Let a circle inside triangle DEF have a radius = 3, and let it
be tangent to EF at point Z. Suppose |EZ| = 6 and |FZ| = 7. What
are the lengths of d, e, and f?
Let R be the region inside x ^2 /9 + y^2 /25 = 1, with x ≥ 0.
(That is, R is the right-hand side of the ellipse below.) (a) (15
pts) Use the change of variables x = 3u, y = 5v to transform ∫ ∫ R
x dxdy to a polar coordinate integral. 3 −5 5 R (b) (5 pts)
Evaluate the polar coordinate integral
Given H = (3R^2/ sin θ) aθ + 54 R cos θ aφ A/m (a) Find J.
(b) Find the total current in the aθ direction through the
conical surface θ = 20◦, 0 ≤ φ ≤ 2π, 0 ≤ R ≤ 5
Please explain (b) thoroughly.