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Question 945694: The town swimming pool is d feet deep. The width of the pool is 10 feet greater than 5 times the depth. The length of the pool is 25 feet greater than the width.
A.Write and simplify an expression to represent the volume of the pool.
B. If the pool holds 51,000 ft3 of water, what are the dimensions of the pool?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The town swimming pool is d feet deep.
The width of the pool is 10 feet greater than 5 times the depth.
w = 5d+10
The length of the pool is 25 feet greater than the width.
L = w + 25
Replace w with (5d+10)
L = (5d+10) + 25
L = 5d + 35
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A.Write and simplify an expression to represent the volume of the pool.
Volume = L*w*d
replace L and w
V = (5d+35)*(5d+10)* d
V = (25d^2 + 50d + 175d + 350)* d
V = (25d^2 + 225d + 350)*d
Factor out 25 and you have
V = 25d(d^2 + 9d + 14)
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B. If the pool holds 51,000 ft3 of water, what are the dimensions of the pool?
25d(d^2 + 9d + 14) = 51000
divide both sides by 25
d(d^2 + 9d + 14) = 2040
the equation
d^3 + 9d^2 + 14d - 2040 = 0
Using the Ti83, I got d = 10 ft is the depth
then
5(10) + 10 = 60 ft is the width
and
5(10) + 35 = 85 ft is length
:
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Check this, find the vol using these values; 85 * 60 * 10 = 51000
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