Homework Statement
I'm trying to find the arc length of a curve over an interval and I've arrived at
\int (y4 +2y2 +1)1/2 dy
and now I'm pretty sure i should use a u substitution in order to integrate.
I tried using u=y2 so du=2y dy so dy=du/2y
Then you have \int (u2+2u+1)1/2 and...
Homework Statement
it's been a long summer and i forgot everything.
i need help integrating 1-cos(t)dt
evaluate g(x) = [\pi,x]integral (1-cos(t))dt
i know by pt2 of fund. thm of calc that g' (x) = 1-cos(x)
but i can't remember how to evaluate the integral and then differentiate to...
Homework Statement
an electron starting from rest acquires 3.53keV of kinetic energy in moving from A to B. how much kinetic energy would a proton acquire moving from B to A.
Homework Equations
1/2mv2
me=9.11e-31 kg
mp=1.67e-29 kg
1eV=1.6e-19 J
The Attempt at a Solution...
it should be (L^2 + d^2) to the 3/2 power. and it is integrated from 0 to 1/2. and lamba is the linear charge density, L is length of rod, d is distance normal to rod
Homework Statement
A rod of length 0.1m has a uniform linear charge density of 3C/m. Determine the Electric field at a point d=P located at a perpendicular distance 1m along a line of symmetry of the rod.
The Attempt at a Solution
I know i have to use super position and integrate but I...
That's not really what i was asking...
So say I already took N=7 measurements and have the best estimated uncertainty for the mean time, which is 0.03.
Now I want to reduce that number to 0.012 by taking some new number of measurements.
Wouldn't I just use the ratio 0.03/0.012 = 2.5 and then...
Homework Statement
I want to lower the uncertainty of an experiment to 0.012 s from 0.03 s by performing x number of more measurements. I already have the mean, std dev, variance.
I know I need the factor of 0.012/0.03 somehow but I don't know where to apply it.
Any suggestions?
Homework Statement
A point charge is at the center of a conducting hollow sphere, with radius 0.011m, that is within another conducting hollow sphere of radius 0.041m. The point charge is Q0=+4.30e-6 C, the inner sphere has a net charge of Q1=-1.70e-6 C, and the outer sphere has a net charge...
Homework Statement
A positive charge is located at the center of a cube.
Are the intersections of the field lines with a side of the box uniformly distributed across that side? Explain
The Attempt at a Solution
I'm trying to picture this in my head and I'm getting stuck. I know the field...
1. Homework Statement
For uncorrelated uncertainties LaTeX Code: \\delta x and LaTeX Code: \\delta y give the values and uncertainties for W in standard format.
A.) W=x+y with x=4.2(0.2) and y=0.7(0.1)
2. Homework Equations
[b]3. The Attempt at a Solution
well i think i am...
So after a bunch of substitutions and algebra solving for Vcore, I got
Vcore=(\rhoavg*V\rhoplanet - \rhomantle*Vplanet) / (\rhocore - \rhomantle) and got 1.206*1026g/cm3.
Solving for the radius I got
r=\sqrt[3]{Vcore/(4pi/3)} and got 3.0665*108cm which is 3065km, roughly 75% of the planet's...