# equals

1. ### Which Expression Equals SAT Question

I have an SAT practice question stating: Which of the following expressions is equivalent to (-4x^3)^2/3? The answer is 2x^2 * 3âˆš2 (or ^2/3, I don't know how to indicate that specifically using keys but the 3 is inside the v of the square root symbol) But my question is how I would...
2. ### Dark matter "equals" dark energy

Dark matter causes an inward acceleration. Dark energy causes an outward acceleration. Where do they offset each other?
3. ### Demonstration that the derivative of ln equals 1/x

Hi! Nice to meet you all <333 I would be tremendously grateful if you could possibly give an answer to my questions and help me with this. I have two questions: first of all, what is the limit of an exponential function as x approaches 0? Is it 1? Second one: how exactly could I...
4. ### Show that one equation equals another

Can anyone help with the following I'm asked to show that (cos2nx + sin2(n+1)x) / (cos(2n+1)x + sin(2n+1)x) is equal to (cos2(n-1)x + sin2nx) / (cos(2n-1)x + sin(2n-1)x) I've tried expanding this using the double angle formulas i.e. sin2(n+1)x = sin(2nx+2x) = (sin2nx)(cosx) +...
5. ### Column Rank equals Row Rank

Consider Ax=0 \begin{vmatrix} a11\\ a21\\ a31\\ a41\\ a51 \end{vmatrix}x1+\begin{vmatrix} a12\\ a22\\ a32\\ a42\\ a52 \end{vmatrix}x2+\begin{vmatrix} a13\\ a23\\ a33\\ a43\\ a53 \end{vmatrix}x3=0 Assume the first two rows are linearly independent (row rank=2). If x1, x2, x3...
6. ### 72 correct equals 75%. Total being...?

A student who correctly answered 72 questions received a score of 75%. How many questions were on the test? I didn't know how to begin this one, but the only way I can come up with for solving it is 1.25 x 75, with the .25 being the percentage left to get 100%. I know the reasoning doesn't...
7. ### Align equals signs

Hi I know this has been mentioned many times but I'm still not clear: What is the exact code for: If $f(x)=x^{3}$, then $f'(x)=3x^{2}$ $=600$ but with all 3 equals signs aligned?
8. ### Minus one equals one ( mathematical paradox)

Hello everyone, I'm not sure whether it's appropriate to call this a "paradox" but anyways. I want you to have a look at this and explain what step isn't right about it : -1 = (-1)^1 = (-1)^2 ^/^2 = ((-1)^2)^1^/^2 = (1)^1^/^2 = 1
9. ### A linear function equals its derivative at every point

Hello there, I am reading Stein and Shakarchi Â«Complex AnalysisÂ», Princeton univeristy lectures. Somewhere in there it says: Â«F is linear and is therefore equal to its derivative at every point.Â» I don't understand what that means. For example, the linear function defined over...
10. ### Greatest Common Divisor may be NP Complete (if so then P equals NP)

Clique (graph theory) - Wikipedia, the free encyclopedia (or any of the other interchangible views of NP Complete) has been called the hardest unsolved math problem and would likely result in solving all the remaining millenium problems if P equals NP and that is proven. On the other hand, most...
11. ### P equals NP if any hashlife scales for Clique on the board

This is exactly the kind of thing you'd expect if P equals NP. http://en.wikipedia.org/wiki/Hashlife Polynomial becomes log? Then what does polynomial^n become? e^log(p) = p. I imagine if P equals NP, then there is such a thing as an average of subconstant time, as in simulating a particle...
12. ### Cardinality of integers equals cardinality of reals

pi squared is an integer because its last digit in base 2 is 0. The surface hypervolumes (or hyperareas/hypervolumes on alternating indexs) are an integer multiple of eachother while having sometimes different and sometimes same exponent of pi. So theres really no important difference between a...
13. ### Solve for x when a trig function equals a polynomial?

I recently came across an interesting type of equation I had completely forgotten about--the kind where a trig function is equal to a polynomial (example below): sin(x) = -(x^2 + 6x - 10)/210 Now, literally, this says sin(x) equals the polynomial on the right at specific points. The only...
14. ### In what situation frac of limits equals to limit of frac?

I mean \frac{\lim_{x\to a}f(x)}{\lim_{y \to a}g(y)}=\lim_{x\to a}\frac{f(x)}{g(x)} , a\in \mathbb {R} or \frac{\lim_{x\to \infty}f(x)}{\lim_{y \to \infty}g(y)}=\lim_{x\to \infty}\frac{f(x)}{g(x)}
15. ### prove this limit equals 0

Hi, Im sure this one has come up before how are people thinking proving this? lim x->0^+ sqrt(x) * e^sin(pi/x) = 0 using the squeeze thereom. Sin(pi/x) DNE,
16. ### Showing limit equals derivative

This is giving me so much trouble and I have no idea why. I just have to show that f'(x) = ( f(x + e) - f(x - e) ) / 2e for x = 5 and e = .001 The actual function is f(x) = e^(sinx) + xln(3 + cosx) and I'm almost positive the derivative is f'(x) = cos(x)e^(sinx) + ln(3 + cosx) - xsinx/(3 +...
17. ### Two equals Sides. One Angle. In a CIRCLE.

Hi, To obtain the area of a a triangle inside a circle with radius 12. and angle pi/3 ( 60deg). A= 1/2 *b*h . = 1/2*12* h h= tan(30deg)*12 = this is correct> we can intersect pi/3 and use tan to equate the height? Zen.
18. ### 0.999... Equals 0.001... Less than 1

0.999... Equals 0.001... Less than 1 http://www.youtube.com/watch?v=H8ExUfaa6f8 Example 0.9 = 0.1? Less than 1 Example 0.99 = 0.01 Less than 1 Example 0.999 = 0.001 Less than 1 Example 0.999... = 0.001... Less than 1
19. ### P equals NP because 3SAT reduces to solving linear equations

3SAT is a set of constraints on n boolean vars. Each constraint is on 3 vars and excludes 1 of 8 combinations of them each being true or false. Create an undirected network of size 8*n*(n-1)*(n-2)/6 with 8 nodes for each set of 3 different boolean vars. Thats a group of 8 nodes for each set of...
20. ### P equals NP - Max Clique using n dim distance constraints

Millenium Prize math problem P vs NP. Max Clique algorithm in n^5 (P) efficiency. What is it good for? Until now, we had no practical way to, for example, given a set of pairs of people on Facebook who each friended eachother, find the biggest group of people who all friended eachother, a...