Recent content by JBD2

Thank you so much, that makes a lot more sense to do it that way. I was wondering though, for your second derivative, is 3yy" supposed to be 3y2y" or is there something I'm forgetting? Thanks again.

Sorry for this unnecessary post, but I don't have much time and need to be sure this is correct.

Homework Statement Consider: x^3+y^3+2xy=4, y=1 when x=1 a.) Find the equation of the tangent line to the curve when x=1. b.) Find y'' at x=1. c.) Is the graph of y=f(x) concave up or concave down near x=1? Homework Equations Any derivative rules... The Attempt at a Solution For Part a...

Homework Statement Let \[f(x)=\begin{cases}{} \frac{6a(x^2+1)}{2x^2+1}+\frac{b\log \big((x+1)^4\big)}{x} &\mbox{if } x<0,\\ -2a-4 &\mbox{if } x=0, \\ \frac{a\sin x}{x}+b &\mbox{if } x>0. \end{cases}\] Find \(a\) and \(b\) such that \(f\) is continuous at \(x=0\). Homework...

Yes, thank you. After I posted I wondered whether you could do that or not (a little unfamiliar with Leibniz notation) but it makes sense now thank you.

Homework Statement If x = cos(3t) and y = (sin(3t))² find dy/dx and d²y/dx². Homework Equations d/dx cosx = -sinx d/dx sinx = cosx The Attempt at a Solution dx/dt = -3sin3t dy/dt = 6sin3tcos3t Not sure what to do now.

Ok well I have two more questions, and rather than clutter the board with another post I'll put them here: Question 2: Homework Statement A new car costs $42 000 and depreciates 20% the first year, then 15% every year after. What is the car worth in 10 years? The Attempt at a Solution 42 000...

Homework Statement If \sum_{n=1}^{4}log_{2}x^{n}=80, determine the value of x.Homework Equations S_{n} = \frac{a(r^{n}-1)}{r-1} S_{n} = \frac{rt_{n}-a}{r-1}The Attempt at a Solution log_{2}1+log_{2}x^{2}+log_{2}x^{6}+log_{2}x^{12}=80? log_{2}x^{20} = 80 2^{80}=x^{20} x=16 Is this right...

Ok thanks so much that makes sense now.

The Question: The figure above shows a portion of the graph of the function f. If f(x+5) = f(x) for all values of x, then f(x) = 0 for how many different values of x between 0 and 12? My attempt: I have uploaded the picture of the graph so you can see what it looks like, but anyways I...

-5 = \frac{-4x}{t} \frac{5}{4} = \frac{x}{t} Oh ok I get it now, thanks so much.

How do I get 5/4 then?

The answer is apparently \frac{5}{4} though, and I don't understand where the 2t² comes from.

Do you mean divide: 2x^{2}=5t^{2} by 2t^{2}? How does that work?

Homework Statement \sqrt{x^{2}-t^{2}}=2t-x If x and t are positive numbers that satisfy the equation above, what is the value of \frac{x}{t}? 2. The attempt at a solution x^{2}-t^{2}=4t^{2}-x^{2} x^{2}+x^{2}=4t^{2}+t^{2} 2x^{2}=5t^{2} I'm unsure of what to do next.