Recent content by RentonT

Homework Statement Let P be any point (except the origin) on the curve r=f(θ). If ψ is the angle between the tangent line at P and the radial line OP, show that tan(ψ)= (r/(dr/dθ)) Hint: Observe that ψ = φ - θ in the figure. Homework Equations Very few equations come to mind except y =...

Nevermind. My poor algebra skills were my downfall this time. I figured out that it's \int \frac{-500}{y(y-1000)}

OK. So what would be on the left-hand side of the equal sign? x=\frac{A}{y}+\frac{B}{1000-y} I understand you multiply the left side by one of the denominators on the right side and then plug in the x value that would have zeroed the denominator. I just don't know what goes on the left side. Is...

I am in fact working on the section over partial fractions. Thank you very much Dick. I see how partial fractions plays into this. Might I ask how you got \frac{A}{y} + \frac{B}{1000-y} I'm having trouble seeing the partial fractions. Most of them I have worked with I use the shortcut to...

Homework Statement "Solve this differential equation algebraically, subject to the initial condition that y=10 at t=0Homework Equations \frac{dy}{dt} = 2y*\frac{1000-y}{1000}The Attempt at a Solution I first reduced the right side to \frac{-y^2}{500} + 2y After that I separated the variables...

I constructed a triangle using the given information. The sin(y) as in the opposite leg over the hypotenuse is equal to sqrt(x)/1

An interesting AP Calculus BC problem I have not been able to solve. Homework Statement "If the substitution \sqrt(x)=sin(y) is made in the integrand of \int\frac{\sqrt(x)*dx}{\sqrt(1-x)} , the resulting integral is ... [5 choices are given] (A) integral(0,1/2,(sin(y))^2,dy) (B)...