# Search results

1. ### Trigonometric Identity Problem

In those steps you didn't distribute the cos back to the 1.
2. ### Compression of a spring

Have you attempted to use conservation of energy principles?
3. ### Finding the domain of a composite function help.

This isn't any different from those. How would you go about finding the domain of the example function you posted?
4. ### General Reimann sum questions

These do start with 41 and 41^2 instead of 1 and 1^2, but the formula they have (the ##\frac{x(x+1)}{2}##) is for the sequence that starts with 1. So that means that you can rewrite the formula given as a sigma notation from 1 to n and then simplify from there.
5. ### General Reimann sum questions

Close, but not quite the right formula. The condensed form that they gave is ##\frac{n^2 + n}{2}##, is that what you meant?
6. ### General Reimann sum questions

For the second one there, what is the sum of all numbers between 1 and n?
7. ### Limit Proof with Rational Functions

I amended the third line of the proof to incorporate that. Thank you!

9. ### Integration by parts help?

Look at the first two terms of your answer. Is there a common factor there that you can pull out?
10. ### Limit Proof with Rational Functions

Homework Statement If r is a rational function, use Exercise 57 to show that ##\mathop {\lim }\limits_{x \to a} \space r(x) = r(a)## for every number a in the domain of r. Exercise 57 in this book is: if p is a polynomial, show that ##\mathop {\lim }\limits_{x \to a} \space p(x) = p(a)##...
11. ### Function domain help

That is true if it is just the quadratic equation, but if you are dividing two numbers what happens if they are each positive? Each negative? One positive and one negative? You need to use the answers to those questions to determine the sign of the division of two functions.
12. ### Inclusion - exclusion principle

I don't know if you want a mathematical method for doing a problem like this, but I would approach it by saying that if a person speaks only English, than they don't speak Spanish or Swahili. So there are 100 people, and at least 60 of them don't fit in the set of people who only speak English...
13. ### Mechanics Pulley question !

It does effect the acceleration of the mass system because as the mass drops, energy is transferred into the pulley as well, instead of remaining in the system.
14. ### Mechanics Pulley question !

The force of gravity on the hanging mass will not only accelerate the system of masses, but also cause the pulley to rotate.
15. ### Range formula on planets

Ah okay :) You said that you get the correct answer when you use the formula with a ##2g## in the denominator instead of just ##g##, and when you use the ##g## formula you get it wrong. But when you use the formula with just a ##g##, did you recalculate your ##V_o##?
16. ### Calculus 1 Integration Problem

But it is, isn't it? ##(x+1)^{12} - 2(x+1)^{11}## ##(x+1)(x+1)^{11} - 2(x+1)^{11}## ##(x+1)^{11}(x+1-2)## ##(x-1)(x+1)^{11}##
17. ### Range formula on planets

I'm confused, if you are able to hit a ball the same distance with the same stroke on two different planets, wouldn't that mean that gravity was the same on each?
18. ### System of two equations with radical expression

So you want to take the square root of each side. If ##y^2 = 1 - x^2## then ##\sqrt{y^2} = \sqrt{1 - x^2}##, which is only the same as ##y = 1 - x## if ##\sqrt{a + b} = \sqrt{a} + \sqrt{b}##.
19. ### System of two equations with radical expression

But wasn't it established already that ##y=\pm\sqrt{1-x^2}##, or do you not agree with how it got to that?
20. ### System of two equations with radical expression

There is no rule that says ##\sqrt{a+b} = \sqrt{a} + \sqrt{b}##.
21. ### Scalar line integral

Did you find dr yet? Did you take the dot product?
22. ### Algebra II Correct Form to Answer Discrimants Problems

Very true. I edited my post to avoid future confusion.
23. ### Finding momentum; I'm doing something wrong

Well if you call heading east to be positive, vi will be positive, Δp will be negative, and your result will be 4.2 If you call going west to be positive, vi will be negative, Δp will be positive, and your result will be -4.2 (and negative refers to going east). So the answer will have the...
24. ### Algebra II Correct Form to Answer Discrimants Problems

Remember with absolute value that it leads to two separate equations; |f(x)| = g(x) leads to f(x) = g(x) or f(x) = -g(x), This also applies to inequalities. |x| < a is the same as x < a or x > -a, which is condensed into -a < x < a. Similarly, |x| > a is the same as x > a or x < -a. With...
25. ### Finding momentum; I'm doing something wrong

Your impulse and your velocity are in opposite direction, so you have to make one or the other negative in order to reflect this. I haven't checked to see if this yields the correct answer based on the rest of your work, but it should. However, I think that it would be simpler if you use...
26. ### Functions range and domain

Is it possible that your book uses fg(x) to refer to something other than f(g(x))? Because the video is incorrect if it is talking about f(g(x)).
27. ### System of two equations with radical expression

If you're using latex, you type \cdot. Otherwise you can't, but in order to avoid confusion you can write (√3)y to illustrate the difference. But before we can help you figure out the problem, you need to show the work you already did.
28. ### Functions range and domain

I'm not sure if the part I bolded is true, I've never heard it before. Where were you told this? The possible domain for fg(x) is the range of g(x), which is true. But that possible domain can still be further restricted based on the domain of f(x).
29. ### Functions range and domain

For this problem I would just look at the final answer for gf(x) because ##\sqrt{x-3}## is a simple solution. But are you more interested in a general way to doing these problems?
30. ### System of two equations with radical expression

Show your attempt, maybe we can help you figure out what went wrong. Based on the answer he gave, I would think that it has to be the first equation that you listed.