1. ### Why is this the answer???

I can't for the life of me figure out why 2 2/5 is the answer to the following question. If anyone can explain this to me then I would appreciate it. Question: John can paint a fence by himself in 6 hours and Jenny can paint the fence in 4 hours. How long will it take them to paint the...
2. ### Langrangean: Simple proof question, answer completely eluding me

Hi everyone, I was hoping someone could help me with the second part of this question. I have found the minumum using the lagrangean solution and found x=y=x=c/3 however with the proof don't both the left hand side and right hand side equal eachother exactly!? Many thanks for any impending help!
3. ### Is the answer wrong? (from textbook)

1. The problem statement, all variables and given/known data The question below, i already have the answer. but I can't work it out. Can anyone help? Questions (Original) In a game, Tom throws a fair dice twice. 1 point is awarded for each '6' thrown, 2 points are awarded if the sum of the...

f(x) = 2ex-5x f'(x) = 2(ex)' - (5x)' f'(x) = 2ex - x5x-1 \\ is there anything is I can do after this?
5. ### Domain and Range questions on a f(x,y) and f(x,y,z) have answer, need explaining!

Fine D and R of the two functions. a) f(x,y)=ln(√(1+x2+y2)) the range can't be determined and the domain is R2... why? b) f(x,y,z)= 1/√(x2+y2+z2-1) domain is R3-B(0,1) = {(x,y,z)|abs(x,y,z)>1}..why is that the domain? I understand it haveing to be greater than one due to the fact...
6. ### y`=y+2 Seems Simple, but i can't match the answer up to it.

The equation is: dy/dx=y+2 The answer is y=Cex-2 Can anyone explain this?
7. ### Which answer is correct?

Evaluate \int \frac{dx}{sin(x)+sin(2x)} Wolfram alpha gave me this answer -\frac23log\left(\frac{3-tan^2\frac x2}{\sqrt tan\frac x2\right)}+c. When I solved this problem, I got this answer \frac16log(1- cos x)+\frac12 log(1+cos x)-\frac23 log...
8. ### Chain Rule. Just need answer for this question

Find the derivative of N(t) = 150 - 600 / sqrt.(16 + 3t^2)
9. ### Integral by Trig Substitution and simplifying answer

Integral(3/(1+9x^2)^(1/2),x) =integral(3/((1/3)^(2)+x^2)^(1/2)),x) x=(1/2)*tan(u) dx=(1/3)sec^2(u)du ... original integral=integral(sec(u),u) =LN[abs(cos(u))/abs(sin(u)-1)]+c (1/3)Tan(u)=x x=ATan(3x) original integral=ln[abs(cos(Atan(3x))/(abs(sin(Atan(3x))-1)]+c using the calculator, I get...
10. ### Plot a graph of the answer to a differential equation solved using laplace transforms

Hello all, How do i plot a graph for the answer to the following Solve the differential equation using laplace transforms, given x(0) = -5 and x'(0) =25 d^2x +6 dx +25x = -150 ____ __ dt^2 dt The answer the the above is a= -6, b= 1, c= 31 Thanks in advance,
11. ### Answer key wrong? Simple trig problem (two right triangles)

There are a lot of discrepancies in the answer key and so I had wanted to verify with another eye if I am correct on this or not. The question simply relates to a pipe going down the side of a cliff with two bends in it, the second steeper than the first. i.e.. From flat ground, pipe bends...

find the sum of 4a^3-7a-5 and -8a^2-2a+7 IS THE ANSWER ANSWER: -4n^2-9a+2 HOW TO do this The sum of four consecutive integers is at least 114. Find the smallest possible values for these numbers.
13. ### Initial-value problem using the method of eigenvalues/eigenvectors (Answer included).

The biggest challenge for me in attempting this problem is using the Linear algebra. If I'm correct, I must: 1) Find eigenvalues. 2) Find eigenvectors. 3) Compute e^(At) 4) Multiply e^(At) by y_0 = y(0) So, assuming what I said is correct, it seems like I know what I am doing but...
14. ### Unsure of how to find the answer.. Matrix question

Hi, I have tried to analyse this question but I dont know how to get the answer for tr B and det B (5 and 0 respectively) The eigenvalues of a certain 2 × 2 matrix A are –2 and 3. Let B = A^2 – 2A – 3I . What are the values of the trace and the determinant of B? Show how you obtained...
15. ### Chromatic Polynomial: Does anyone else get the same answer as me?

I lost my notes which included the answer to this question, so I was just wondering if I had done it correctly: I get: k(k-1)^2(k-2)^2 - k(k-1)(k-2)^2 - k(k-1)(k-2)^2 = k(k-1)^2(k-2)^2 - 2k(k-1)(k-2)^2 =k(k-1)(k-2)^2(k-3) Thanks.
16. ### Need help differentiating an expression. Answer is given just unsure of the steps.

Hello, this problem states to differentiate the expression with respect to q. I am not sure of the steps taken to get the final result. This is an economics problem differentiating the variable cost function to get the marginal cost function.
17. ### Find the parametric equations of the tangent line to a line (Answer included)

The question and answer are attached. I'm having trouble with the material in this course (Intermediate Calculus). I'm also particularly having trouble with parametric equations which I believe I should know already but I don't so please illustrate how to do this problem. Any help would be...
18. ### Did I get the right answer? (Cramer's rule)

Use Cramer's rule to solve x1 + x2 - x3 = 1 x1 + x2 + x3 = 2 x1 - x2 = 3 To skip to the end.. Unique solutions: x1 = 9/4 x2 = -3/4 x3 = 1/2 Are these answers right?
19. ### How do I simplify from my answer to the tutor's answer?

Hi There's an algebra problem I've been working on - I've got as far as I can. My tutor says my answer is correct but can be simplified down to his answer - but I can't see how. If anyone can explain the steps on how to simplify to the answer I'd be really grateful! My answer...