BuyFind

Precalculus: Mathematics for Calcu...

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

Precalculus: Mathematics for Calcu...

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

Solutions

Chapter 1.2, Problem 93E

(a)

To determine

To identify: the sign of expression b5 .

Expert Solution

Answer to Problem 93E

  b5<0

Explanation of Solution

Given information:

Three real numbers a,b,c such that a>0,b<0 , and c<0 .

Calculation:

Consider the given expression.

  b5

Now, b<0

So, sign of b5 can be determined as shown:

  b5=bbbbb

If negative sign is multiplied odd times, the result becomes negative.

Here, in the expression b5 , b is multiplied 5 times.

So, b5<0 .

(b)

To determine

To identify: the sign of expression b10 .

Expert Solution

Answer to Problem 93E

  b10>0

Explanation of Solution

Given information:

Three real numbers a,b,c such that a>0,b<0 , and c<0 .

Calculation:

Consider the given expression.

  b10

Now, b<0

So, sign of b10 can be determined as shown:

  b5=bbbbbbbbbb

If negative sign is multiplied even times, the result becomes negative.

Here, in the expression b10 , b is multiplied 10 times.

So, b10>0 .

(c)

To determine

To identify: the sign of expression ab2c3 .

Expert Solution

Answer to Problem 93E

  ab2c3<0

Explanation of Solution

Given information:

Three real numbers a,b,c such that, a>0,b<0 and c<0 .

Calculation:

Consider the given expression.

  ab2c3

Now, a>0,b<0 and c<0 .

So, sign of ab2c3 can be determined as shown:

  (+)()2()3=(+)(+)()=(+)()=()

So, ab2c3<0 .

(d)

To determine

To identify: the sign of expression (ba)3 .

Expert Solution

Answer to Problem 93E

  (ba)3<0

Explanation of Solution

Given information:

Three real numbers a,b,c such that, a>0,b<0 and c<0 .

Calculation:

Now, a>0,b<0 and c<0 .

So, sign of (ba)3 can be determined as shown:

Consider the given expression.

  (ba)3

  ((+))3=()3=

So, (ba)3<0 .

(e)

To determine

To identify: the sign of expression (ba)4 .

Expert Solution

Answer to Problem 93E

  (ba)4>0

Explanation of Solution

Given information:

Three real numbers a,b,c such that, a>0,b<0 and c<0 .

Calculation:

Consider the given expression.

  (ba)4

Now, a>0,b<0 and c<0 .

So, sign of (ba)4 can be determined as shown:

  ((+))4=()4=(+)

So, (ba)4>0 .

(f)

To determine

To identify: the sign of expression a3c3b6c6 .

Expert Solution

Answer to Problem 93E

  a3c3b6c6<0

Explanation of Solution

Given information:

Three real numbers a,b,c such that, a>0,b<0 and c<0 .

Calculation:

Consider the given expression.

  a3c3b6c6

Now, a>0,b<0 and c<0 .

So, sign of a3c3b6c6 can be determined as shown:

  (+)3()3()6()6=(+)()(+)(+)=()(+)=()

So, a3c3b6c6<0 .

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