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elixir [45]
2 years ago
10

Given the formula, Sn=a 1-r^n/1-r, what is the sum of the first nine terms of the geometric series: 324, -108, 36, -12...

Mathematics
1 answer:
vlada-n [284]2 years ago
3 0

Answer:

243.01.

Step-by-step explanation:

The first term (a) = 324.

The common ratio (r) = -108/324 = -1/3.

So sum of 9 terms is:

S(9) = 324 * (1 - (-1/3)^9) / ( 1 - (-1/3)

= 324 ( 1 - (-0.00005076)) / 4/3

= 324 * 1.00005076 / 1.33333

= 243.012.

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Answer:

width = 5 in

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height = 2(5)= 10 in

Step-by-step explanation:

A gift box has a volume of 450 cubic inches.

Let 'w' be the width of the box

The width of the box is 4 inches less than the length.

length = w+4

The height is twice the width.

height = 2 \cdot width

height = 2w

Volume of box = length times width times height

V=(w+4)(w)(2w)

450=(w+4)(w)(2w)

450=2w^3+8w^2

2w^3+8w^2-450=0

\quad 2\left(w-5\right)\left(w^2+9w+45\right)=0

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\quad\left(w^2+9w+45\right)=0, this gives two complex values

so width = 5

length = 5+4=9

height = 2(5)= 10

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