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Vladimir79 [104]
3 years ago
10

The center of the basketball court has a diameter of 12 feet. What is the area of the circle

Mathematics
1 answer:
jekas [21]3 years ago
5 0

Answer:36π squared feet

Step-by-step explanation:

Diameter=12

Radius=diameter/2

Radius=12/2

Radius=6 feet

Area of circle=π x Radius x Radius

Area of circle=π x 6 x 6

Area of circle=36π

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Step-by-step explanation:

* Lets revise the geometric series

- Geometric series:

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- Ex:

# 5  ,  10  ,  20  ,  40  ,  80  ,  ………………………. (×2)

# 5000  ,  1000  ,  200  ,  40  ,  …………………………(÷5)

* General term (nth term) of a Geometric Progression:

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- Un = ar^n-1, where a is the first term , r is the constant ratio

 between each two consecutive terms  and n is the position of the

  number in the sequence

* In the problem

∵ The Un = -4(1/3)^n-1

∴ a = -4

∴ r = 1/3

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∴ U4 = -4(1/3)^(4 - 1) = -4(1/3)^3 = -4(1/27) = -4/27

* The first four terms are -4 , -4/3, -4/9 , -4/27

b) If IrI < 1  then the geometric series is converge and if IrI > 1

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∵ r = 1/3

∴ The series is converge  

c. The convergent series has sum to ∞

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∴ S∞ = -4/(1 - 1/3) = -4/(2/3) = -4 × 3/2 = -6

* The sum of the series is -6

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