Homework Statement
I am trying to solve the following homework problem:
1) A laser beam of light with wavelength λ=600nm shines perpendicular to a slide that has a
rectangular pattern of small holes that can be viewed as point sources. The spacing
between the holes is a=40μm and b=30μm...
In organic lab this week we were mixing (1-R, 2-S) ephedrine with mandelic acid to get crystals. I dissolved both compounds in 6 mL 95% EtOH and then poured them together. After cooling + glass prodding I should have had no trouble getting crystals. HOWEVER, during the cooling I accidently...
I understand entropy is a state function, insofar as we deny the existence of irreversible cycles. However, for a said change of state, the heat transferred as a result of a reversible change is greater than that for an irreversible change. This is simply a reiteration of the Clausius...
I'm trying to find the largest sphere that be inscribed inside the ellipsoid with equation 3x^2 + 2y^2 + z^2 = 6.
Homework Equations
I know I will need at least 2 equations. One of them is the constraining equation (f(x) = a, where 'a' is a constant) and the other is the equation you...
A cylindrical hole is put through a ball of radius a (>b) to form a ring. I am trying to find the outer surface area of the ring. I know i am supposed to parametrise the ring in some way, as we are learning about parametrizing surfaces. But I don't really know how to go about solving this...
p = rho
a = phi
b = theta
p^2[cos(a)sin(a)(cosb)^3 + (sina)^2(sinb)^3 + cos(b)cos(a)sin(a)(sinb)^2 + sin(b)(sina)^2(sinb)^2].
I differentiated with respect to rho in the first column, phi in the second column, and theta in the third.
Thanks.
I'm trying to see near which points of R^3 I can solve for theta, phi, and rho in terms of x,y, and z. I know i need to find the determinant and see when it equals zero; however, I get the determinant to equal zero when sin(phi) = 0, and when tan(theta) = -cot(phi). The first is right, but...
we haven't learned that quite yet, but thanks; I have a strong feeling the gradient of the surface is involved, but I don't see how one can get the curves by taking the path of maximum descent.
We have an ellipsoid with the equation 4x^2 + y^2+ 4z^2 = 16, and it is raining. Gravity will make the raindrops slide down the dome as rapidly as possible. I have to describe the curves whose paths the raindrops follow. This is probably more vector calculus than physics, but i wasn't sure...
Ok converting to polar coordinates seems like a good idea; however, the denominator is still causing me problems.
I will show all the work I have done so far:
We want to show that the limit of the function:
\frac{2x^2 + y^2}{x^2+ y^2} is 1.2 as one approaches the point (-1,2).
We...