Chapter 1.5, Problem 36WE

a.

To determine

Tocalculate:

The value of $y$ for given expression.

Answer to Problem 36WE

The value of $y$ for $\left(1-y\right)\left(3-y\right)\left(6-y\right)$ is $-3,060$ .

Explanation of Solution

Given information:

Expressions:

  $\left(1-y\right)\left(3-y\right)\left(6-y\right)$

Given value: $18$

Calculation:

Now consider the expression $\left(1-y\right)\left(3-y\right)\left(6-y\right)$

To get the value of expression at $y=18$

  $\left(1-y\right)\left(3-y\right)\left(6-y\right)=\left(1-18\right)\left(3-18\right)\left(6-18\right)$

Substitute $18$ for $y$

  $=\left(-17\right)\left(-15\right)\left(-12\right)$

Simplify,

  $=\left(255\right)\left(-12\right)$

Now multiply,

  $=-3,060$

Hence, the value of $y$ for $\left(1-y\right)\left(3-y\right)\left(6-y\right)$ is $-3,060$ .

b.

To determine

To calculate:

The value of $y$ for given expression.

Answer to Problem 36WE

The value of $y$ for $\left(1-y\right)\left(3-y\right)\left(6-y\right)$ is $18$ .

Explanation of Solution

Given information:

Expressions:

  $\left(1-y\right)\left(3-y\right)\left(6-y\right)$

Given value: $0$

Calculation:

Now consider the expression $\left(1-y\right)\left(3-y\right)\left(6-y\right)$

To get the value of expression at $y=0$

  $\left(1-y\right)\left(3-y\right)\left(6-y\right)=\left(1-0\right)\left(3-0\right)\left(6-0\right)$

Substitute $0$ for $y$ and multiply

  $\begin{array}{l}=\left(1\right)\left(3\right)\left(6\right)\\ =18\end{array}$

Hence, the value of $y$ for $\left(1-y\right)\left(3-y\right)\left(6-y\right)$ is $18$ .

c.

To determine

To calculate:

The value of $y$ for given expression.

Answer to Problem 36WE

The value of $y$ for $\left(1-y\right)\left(3-y\right)\left(6-y\right)$ is $393,908$ .

Explanation of Solution

Given information:

Expressions:

  $\left(1-y\right)\left(3-y\right)\left(6-y\right)$

Given value: $-70$

Calculation:

Now consider the expression $\left(1-y\right)\left(3-y\right)\left(6-y\right)$

To get the value of expression at $y=-70$

  $\left(1-y\right)\left(3-y\right)\left(6-y\right)=\left(1-\left(-70\right)\right)\left(3-\left(-70\right)\right)\left(6-\left(-70\right)\right)$

Substitute $-70$ for $y$ and multiply

  $\begin{array}{l}=\left(71\right)\left(73\right)\left(76\right)\\ =393,908\end{array}$

Hence, the value of $y$ for $\left(1-y\right)\left(3-y\right)\left(6-y\right)$ is $393,908$ .

d.

To determine

To calculate:

The value of $y$ for given expression.

Answer to Problem 36WE

The value of $y$ for $\left(1-y\right)\left(3-y\right)\left(6-y\right)$ is $-2,422,602$ .

Explanation of Solution

Given information:

Expressions:

  $\left(1-y\right)\left(3-y\right)\left(6-y\right)$

Given value: $120$

Calculation:

Now consider the expression $\left(1-y\right)\left(3-y\right)\left(6-y\right)$

To get the value of expression at $y=120$

  $\left(1-y\right)\left(3-y\right)\left(6-y\right)=\left(1-120\right)\left(3-120\right)\left(6-120\right)$

Substitute $120$ for $y$ and multiply

  $\begin{array}{l}=\left(-119\right)\left(-117\right)\left(-174\right)\\ =-2,422,602\end{array}$

Hence, the value of $y$ for $\left(1-y\right)\left(3-y\right)\left(6-y\right)$ is $-2,422,602$ .

e.

To determine

To calculate:

The value of $y$ for given expression.

Answer to Problem 36WE

The value of $y$ for $\left(1-y\right)\left(3-y\right)\left(6-y\right)$ is $-\frac{391}{512}$ .

Explanation of Solution

Given information:

Expressions:

  $\left(1-y\right)\left(3-y\right)\left(6-y\right)$

Given value: $3\frac{1}{8}$

Calculation:

Now consider the expression $\left(1-y\right)\left(3-y\right)\left(6-y\right)$

To get the value of expression at $y=3\frac{1}{8}=\frac{25}{8}$

  $\left(1-y\right)\left(3-y\right)\left(6-y\right)=\left(1-\frac{25}{8}\right)\left(3-\frac{25}{8}\right)\left(6-\frac{25}{8}\right)$

Substitute $3\frac{1}{8}=\frac{25}{8}$ for $y$ and multiply

  $\begin{array}{l}=\left(\frac{8-25}{8}\right)\left(\frac{24-25}{8}\right)\left(\frac{48-25}{8}\right)\\ =\left(\frac{-17}{8}\right)\left(\frac{-1}{8}\right)\left(\frac{23}{8}\right)\end{array}$

Multiply,

  $\begin{array}{l}=\left(\frac{-17}{8}\right)\left(\frac{-1}{8}\right)\\ =\left(\frac{17}{64}\right)\left(\frac{23}{8}\right)\\ =-\frac{391}{512}\end{array}$

Hence, the value of $y$ for $\left(1-y\right)\left(3-y\right)\left(6-y\right)$ is $-\frac{391}{512}$ .