Simplifying Definition and 487 Threads

m * g * h + (1/2) * m * v² = m * g * y Simplifying the equation: g * h + (1/2) * v² = g * y Substituting the values: g * 0.614 + (1/2) * v² = g * 2.73 * sin(26.7°) Now, let's solve for v: (1/2) * v² = g * 2.73 * sin(26.7°) - g * 0.614 v² = 2 * (g * 2.73 * sin(26.7°) - g * 0.614) v = √(2...

How did they get y^7 in the bottom fraction? I got their answer except I had y^6. Would some please be able to help? Many thanks!

14) here i tried 3x^3 + 3/8x^3 to to get 27/8x^3 but the answer is 3/2 x^3, why? 15) here i did 9x^3/2 - 1/x^3/2 to get 9x^9/4 - 1/x^3/2 but that's not in the right form, how do i do it correctly?

Hey all, I am currently trying to solve the following equation for C: where C is a purely imaginary value, ##F_{+}##, ##F_{-}## and ##G_{+}## and ##G_{-}## are all complex valued constants (so ##G_{+}^{*}## just means complex conjugate of ##G_{+}##. I am not really sure where to start with...

Is it possible to simplify the function below so that the sums disappear. $$\displaystyle g \left(x \right) \, = \, \sum _{j=-\infty}^{\infty} \left(-A +B \right) \sum _{k=-\infty}^{\infty} \frac{1}{2}~\frac{\sqrt{2}~e^{-\frac{1}{2}~\frac{\left(x -k \right)^{2}}{\sigma...

I am not seeing how the v goes away in the third equal sign of equation (1.8). It seems to be that it must be cos(z*sinh(u+v)), not cos(z*sinh(u)). In the defined equations (1.7), the variable "v" can become imaginary, so a simple change of variables would change the integration sign by adding...

So I simplify the expression and get 2 x 3^2 x 7 = 84 and get ##2 \sqrt{21(y−2)^{3/2}}## I don't follow how the answer is ##2(y -2) \sqrt{21 ( y - 2) }##

Hello, I have posted a similar thread on this question before, but I'd like to get some help to simplify the answers I've got so far in order to match the solutions provided. If anyone could help me, I would really appreciate it. Since (c) is quite similar to (b), I'll leave here what I've done...

Hello! I have a function ##f(t)## such that ##\int_a^b{f(t)dt}=f_0##. Is there a way to calculate (or bring it to a simpler form) ##\int_a^b{f(a)e^{t}}dt##? Thank you!

having trouble with the following, if anyone could provide assistance it would be appreciated. Solve for x: and Simplify the following:

Dear Everyone, This post is not a homework assignment... I want to use the quartic formula. In one step is to solve the resolvent cubic. I know that there is 3 real solutions this particular resolvent cubic. I want to know how Bombelli got his answers before the discovery of the trigonometric...

I have a test on simplifying and expanding expressions, could someone help me with this. I don't understand the formula and the way you do it

Hello, I have been trying to solve the top line equation to get the result (the bottom line). I am searching for a clue (the steps) on how to obtain those four brackets as a result.

I'm trying to determine why $$ \lim_{N \rightarrow +\infty} ln( \frac {N!} {(N-n)! N^n}) = 0$$ N and n are both positive integers, and n is smaller than N. I want to use Stirling's, which becomes exact as N->inf: $$ ln(N!) \approx Nln(N)-N $$ And take it term by term: $$ \lim_{N...

Given the circuit above, I have to solve for the labelled currents, find V total and R total accordingly. 1A is flowing through the 5Ω resistor as shown. Assuming electron flow (negative terminal to positive) for circuit. The connector in the middle was somewhat confusing. Without it, this...

I was studying how to compute an unpolarized cross-section (QFT Mandl & Shaw, second edition,https://ia800108.us.archive.org/32/items/FranzMandlGrahamShawQuantumFieldTheoryWiley2010/Franz%20Mandl%2C%20Graham%20Shaw-Quantum%20Field%20Theory-Wiley%20%282010%29.pdf) and came across the following...

The following is the questions given. I solved the first one, which steps are shown below. But I am not sure if this is how the question wants me to solve the problem. Would you tell me if the way I solved the problem is the proper way of simplifying the expression using euler's formula...

The first part is actually fine. You just note that since r=r1+r2 that means r1=r+r2 and r2=r1-r and you substitute that into the center of mass, R, and simplify to get r1=R+(μ/m1)r, and r2=R-(μ/m2)r But the next part is where I'm very confused. The general idea is that you want to prove ∇1 =...

I have a matrix equation (left side) that needs to be formatted into another form (right side). I've simplified the left side as much as I could but can't seem to get it to the match the right side. I am unsure if my matrix algebra skills are lacking or if I somehow messed up the starting...

Hi, Please see the attached image. I have a matrix and would like to split it up into a nice compact equation if possible. Matrix A seems to be a nice pattern that would lend itself to writing in equation form but I’m not sure what to do. Is it possible? Also do you know how I could correctly...

$$10π \left( \frac V {4π} \right)^{2/3} = 5\sqrt[3] {{V^2}\frac π 2}$$Not sure how to deal with the $$10π$$ and how we get $$\frac π 2$$.

The other day in a fit of boredom I decided to dust off my old math books (high school and undergrad) and see if I can still crank through the basics. 1. Homework Statement Show the following: $$ \frac { 3 cos^2(x) } { 2 - 2 sin(x) } = \frac { 3 }{ 2 } ( sin(x) + 1 ) $$ Homework Equations $$...

Homework Statement I have solve the integral for:to be: But I cannot figure out how to simplify the answer to the form shown above. Homework Equations The Attempt at a Solution Here is my progress so far: Any help would be appreciated

Homework Statement (x+3)(x-2)/x2-2x Homework EquationsThe Attempt at a Solution (x+3)(x-2)/x(x-2) = (x+3)/x What I don't understand is why I can't simplify this further for instance the x's cancel to give 1: (1+3)/1 = 4/1 = 4 Is it because there is no x next to the 3? Many thanks :)[/B]

Not sure where the 2ah is coming from in the middle step. f(a+h)=-5(a+h)^2+2(a+h)-1 = -5(a^2 + 2ah +h^2) +2a +2h -1 = -5a^2 - 10ah -5h^2 +2a +2h -1 Please enlighten me

Homework Statement "Prove that ##\sum_{n=0}^\infty s^n e^{-\lambda} \frac{\lambda^n}{n!}\sum_{m=0}^\infty s^m e^{-\mu}\frac{\mu^m}{m!}=\sum_{m+n=0}^\infty s^{n+m} e^{-(\lambda+\mu)} \frac{(\lambda + \mu)^{m+n}}{(m+n)}!## Homework Equations Binomial theorem: ##(x+y)^n=\sum_{k=0}^n x^ky^{n-k}##...

Homework Statement Simplify √(53 - 8√15) Homework Equations Numbers can be represented as √a - √b The Attempt at a Solution I had tried to make in an equation where the 2 expressions were equal, but after squaring both sides, I didn’t really know what to do. I had also tried to use something...

I have the expression ##|nr^n|^{1/n}##. A quick question is whether I can allow the exponent to go inside of the absolute value. I know that if it were an positive integral exponent then because of the multiplicativity of the absolute value function that would be allowed. But I'm not sure what...

Homework Statement I was solving a problem and came to a part where I was dealing with the expression, 1 - e-t -------- 1 - et It turns out that this can be simplified to -e-t but I had no idea from simply looking at the first expression that it could be simplified, and I tried to continue...

Homework Statement Simplify: $$sin^2\left(x\right)+sin^2\left(x\right)tan^2\left(x\right)$$ Homework Equations All trigonometric identities. The Attempt at a Solution (i) ##sin^2\left(x\right)+sin^2\left(x\right)tan^2\left(x\right)## (ii)...

When I was in school for Biomedical Engineering, while playing with numbers I noticed a pattern while calculating an equation, so I tested it. This is for relatively simple equations but maybe there is a way to incorporate it at a higher level. I would imagine while crunching numbers there may...

Homework Statement An appropriate correlation for heat transfer by natural convection from a horizontal pipe to the atmosphere is Nu=0.53Gr^0.25 Pr^0.25 Where, Gr= (αp^2 d^3 (T_1-T_f )g)/μ^2 And Pr⁡〖= (C_p μ)/k〗 Show the above correlation can be simplified to h...

Hello everyone! I have this expression which I have to simplify: ∑i=1log(n) 1(log(n) - i) And my book apparently simplifies it to being log(n). I am struggling to figure out why this is the case. Could anyone help? Thanks!

Hi, I am trying to simplify a double summation and was wondering if anyone would be able to help me. The sum is $$ \sum_{i=1}^{n-1} \sum_{j=i+1}^n a_i a_j $$ Is it possible to simplify it down and maybe lose one of the sigmas? Thank you in advance :)

What exactly does it mean to simplify an expression. I understand that an expression becomes more simple when you combine like terms but what other conditions are there? Is x(5x+1) more or less simple than 5x^2 +x? Do square roots need to be moved to the numerator?

Hello. I have this function ## v(x) = -\sum_{i=1} x^i \sqrt{2}^{i-2} \int_{-\infty}^{\infty} m^{i-1} \cosh(m)^{-4} dm## which I can not seem to figure out how to simplify.I tried looking at some partial integration but repeated integration of ## \cosh ## gives polylogarithms which seemed to...

Homework Statement The problem is given in the picture attached. It is a network of switches.Homework EquationsThe Attempt at a Solution I managed to simplify the expression to this: ## (S + x'(w+y) + xvz)(x'+y)(v+z') ## but I just can't find a way to simplify it to 9 literals. I've tried all...

Hi, just wondering if anyone could help me simplify (if possible) the following two equations. x = sin((cos(((1-(cos(θ/2)^2))*360)/2)+1)/2*θ)*(d/2) x = cos((cos(((1-(cos(θ/2)^2))*360)/2)+1)/2*θ)*d/2)*2 My math is pretty crap, so any help would be appreciated. Thanks

Homework Statement [/B] A.) Simplify the circuit (Figure 1) by using a Y-to-Δ transformation involving the resistors R2, R3, and R5 as shown in (Figure 2) . Determine the resistances of the equivalent Δ. B.) Determine the equivalent resistance Rab in the circuit. Hopefully these two figures...

Homework Statement Simplify the block diagram. I uploaded a single image as it's the easiest way to do this problem. Homework Equations None at this stage. The Attempt at a Solution Please see the image.

Homework Statement Please see attachment. Homework Equations I don't know how to get the final product on the ones with the question marks (textbook answers written next to them). I've gotten to the last step (except for # 29 but don't mind that one, I haven't exhausted all ideas). I've...

Homework Statement Evaluate the derivative of the following function: f(w)= cos(sin^(-1)2w) Homework Equations Chain Rule The Attempt at a Solution I did just as the chain rule says where F'(w)= -[2sin(sin^(-1)2w)]/[sqrt(1-4w^(2)) but the book gave the answer as F'(w)=(-4w)/sqrt(1-4w^(2))...

Hello. I have been looking into trigonometric identities that helps to simplify a question in mathematics. But the question that I have is, why do I need to simplify a question? For instance: Sin(x) * Cos(x) means Sin(2*x)/2. I have no answer that tells me why I simplify Sin(x) * Cos(x) to its...

I read a paper and i can't understand how can we make the conversion (that attached in photo) i mean how i get formula (5) from previous one

Homework Statement How to show a block diagram can be simplified to a standard first order form for the diagram shown in the image attached and the question is shown in 1.a Homework Equations Standard first order form K/(1+tD) where K gain and t is time constant The Attempt at a Solution...

\sqrt{3} + \sqrt{2} / \sqrt{3} - \sqrt{2}

In this Khan Academy video they say that it is ok to break the square root ##\sqrt{a\cdot b}##, with ##a, b \in \mathbb{R}##, into the product of two square roots ##\sqrt{a}\cdot \sqrt{b}##, only when: (1) both are non negative, (2) one of the two is negative and the other is possitive. I...

I have the expression ##e^{\frac{1}{2} \log|2x-1|}##. I am tempted to just say that this is equal to ##\sqrt{2x-1}## and be done with it. However, I am not sure how to justify this, since it seems that then the domains of the two functions would be different, since the latter would be all real...

For the expression: (B and C) or (not B and not C) or (A and (not B) and not C) I get two different answers depending on the order I do the simplification. 1. If I factor C out of the first and third terms I get (B and C) or (A and C) or (not B and not C) 2. If I factor not B out of the...

[ Mod Note: relocated to homework forum so template is missing ] Hi Iwas soving a problem and the question is to simplify the circuit . Ididnt understand how the whole circuit is the same as the sum of I1 and I2 and U1 (which is a voltage source ) and I3 and R1 don't play a role Thank you