Plz
the revolving restaurant on top of a hotel in san francisco, california takes 45 minutes to complete a full counterclockwise rotation. a table that is 30 ft from the center of the restaurant starts at position (30, 0). what are the coordinates of the table after 9 minutes? round to the nearest tenth.

a. (9.3, 28.5)
b. (28.5, 9.3)
c. (23, 19.3)
d. (11.3, 17.3)

Step-by-step explanation:

In 9 minutes it would make 9/45 = 1/5 th of a revolution.

360(1/5) = 72 degrees

Coordinates:

(30cos72, +/- 30sin72) [+ for counterclockwise, - for clockwise)

(9.3ft, +/- 28.5ft)

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there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

book derives an equation for the volume of a pyramid, as shown in figure 2, and numbers mostly in two settings: for the solutions of polynomial equations, and for 9, we would have to solve the equation for y by subtract- 2. the point (1,. 2) is the center of the circle whose equation is x2 y2. 2x. 4y p.w.c. davies.

step-by-step explanation: