but as things get more challenging and the class builds off of material previously covered, it will soon land you in a mess of trouble that will take more time than trying to understand the material in the first place would have.

Your response seemed like it was asking for the plain answer, something that is generally considered against the spirit of this subreddit from my experience.

Weed_O_Whirler gave an elegant and understandable(I am a fellow physics student, HS, non AP) explanation of how to solve the problem, all that was required of you was that you take a bit of time to understand what he was saying, what the meant in terms of physical properties, and local rediquette would require an apology. Just a hint.

P.S. I wish I gave explanations half as well as he does.

2 points

·
25th Oct 2014

http://www.filedropper.com/report-writingguidelines These are the guidelines I use to write my psychology/linguistic research reports. I'm not sure of what a research 'paper' is but it seems you don't have the experimental side of it or something, so maybe it isn't too relevant, but it has good ideas for the other sections of the paper? (BTW this link will only work for 30 days). Also I think one of the best places to start with debilitating psychological disorders is schizophrenia, it's very debilitating and very interesting, especially when looking at historical treatments and such. Best of luck with your research paper!

2 points

·
11th Oct 2012

https://www.dropbox.com/s/vxhao7eqyhldo2f/AP%201%20-%20Rewrite%20-%20Proofread.docx

Also, if your thesis is "these three dudes' ideas laid the foundation of the Declaration of Rights of Man" you should probably explicitly state it somewhere.

2 points

·
14th Feb 2016

If they are all the same length and format, I would use the substring method. For example,

String firstNumber = originalString.substring(3,5);

Note the inclusivity and exclusvity of the substring parameters. This is assuming you need the number in string form; if you need it in integer format use

Integer.parseInt(originalString.substring(3,5));

2 points

·
16th Feb 2014

I haven't done a ton of visual basic, but the general gist is that the 1's digit needs to become the new highest digit, 10's digit the second highest, and so on. The psuedo-code would look something like:

input number 'input' int output = 0 while(input > 0){ newdigit = input mod 10 output = (output * 10) + newdigit // shift over output one digit, dd new digit input = (input - newdigit ) / 10; remove 1's digit from input, shift over. } output 'output' variable.

An implementation in Javascript can be seen at: http://jsfiddle.net/kayco2002/2nt7M/

2 points

·
7th Feb 2020

So convert 5.6 rad to deg (are you aware of the formula?):

5.6 x ( 180 / **π** ) = 320.85637

You need to find the angle between it and the x-axis

320.85637 - 90 = 230.8563

-90 = 140.8564

-90 = 50.8564

To find that angle from the x-axis, you -90

90 - 50.8564 = 39.14363

Then convert back to rad

39.14363 = ( 180 / **π** ) x r

(39.14363 **π** ) / 180 = r

r = 0.6832

​

this calculator can help you understand better

2 points

·
20th May 2021

Yeah sure.

So the base equation would be:

vase_price + x_roses * rose_price

So for the first example:

32.85 = v + 12r

Second Example:

50.85 = v + 20r

Then solve with substitution.

If you need help for solving with substitution, here's an excellent guide on it for a seperate example equation (first answer).

Just use the same method with your own equation, let me know if you need help with that.

2 points

·
30th Mar 2012

2 points

·
18th Sep 2014

I don't know what 'college authorized' means, but for book searches, the quickest way I know of to find a good book is to go to a university library's website or WorldCat and search. When the results come up, look for a book/article that's either published by a university press or is in a peer-reviewed journal.

This is by no means a guarantee of quality, but it's a good way to get started.

WorldCat search: http://www.worldcat.org/search?q=rms%20lusitania

2 points

·
4th Apr 2017

The main thing is you've switched the x-axis effect and the y-axis effect.

The thing that happens to the x axis is always with the x's, and the thing that happens to the y axis is always outside the whole thing.

To see that more clearly I'd recommend playing around with the function on Desmos.com, it's an online graphing calculator. I found a nice example on there, don't worry about the 2π in the cos function.

2 points

·
19th Mar 2017

I'm on mobile so can't type a lot. Here some resources that should help you out.

2 points

·
7th Mar 2017

First of all it's a piecewise functions on 3 Domains

(-inf,-3) v (-3,4) v (4,inf)

Most Intense part is the Middle:

Denominator should be (x+3)(x-4) = x^(2)-x-12

Now the y intercept is 1 such that f(0) = +1

Now the x intercept is at x = 2 so then you know that the fractional part of f(x) must equal -1.

So now we have a denominator of -10, because [2^(2) -2-12 = -10 ]

And from the slope you know that there must be an x^(3) not a -x^(3) because our denominator is always negative on (-3,4)

So now you have 8/-10 for x = 2.

So how do we get to +10, we could add +2 but that would not work for f(0) = 1 . We could just add +x. And so we do.

for D: (-3 < x < 4) we have f(x) = [(x^(3) + x)/(x^(2)-x-12)] +1

and for D: (-3 > x) v (4 < x) we can just have f(x) = (-1)/(x^(2)-x-12)

you can confirm this on desmos.com/calculator

Just note that after your function you can just put (f(x)){x<-3,x>4}

Side note if you do not mind me asking what grade level is this? It's been several years since pre-calc for me.

2 points

·
28th May 2016

It's similar to a hyperbola of equation x^(2) - y^(2) = 4: https://www.desmos.com/calculator/uymrxyc8wg

The implied domain (over the reals) is where the value under the square root is greater than 0.

2 points

·
2nd Mar 2016

GENERAL EQUATION: Af(Bt – C) + D

- trigonometric function: f
- amplitude: A
- period: 2π/|B|
- phase shift: C/B
- vertical shift: D
- flip horizontally: if A is negative

y = 3 - cos(2t)

- trigonometric function: cosine
- amplitude: A
- period: π
- phase shift: 0
- vertical shift: 0
- flip horizontally: yes

- Start at t = 0. At t = 0, y = 2, so plot (0, 2).
- You know that the period is π. Therefore, at t = π, y = 2.
- Based on your knowledge of cosine graphs and the fact that the graph must be flipped horizontally because A is negative, you know that at the midpoint between the two points, y reaches its maximum (because at t = 0 and t = π it is at its minimum). This point is (π/2, 4).
- In between the first two points and second two points, at y = π/4 and at y = 3π/4, cos(2t) = 0. Here you get two more points, (π/4, 3) and (3π/4, 3).
- Connect the points and repeat the pattern.
- Check here and see if you got it right.

- trigonometric function: sine
- amplitude: 5
- period: 8π
- phase shift: 0
- vertical shift: 0
- flip horizontally: yes

From the information above (which I've simply determined from looking at the graph), we can determine the coefficients (A, B, C, and D).

- A = -5
- B = 2π/8π = 1/4
- C = 0
- D = 0

**y = -5sin(t/4)**

That's just one of the solutions possible. The following list contains the general form of all solutions possible. See if you can figure out how I derived them.

- y = 5sin(t/4 + (2n - 1)π), where n is any integer
- y = -5sin(t/4 + 2nπ), where n is any integer
- y = 5cos(t/4 + (4nπ + π)/2), where n is any integer
- y = -5cos(t/4 + (4nπ - π)/2), where n is any integer

f(x) = x + 2; g(x) = x^2 + 2x + 3

g(f(x)) = (x+2)^2 + 2(x+2) + 3

g(f(x)) = x^2 + 4x + 4 + 2x + 4 + 3

**g(f(x)) = x^2 +6x + 11**

f(g(3)) = g(3) + 2

g(3) = 3^2 + 2(3) + 3 = 15

**f(g(3)) = 17**

2 points

·
31st Dec 2015

I would suggest that you try to solve this by the following steps:

- Plan out a 'path' through that graph from Start to End. By 'path' I mean a sequence of points, that cover as many icons on the graph as possible. So for example (-10,-2), (-9,-3), (-8,-2), (-7,5), ... (10,1). Where the ... is whatever other points you choose.
- Now look at the points 'pair by pair', unless there is an
*obvious*equation that pops out at you. For example, it is "obvious" that there exists a parobola that would hit all the first three points, since the points are symmetric on the middle one. (This isn't the case generally, so you'll have to go 'pair by pair'). - Example: Look at the points (-8,-2) and (-7,5). In my case, the easiest way I think to find the equation for such a parobola is to make one of the points a vertex. So f(x) = a(x-h)^2 + k, where 'a' is a constant and (h,k) is the vertex. In this case we make (-7,5) the vertex (making the second point the vertex will generally be better). So we have f(x)= a(x-(-7))^2 +5 = a(x+7)^2 +5. Now you have to stretch this parobola so it also goes through (-8,-2). Right now we have f(-8) = -2 = a(-8+7)^2 +5 => a = -7. So a parobola that goes through (-8, -2) and (-7,5) is f(x) = -7(x+7)^2 + 5.

Do something similar for the other points you choose. How hard you want to work at this depends on how many points you want. You can have a total of 20 points, if your step size = 1, starting from -10. Or you can have less, if your step size is bigger.

And try to graph the functions on a online-grapher to make sure your equations are correct. Here is one that does piece-wise graphing, but it take some time to get used to its interface. You might just prefer a simpler one like this one.

2 points

·
3rd Jun 2015

Let y = f(x) = x^(2), makes this easier.

A compression about the y axis is given with f(ax), where the SF = 1/a

A reflection in the y axis is given by f(-x)

A translation of a units parallel to the y axis is given by f(x) + a.

So, combining these, we have f(-4x) - 2. Substituting f(x) for x^(2) we have (-4x)^(2) - 2 = 16x^(2) - 2.

If we apply the reflection in the y axis without shifting the graph horizontally, then the graph looks exactly the same, since it is symmetric about the y axis.

See the graph of the different transformation effects here: https://www.desmos.com/calculator/dbvlawqqof