Simplifying Definition and 498 Threads

Homework Statement (sec^2 x - 1)/(sin^2 x) Homework Equations The Attempt at a Solution i know that the answer is sec^2 x, but i have no idea what steps to take to get there

is it possible to simplify this more?? Ln(log7-log76)= Ln(log77)

Homework Statement \frac{1 + \sqrt{\frac{1}{1 + \left(\frac{s}{u}\right)^{2}}}}{1 - \sqrt{\frac{1}{1 + \left(\frac{s}{u}\right)^{2}}}} Should equal \left(\sqrt{1 + \left(\frac{u}{s}\right)^2} + \left(\frac{u}{s}\right)\right)^{2} Homework Equations above The Attempt at a Solution...

Hey guys. So, complex numbers. Its been a while since I've dealt with them. I've been wondering a few things about them. When expressed in the form a + ib, is there a particular way that you square them? And when you have a rational number, with an i term on the bottom, how exactly...

Homework Statement (secx-1)/x^2 limit x--->0 Homework Equations secx=1/cosx (1-cosx)/x=0 The Attempt at a Solution I have done obvious thing, solved to make secent cosine and got common denominators in the top portion of the fraction, then subtracted. Ended up with...

Homework Statement Find the derivative of f(x)=2x^3+cos^2(x^3) The Attempt at a Solution f'(x)=6x^2+2cos(x^3)*-sin(x^3)*3x^2 f'(x)=6x^2-6x^2cos(x^3)sin(x^3) The book has a different solution since they always simplify, but how would I simplify it? I know it has something to do...

How could I go about expressing |x|-|x-6| without using absolute value signs?

isotropic equation, so k, ρ, and c are constant, where k is thermal conductivity, c is specific heat, and ρ is the density of the body. the equation boils down to \left( \frac{c\rho}{k}\right) \left(\frac{\partial u}{\partial t}\right) - \left(\frac{\partial^{2} u}{\partial...

Homework Statement What is the steps between the two equations? Homework Equations P = a^{2}P+b^{2}P^{2}/(P+1) \Rightarrow P^{2}-(a^{2}+b^{2}-1)P-b^{2} = 0 Thanks!

Hello. I wrote a simple program that helps me simplify radicals: #include <iostream> #include <math.h> typedef struct { unsigned int x, y; }pair; bool breakcube(unsigned int radi, unsigned short inx, pair& pr) { unsigned int cb = 0; for (unsigned int i = 2; i < radi; i++) { cb=i...

Alright It's been a while since I did algebra and now I'm getting back into it in honors algebra 2 (shakes head) [high school]. Anyways I got a question on factoring numerators. 6x^{2} + 7x + 2 ------------- 4x^{2} - 1 I don't know where to start, if someone can be a guidance this would...

Homework Statement Simplify and write the trigonometric expression in terms of sine and cosine: (sec (t) - cos (t))/sec (t) = (f(t))^2 Homework Equations sec (t)=1/cos (t) The Attempt at a Solution (sec (t) - cos (t))/sec (t) = ((1/cos (t))-cos(t)) / (1/cos (t)) =...

Homework Statement Prove \frac{sin 2 \alpha}{1+cos 2 \alpha}-\frac{cos \alpha}{1+cos \alpha}=tan \frac{ \alpha}{2} Use half and double angle formulas, I get; The given expression is equal to: \frac{(2 tan \frac{\alpha}{2})(1+tan^{2}...

cos(4x) + \sqrt{2}cos(3x) + cos(2x) = 0 --------------------------------------------------- Ok, so break down everything to a double angle and i get: 2cos^2(2x) - 1 + sqrt(2)*(sqrt((cos(2x) + cos^2(2x))/2) - sqrt((1-cos^(2x)*(1-cos(2x))/2) + cos(2x) = 0 ...which is quite complicated to...

Homework Statement Simplify (1+i\sqrt{2})^5-(1-i\sqrt{2})^5 Homework Equations z=a+bi z=r(cos\varphi+isin\varphi) tg\varphi=\frac{b}{a} r=\sqrt{a^2+b^2} The Attempt at a Solution...

Homework Statement I'm trying to simplify a summation. I have something that looks like \sum \sqrt{(1/4)(i)} (1/4) Granted I might have made a mistake setting this up which would make my question irrelevant but anyway. Homework Equations there are equations for i, i squared and i cubed The...

Simplifying an arc length problem I have L= Int(-2..2) sqrt(16*cosh(4*t)^2+9*sinh(4*t)^2+9) and can use Maple to simplify this to sqrt(25*cosh(4*t)^2) but I just can't see how that is done. (or how to get maple to show me the steps!) Can anyone help by showing the steps, including any...

Homework Statement 1/(a-b)(a-c) + 1/(c-a)(c-b) + 1/(b-a)(b-c) Homework Equations Is there a way to simplify this? If I start multiplying out everything to get the LCD my final answer will be huge. The Attempt at a Solution As I said, without somehow simplifying it at the start...

Hi all, I'm retaking the GRE soon and I keep making stupid algebra mistakes in my calculus problems so I'm going through a textbook from 1965 that is helpful but has me stumped on some problems. I hope someone can steer me in the right direction. 1/(a-b)(a-c) + 1/(c-a)(c-b) +...

Is this correct? (bcos30-85.7)(bcos30-85.7)=b²cos²30-85.7cos30-85.7bcos30+85.7²

tan x/sin x + 1/cos x The choices are A. 2tan^2x B. 2cosx C. 2cosx-1 D. 2secx Do I make the tan sin/cos and multiply by reciprocal of sin? I did that and end up with 1/cos + 1/cos

im having trouble trying to figure out a problem. can someone help me. (2/6 -root3)^2 - (2/6+root3)^2 if that makes sense to anyone help. I think that the denominator of both has to be rationalised but do i expand the squared brackets first or later or what? any ideas welcome thanks

I was looking at the web page containing a derivation for the Poisson distribution: http://en.wikipedia.org/wiki/Poisson_distribution which derives it as the limiting case of the binomial distribution. There is a simplification step which I am missing, which is the step(s) between...

Homework Statement Find f '(x) two ways: By using the product or quotient rule, and by simplifying first. f(x) = ((x^3) + 9)/ (x^3) Homework Equations f '(x)= (G(x) * F '(x) - F(x) * G '(x)) / [G(x)^2] The Attempt at a Solution f...

Hello Here is an integral question I have. It's a surface area problem, but i just have issues simplifying the square root before solving. Any help appreciated! y=(1-x^{2/3})^{3/2}, 0\leqx\leq1 My work: dy/dx=-x^{-1/3}(1-x^{2/3})^{1/2} (dy/dx)^{2}=-x^{-2/3}(1-x^{2/3})...

Homework Statement How can I simplify sum from j=0 to infinite of x^(2j) ? Homework Equations The Attempt at a Solution THis is close to the geometric series but I'd have to square each individual term

Homework Statement An equation in a book lists this equation: (c - 18)^{2} = (-3\sqrt{c})^{2} And it simplifies it as: c^{2} -45c + 324 = 02. The attempt at a solution When I do out the equation, I get: c^{2} + 324 = 9 + c i squared c, then -18 for the left side of the equation, then for the...

Homework Statement Simplify: 2csc^2 - csc^4 + cot^4 Homework Equations The Attempt at a Solution 2(1/sin^2) - 1/sin^4 + cos^4/sin^4 So here, i figured that if i re-write them, that maybe it will leave me more options, but I don't see anything that will cancel out. Then i...

Homework Statement Simplify these equations and functions 1. xyz’ + x’ (x + z) + x’yz + x’y’z’ 2. xy (z + z’) + x’y’z 3. wxyz + w’xy’z + wx (y’ + z) + w’x’z 4. F(A, B, C, D, E) = ∑(0, 1, 5, 6, 13, 15, 20, 21, 22) 5. F(w, x, y, z) = ∑(0, 1, 2, 3, 11, 13, 15) Homework Equations...

Homework Statement Show 2a^2*b^2*c^2 + (a+c)^2*(a+b)^2*(b+c)^2 - a^2*c^2(a+c)^2 - (a+b)^2 * a^2 * b^2 - (b+c)^2*b^2*c^2 = 2abc(a+b+c)^3 Homework Equations The Attempt at a Solution Well I actually tried to expand all of the exponential terms but that ended up being a total...

How do I simplify this? \frac{1}{x-2} - \frac{1}{x^2-4} = \frac{(x^2-4)-(x-2)}{(x^2-4)(x-2)}

[b]1. Simplify the following equations using boolean algebra [b]2. a) abc + ab'c'+ ab'c b) (abc)'+(a+c)'+b'c' [b]3. Please help me to solve the above equations

Homework Statement (this is really only part of my problem it's an optimization problem but this is where I'm stuck) Find the zeros of: cos^2(x)-sin^(x)+cos(x) Homework Equations The Attempt at a Solution I've been trying to use trig identities such as sin^2 + cos^2 = 1 but it's...

[SOLVED] current and potential difference, simplifying circuit diagrams Consider the circuit shown in Figure P31.69, in which RA = 25 and RB = 7 . Tabulate the current through, and the potential difference across, each resistor. Figure P31.69 resistor current (A) potential...

[SOLVED] How simplifying this ratio test for series? Basically, we are asked if (n!n^2)/(2n)! converges absolutely... I got to the point where lim as n --> infinity of [(n+1)!(n+1)^2]/(2(n+1))! X (2n)!/n!n^2 by the ratio test. But I don't know how to manipulate the factorials...

w=\frac{k}{1-n}(v^{1-n}_{2}-v^{1-n}_{1}) let k=pv^n \frac {p_{2}v^{n}_{2}v^{1-n}_{2} - p_{1}v^{n}_{1}v^{1-n}_{1}}{1-n} how can this become w=\frac {p_{1}v_{1} - p_{2}v_{2}}{n-1} thanks

[SOLVED] Simplifying Trig Products Homework Statement Express the following as a product and simplify. sin60° + sin20° Homework Equations The Attempt at a Solution I don't understand what the question is trying to say. For example, do I convert sin60° and then add. I don't...

I am trying to solve for the variable lambda in terms of A. After multiplying the denominator term over to the other side, how do I go on from there? I don't know how to get rid of the exponential terms. Thanks on advance. http://img521.imageshack.us/img521/4006/picture1ug1.th.png

Homework Statement Given a general solution to a system of differential equations: Y(t)= C1(1;2i)e^(2it)+C2(1;-2i)e^(-2it) side note: i is sqrt of -1, and the (1;2i) is a 2 by 1 matrix. The idea is to simplify the solution such that the imaginary components go away. Homework...

Homework Statement [3x^2 + 2(sqrt x)] / x My book says it simplified it to: 3x + 2x ^-1/2I understand the 3x part since 3x^2/x = 3x But where did the second part come from? I tried to make sense with the power rule but it still doesn't seem clear to me. Anyone get it?

Homework Statement Sec^2x X cotx --------------------- csc xAlso, if anyone wants to explain cofunction identities and how to use them, to be that would be very much appreciated. Homework Equations The Pythagorean identities as well as the basic identities of trig functions. Any...

can someone please simplify? \sin \frac{\pi}{n} \sin \frac{2\pi}{n} ... \sin \frac{(n-1)\pi}{n}

Simplifying a fraction as a surd?? If I have a rather large fraction such as 115/36 there is no obvious way of cancelling this, but is there a way of expressing it as a surd?

Does anyone know the steps involved in reducing ((1+u/c)/(1-u/c))^0.5 - 1 = u/c ?

Homework Statement I am reviewing some old exam solutions and came across something I cannot figure out. I'm don't understand how they simplify from the first equation to the second. I looked up a table of trig identies but could not find anything that would help. Homework Equations...

Homework Statement (2n-1)!/(2n+1)! Homework Equations The Attempt at a Solution ...2n-2*2n-1 ------------ (pretend that's a divider) ...2n-2*2n-1*2n*2n+1 Is the answer 1/[2n*2n+1]?

I am trying to find a formula for f(x) = a*f(x-1) + b*f(x-2) for x≥1, assuming f(-1) and f(0) are known. In other words, I need some expression for f(x) just in terms of a, b, f(-1), and f(0). I tried plugging in stuff and factoring on paper for the first few iterations, but it quickly got out...

I'm supposed to simplify this, help please! \frac{a^4-b^4}{4a^2+4b^2}:(a+b) Sorry for posting in the wrong section, could someone move it?

Without using a calculator This is part of a GCSE maths question from a non-calc paper How does \frac{25\pi}{3}-\frac{25}{2}sin120 become simplified?

Hi, To solve the following d.e.: xdy-ydx = 0 1 you get ln(y)-ln(x)=C 2 no clearly you can simplify to: ln(y/x)=c 3 which after taking exponentials gives: y=Ax where A=e^c 4 however what interests me is if you do not simplify...