Consider the function f(x, y) = -3x^2-2y^-2. Find the directional derivative of f at the point (1,-4) in the direction given by the angle theta = 2pi/5.
Find the unit vector which describes the direction in which f is increasing most rapidly at (1,-4).

I have already confirmed the directional derivative to be exactly
-6cos(2pi/5) + 16sin(2pi/5)

I believed the unit vector should have been (cos(2pi/5), sin(2pi/5)), but when I checked my answer the only correct part was the sin(2pi/5). If the other part is not cos(2pi/5), then what is it and How would that be calculated or inferred?

A picture of the original format and my answers is also included.

the figures below are made out of circles, semicircles, quarter … find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations). remember that we'll also have to cut whatever areas we get in half, since we're only dealing im pretty sure that is the right answer

step-by-step explanation:

36/60

36/2=18

60/2=30

18/30

18/3=6

30/3=10

6/10

6/2=3

10/2=5

your final answer would be 3/5 of an

hope this !

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3