Find the area of the shaded regions. give your answer as a completely simplified exact value in terms of π (no approximations).
(i got 16.3 repeating, can anyone check me on this? )

This is the same as (40pi)/3

Explanation:

A = area of the smaller circle OB

A = pi*r^2

A = pi*3^2

A = 9pi

Circle OB has an exact area of 9pi square cm

We don't want the whole circle area, since we only are focusing on a 120 degree slice. Note how 120 degrees is 120/360 = 1/3 of a full circle; therefore we want 1/3 of the area to get the area of the slice

area of slice DOB = (1/3)*(area of circle OB)

area of slice DOB = (1/3)(9pi)

area of slice DOB = 3pi

We'll use this later so let's call this M

M = 3pi

B = area of larger circle OA

B = pi*r^2

B = pi*7^2

B = 49pi

We take 1/3 of this for similar reasons as mentioned earlier. So the area of pizza slice COA is (1/3)*(49pi) = 49pi/3

We'll use this later so let N = 49pi/3

Subtract the values of N and M.

Shaded area = N - M

Shaded area = (49pi/3) - (3pi)

Shaded area = (49pi/3) - (9pi/3)

Shaded area = (49/3)pi - (9/3)pi

Shaded area = (49/3 - 9/3)pi

Shaded area = (40/3)pi

side note: I think you computed 49/3 = 16.333 repeating which was the result for the area of circle OA; however it's not the final answer

another note: leave 40/3 as a fraction and don't convert it to 13.333 repeating. This is because the fraction 40/3 is exact while 13.333 is approximate

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

well we know there are 4 clubs in 52 cards so it’s replaced so it should be 3/51

step-by-step explanation: