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}...
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...
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...
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...
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...
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...
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...
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...
The exact wording for this problem:
f(x) = 3x + 1 + \sin(x) with domain [-\pi/2, \pi/2]. Without your calculator, determine the value of f^{-1}(1).
Since this is an inverse function, I was going to try to solve for the inverse function, then solve for f^{-1}(1)
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...
So my next step would be to simplify the right side using log laws, yes?
log(y)=log(3-4e^x)-log(6-10e^x)
This seems wrong but it's the only way I know.
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...