A graphing calculator is recommended.In this problem you are asked to find a function that models a real-life situation and then use the model to answer questions about the situation. Use the guidelines on page 237 to help you.A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 14 in. by 20 in. by cutting out equal squares of side x at each corner and then folding up the sides(see the figure)20 in.ххх14 inхXX(a) Find a function that models the volume V of the box280x 32x24x3XV(x)(b) Find the values of x for which the volume is greater than 230 in3. (Round your answers to three decimal places. Enter your answer using interval notation.)(c) Find the largest volume that such a box can have. (Round your answer to three decimal places.)in3

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Asked Oct 12, 2019
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A graphing calculator is recommended.
In this problem you are asked to find a function that models a real-life situation and then use the model to answer questions about the situation. Use the guidelines on page 237 to help you.
A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 14 in. by 20 in. by cutting out equal squares of side x at each corner and then folding up the sides
(see the figure)
20 in.
х
х
х
14 in
х
X
X
(a) Find a function that models the volume V of the box
280x 32x24x3
X
V(x)
(b) Find the values of x for which the volume is greater than 230 in3. (Round your answers to three decimal places. Enter your answer using interval notation.)
(c) Find the largest volume that such a box can have. (Round your answer to three decimal places.)
in3
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A graphing calculator is recommended. In this problem you are asked to find a function that models a real-life situation and then use the model to answer questions about the situation. Use the guidelines on page 237 to help you. A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 14 in. by 20 in. by cutting out equal squares of side x at each corner and then folding up the sides (see the figure) 20 in. х х х 14 in х X X (a) Find a function that models the volume V of the box 280x 32x24x3 X V(x) (b) Find the values of x for which the volume is greater than 230 in3. (Round your answers to three decimal places. Enter your answer using interval notation.) (c) Find the largest volume that such a box can have. (Round your answer to three decimal places.) in3

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Expert Answer

Step 1

(a) Obtain the function that models the volume of the box as follows.

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Let the height of box be x, that is square of side x is cut from each corner Lenghth of the box = 20 2x Width of the box 14-2x Height of the box x Volume of the box Length x Breadthx Height =(20-2x)(14-2x)(x) = 4x3 - 68x2 +280x

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Step 2

(b) Obtain the value of x such that the volume i...

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Volume of the box > 230 Plot V (x) 4x68x2 +280x and V (x)= 230 as follows 400 (2.704, 339.013) 300 (1.093, 230) |(11.216, 230) 4.691, 230) 200 100 The interval for which the volume is greater than 230 is (1.093,4.691)

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