Recent content by professordad

Homework Statement A spherical capacitor consists of a spherical conducting shell charge -Q concentric with a smaller conducting sphere of radius 4.0 cm and charge Q. The larger conducting shell has inner and outer radii of 11.0 cm and 13.0 cm, respectively. What is the capacitance of the...

Homework Statement If \vec{r}(t) = t^2\vec{i} + t\cos{(\pi t)}\vec{j} + \sin{(\pi t)}\vec{k}, evaluate \int_{0}^{1} \vec{r}(t) \text{dt}. Homework Equations The Attempt at a Solution So I tried integrating each individual part, and I got \frac{1}{3}t^3\vec{i} + (-\pi t\sin{(\pi t)} -...

@ DDarthVader: Yes, but you're not substituting n + 1 in for 2n - 1 or anything, you're subbing it in for n...

Homework Statement A stone is thrown upward from the top of a building at an angle of 30.0 degrees to the horizontal and with an initial speed of 20.0 m/s. The height of the building is 45.0 m. Where does the stone strike the ground? Homework Equations v_{x0} = v_0\cos{\theta_0} where...

You're only working with odd numbers, so the next term wouldn't be 2n..

@ Infinitum, wait, really? Because Wolfram Alpha and I both got the provided answer... @ synkk: \displaystyle \sum_{p=1}^{n} 4p + 5 = \displaystyle \sum_{p=1}^{2} 4p + 5 + \displaystyle \sum_{p=3}^{n} 4p+5

Hint: If a,b,c are three consecutive terms of a geometric sequence, b^2 = ac.

Yes :) because \sqrt{3100} = 55.68 as obtained in my first method, but why doesn't the second method work?

Homework Statement A model rocket is launched straight upward with an initial speed of 50.0 m/s. It accelerates with a constant upward acceleration of 2.00 m/s^2 until its engines stop at an altitude of 150 m. How long after lift off does the rocket reach the maximum height? from...

Here's how I would do it: cube the entire thing. Something helpful: If you have S = A + B, then S^3 = A^3 + B^3 + 3AB(A + B). And what is A + B? :)

@ SammyS: Oops yeah, I did forget to define variables. In this case v_0 is the starting velocity, t is the time which it takes for the pebble to hit the water, and x is the displacement. (in this case it's also the distance because the pebble doesn't go back) And v is the velocity when the...

Homework Statement A pebble is dropped into a deep well, and 3.0 seconds later the sound of a splash is heard as the pebble reaches the bottom of the well. The speed of sound in air is about 340 m/s. (a) How long does it take for the pebble to hit the water? (b) How long does it take for...

2a: Expanding sin(a+b) gives sin(a)cos(b) + cos(a)sin(b). So we need to find cos(b) and sin(a). Since angle a is in quadrant 4, sin(a) is negative. So it is -\sqrt{1 - \left(\frac{4}{5}\right)^2}, or -1/5. Since angle b is in quadrant 2, cos(b) is negative. So it is -\sqrt{1 -...

Please give only hints, no full solutions :) Homework Statement Use series to approximate the definite integral to within the indicated accuracy: \int_0^{0.1} \frac{dx}{\sqrt{1 + x^3}}, |\text{error}| < 10^{-8} Homework Equations Taylor series and Maclaurin series The Attempt at a Solution...

Homework Statement A light in a revolving lighthouse located 1 mile away from a straight shoreline turns at 1 revolution per minute. Find the speed of the spot of light along the shore when it is 2 miles away from the point of shore nearest the light. Homework Equations \frac{dx}{dt} =...