EBK PRECALCULUS W/LIMITS

4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter A.5, Problem 100E

(a)

To determine

Find what the given expression represents

(a)

Expert Solution

Answer to Problem 100E

The expression $x2(x−3)$ represents the volume of water.

Explanation of Solution

Given:

The figure shows a glass cube partially filled with water.

EBK PRECALCULUS W/LIMITS, Chapter A.5, Problem 100E , additional homework tip 1

The given expression is $x2(x−3)$

Consider the following expression:

$x2(x−3)$

A glass cube of side $x$ feet, height of a glass cube filled with water is $(x−3),$ and area of a base of a glass cube is $x2$ .

Therefore, above expression represents a product of base area $x2$ and height $(x−3)$

Because volume of a cube is,

length $×$ breadth $×$ height

Here length of a cube is $x$ feet, breadth of a cube is $x$ feet and height of a glass cube filled with water is $(x−3)$ feet

Above can be written as follows:

$x2(x−3)=x×x×(x−3)$

Hence, expression $x2(x−3)$ represents the volume of water.

(b)

To determine

Find the capacity of the cube.

(b)

Expert Solution

Answer to Problem 100E

The capacity of cube is $512ft3$

Explanation of Solution

Given:

The figure shows a glass cube partially filled with water.

EBK PRECALCULUS W/LIMITS, Chapter A.5, Problem 100E , additional homework tip 2

The given expression is $x2(x−3)=320$

Consider the following equation:

$x2(x−3)=320$

To find capacity of the cube, factorize the above expression for the value of $x$

Above equation is factorable, factorize the equation by appropriate method.

Distribute $x2$ over the equation $x2(x−3)=320$

$x3−3x2=320$

Subtract 320 from both sides:

$x3−3x2−320=320−320$

Combine like terms to simplify the expression:

$x3−3x2−320=0.......(1)$

Put $x=8$ in the above expression.

$x3−3x2−320=083−3×82−320=0512−192−320=00=0$

Therefore $x=8$ is a zero of equation (1)

Hence above equation (1) can be written as follows:

$(x−8)(x2+5x+40)=0........(2)$

Further solve the equation (2) $(x−8)(x2+5x+40)=0$ by zero product rules

Set factor $(x−8)$ equal to zero:

$x−8=0$

Simplify this expression for the value of $x$

$x=8$

Further put another factor $x2+5x+40=0$

Use quadratic formula to solve the above quadratic expression

$x=−5±52−1602=−5±25−1602=−5±−1352$

This gives no real roots.

Hence the side length of cube is $x=8ft$

The volume of cube is product of base area and its height.

Since the base is square,

Area of base is $x2$ and height is $x$

Therefore, the volume is $x2⋅x=x3$

For $x=8$ the volume is given by

$(8)3=512$

Hence, the capacity of cube is $512ft3$

Chapter A.5, Problem 99E

Chapter A.6, Problem 1E

Chapter A Solutions

EBK PRECALCULUS W/LIMITS

Ch. A.1 - Prob. 1E Ch. A.1 - Prob. 2E Ch. A.1 - Prob. 3E Ch. A.1 - Prob. 4E Ch. A.1 - Prob. 5E Ch. A.1 - Prob. 6E Ch. A.1 - Prob. 7E Ch. A.1 - Prob. 8E Ch. A.1 - Prob. 9E Ch. A.1 - Prob. 10E

Ch. A.1 - Prob. 11E Ch. A.1 - Prob. 12E Ch. A.1 - Prob. 13E Ch. A.1 - Prob. 14E Ch. A.1 - Prob. 15E Ch. A.1 - Prob. 16E Ch. A.1 - Prob. 17E Ch. A.1 - Prob. 18E Ch. A.1 - Prob. 19E Ch. A.1 - Prob. 20E Ch. A.1 - Prob. 21E Ch. A.1 - Prob. 22E Ch. A.1 - Prob. 23E Ch. A.1 - Prob. 24E Ch. A.1 - Prob. 25E Ch. A.1 - Prob. 26E Ch. A.1 - Prob. 27E Ch. A.1 - Prob. 28E Ch. A.1 - Prob. 29E Ch. A.1 - Prob. 30E Ch. A.1 - Prob. 31E Ch. A.1 - Prob. 32E Ch. A.1 - Prob. 33E Ch. A.1 - Prob. 34E Ch. A.1 - Prob. 35E Ch. A.1 - Prob. 36E Ch. A.1 - Prob. 37E Ch. A.1 - Prob. 38E Ch. A.1 - Prob. 39E Ch. A.1 - Prob. 40E Ch. A.1 - Prob. 41E Ch. A.1 - Prob. 42E Ch. A.1 - Prob. 43E Ch. A.1 - Prob. 44E Ch. A.1 - Prob. 45E Ch. A.1 - Prob. 46E Ch. A.1 - Prob. 47E Ch. A.1 - Prob. 48E Ch. A.1 - Prob. 49E Ch. A.1 - Prob. 50E Ch. A.1 - Prob. 51E Ch. A.1 - Prob. 52E Ch. A.1 - Prob. 53E Ch. A.1 - Prob. 54E Ch. A.1 - Prob. 55E Ch. A.1 - Prob. 56E Ch. A.1 - Prob. 57E Ch. A.1 - Prob. 58E Ch. A.1 - Prob. 59E Ch. 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