# Search results

1. ### Cross products problem

Homework Statement Find the magnitude of \vec{v} \times \vec{B} and the direction of the new vector. \vec{v}=\left \langle 0,0,20 \right \rangle \vec{B}=\left \langle 1,1,0 \right \rangle Homework Equations |\vec{v}|=\sqrt{0^2+0^2+20^2}=20 |\vec{B}|=\sqrt{1^2+1^2+0^2}=\sqrt{2}...
2. ### 3D kinematics problem

Homework Statement I know pictures aren't the best, but here it is. Homework Equations The Attempt at a Solution This is my work for this problem. Disregard the drawing as it isn't right. I'm not sure if I'm misinterpreting the horizontal range part or what. I feel pretty...
3. ### Integral to find the volume of a torus

Homework Statement Find the volume of the torus formed when the circle of radius 2 centered at (3,0) is revolved about the y-axis. Use geometry to evaluate the integral. Homework Equations Formula for the semi-circle: y=\sqrt{4-x^2} Solving for x give x=\pm\sqrt{4-y^2} The Attempt...
4. ### Limit of a geometric series

Homework Statement Evaluate the problem: \sum_{k=1}^\infty \frac{3^{(k-1)}}{4^{(k+1)}} Homework Equations \displaystyle\lim_{n\rightarrow\infty} S_n = \frac{a}{1-r} The Attempt at a Solution I know that the limit of the partial sequence is what i need to help solve this, but can't...
5. ### Anti-derivative of a trig equation

Homework Statement I just need to find the anti-derivative of this equation: \int x(sin^2(3x)cos(3x))dx Homework Equations sin^2(x)+cos^2(x)=1 The Attempt at a Solution I'm not really sure where to start here. I tried to do a substitution first but couldn't make it work. So then...
6. ### General help for trigonemtric u-substitution

I'm currently in calculus 2 and we are learning about u-substitution and I am having a little bit of difficulty seeing how to start problems that involve trig functions. I know sometimes I can rewrite them to help suit my needs but this isn't always evident. I have for example the indefinite...
7. ### Optimization problem (minimization)

Homework Statement I have a sector of a circle with area 12 square meters. If radius r and angle \theta are chosen so that the that perimeter of the sector is the smallest possible, then what is the radius? Homework Equations I have area of sector as A=\frac{\theta r^2}{2} which is 12...
8. ### Making a function continuous

Homework Statement f(x) = x^2 - c^2 \mbox{ if } x < 5 f(x) = cx+11 \mbox{ if } x \geq 5 Find the two values of c for which the function would be continuous. Homework Equations The Attempt at a Solution I set these two equations equal to each other, plug in the value 5...
9. ### Inverse trig function

Homework Statement My problem is as follows: find the inverse of 3x+1+\sin(x) with the domain [-\frac{\pi}{2},\frac{\pi}{2}] Homework Equations The Attempt at a Solution for this would I just try to solve as normal by setting y=f(x) then using the fact that \arcsin(x) = y or is...
10. ### Inverse of a logarithmic function

Homework Statement Greetings everyone! I am having problems getting started with this question, which asks: Find the inverse of y = \frac{3-4e^x}{6-10e^x} Homework Equations The Attempt at a Solution I'm usually pretty good with these kinds of problems, but for some reason I seem to be...