While working on an integration problem I found that I will arrive at two different solutions depending on how I approach it.
I'm finding the arc length of y=ln(1-x2) on the interval [0,0.5]
The formula for finding the arc length is ∫sqrt[1+[f'(x)]2]dx
So f'(x) = -2x / ( 1-x2 )
Here...
Thanks a lot. I get the first part now. But I still don't get the second part. We only know the two triangles share the same height so how can we deduce that their areas are in the same proportion without knowing the relationship between the heights.
Sorry, but I really suck in geometry.
Homework Statement
Let A, B, C be three points on a plane and O be the origin point on this plane. Put a = OA and b = OB, and c = OC, (a,b and c are vectors). P is a point inside the triangle ABC. Suppose that the ratio of the areas of the triangles PAB, PBC and PCA is 2:3:5
(i) The...
Homework Statement
int[1/1+3cos^2(x)]dx
Homework Equations
The Attempt at a Solution
It shouldn't require any techniques of integration other than u-substitution. I tried letting u = sqrt(3)cos(x) and u = tan(x/2) but both didn't work so I think I need to multiply some...
Homework Statement
Show that the integral (from 0 to infinity) of e-axJp(bx)dx = [sqr(a2+b2) - a] / bpsqr(a2+b2)
Homework Equations
Jp(bx) =
summation [ (-1)k(bx/2)2k+p ] / k! Gamma(k+p+1)
Gamma(x) = integral (from 0 to infinity) of e-ttx-1dt
The Attempt at a Solution...
Homework Statement
2.5-13. Let x equal the number of flips of a fair coin that are required to observe heads-tails on consecutive flips
(a) Find the p.m.f. of x
(b) Determine the values of the mean, variance and standard deviation.
2.5-17. From 1999-2002 Red Rose Tea randomly placed one...
Homework Statement
In the circuit shown in the figure below the current through the 12.0V battery is measured to be 70.6 mA in the direction shown. What is the terminal voltage Vab
Homework Equations
V=E-IR
I1=I2+I3
The Attempt at a Solution
First I set Vab= E-IR= 24 - 10(I1)...
The potential difference is V=k(integral)dq/r
V=-(integral)Eds=-(integral)Edr=-(integral)kQ/r2dr=-kQ(integral from a to b)dr/r2=kQ(1/b - 1/a)
Is this right
Yes, I have, but using the law is quite confusing. How will finding the potential difference make any difference, since my Va would be 0 and what's left is Vb which is kq/r?
Homework Statement
Consider two thin conducting spherical shells. The inner shell has a radius r1=15cm and a charge of 10.0 nC. The outer shell has a radius r2=30cm and a charge of -15.0 nC.
Find
a)the electric field E and
b)the electric potential V in A, B and C, with V=0 t r=infinity...
Homework Statement
The auditory canal of the human ear extends about 2.5 cm from the outside ear to the eardrum
(a)Explain why the human ear is especially sensitive to sounds at frequencies around 3500Hz.
Homework Equations
Speed of sound v=344m/s
The Attempt at a Solution
I know...