# Whether the post office accept a package that is 6 in. wide, 8 in. deep and 5 ft long and the post office accept a package that measures 2 ft by 2ft by 4 ft. ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.1, Problem 79E

(a)

To determine

## Whether the post office accept a package that is 6 in. wide, 8 in. deep and 5 ft long and the post office accept a package that measures 2 ft by 2ft by 4 ft.

Expert Solution

Yes the post office will accept a package that is 6 in. wide, 8 in. deep and 5 ft long.

No, the post office will not accept the package that measures 2 ft by 2ft by 4 ft.

### Explanation of Solution

Given:

The post office will only accept packages for which the length plus the girth (that is the distance 2(x+y) ) is less than 108 inches.

L+2(x+y)108

Formula used:

The formula to convert feet into inches is,

1ft=12in.

Calculation:

The post office accepts only those packages which are less than 108 inches and is given by,

L+2(x+y)108 (1)

Convert feet into inches,

1ft=12in.5ft=5×12in.=60in.

Substitute 6 in. for x, 8 in. for y and 60 in. for L in equation (1).

60+2(6+8)10860+2(14)10860+2810888108

The above inequality holds.

Hence, the post office will accept the package that is 6 in. wide, 8 in. deep and 5 ft long.

The post office accepts only those packages which are less than 108 inches and is given by,

L+2(x+y)108 (1)

Substitute 24 in for x, 24 in for y and 48 in for L in equation (1).

48+2(24+24)10848+2(48)10848+96108144108

The above inequality does not holds.

Hence, the post office will not accept the package that measures 2 ft by 2ft by 4 ft.

(b)

To determine

### The greatest acceptable length for a package that has a square base measuring 9 in. by 9 in.

Expert Solution

The greatest acceptable length for a package that has a square base measuring 9 in. by 9 in. is 72 in..

### Explanation of Solution

Given:

The post office will only accept packages for which the length plus the girth (that is the distance 2(x+y) ) is less than 108 inches.

L+2(x+y)108

Calculation:

The post office accepts only those packages which are less than 108 inches and is given by,

L+2(x+y)108 (1)

Substitute 9 in. for x, 9 in. for y in equation (1).

L+2(9+9)108L+36108L10836L72

Hence, the greatest acceptable length for a package that has a square base measuring 9 in. by 9 in. is 72 in.

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