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# In need of desperate HELP!

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1. A box without a top is to be made from a rectangular piece of cardboard, with dimensions 8 in. by 10 in., by cutting out square corners with side length x and folding up the sides.

a. Write an equation for the volume V of the box in terms of x.

b. Use technology to estimate the value of x, to the nearest tenth, that gives the greatest volume. Explain your process.

2. A cube-shaped aquarium has edges that are 3 ft long. The aquarium is filled with water that has a density of .

a. Should the aquarium be placed on a table that can support a maximum weight of 200 lb? Explain why or why not.

b. Would the density of the water change if the aquarium was only half full? Explain.

3. Use the Fermi process to estimate the number of bricks needed to fill an empty bathtub. Show your work.

#1
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1) The  new volume, V,   is given by

(8 - 2x) (10 - 2x) x =

(80 - 36x  + 4x^2) x  =

4x^3 - 36x^2 + 80x

We can find the  maximum of this curve  using  Calculus

12x^2 - 72x + 80  = 0   divide through by 4

3x^2 - 18x + 20  = 0

Using the quadratic formula and solving for x  we have that  there are two possible solutions

x = 3 - √(7/3) ≈  1.4725  = 1.5    or    x  =   3 +√(7/3) ≈  4.5275  = 4.5

Looking  at the graph of the volume function here, it's clear  that the first answer produces the maximum  volume  : https://www.desmos.com/calculator/fdqkzsy7cq

CPhill  Jun 8, 2017
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2. The volume  =  side^3  = (3 ft)^3 = 27 ft^3

Water has a weight of about 62.416 lbs/ ft^3

So.....the weight of the water  =   27 * 62.416  ≈ 1685 lbs

No way the table supports that  !!!!

The density of water doesn't change no matter how much is in the aquarium....

CPhill  Jun 8, 2017
edited by CPhill  Jun 8, 2017
edited by CPhill  Jun 8, 2017
edited by CPhill  Jun 8, 2017