2. (a) what is the multiplicative inverse of $\frac{1}{3}$? (b) what is the multiplicative inverse of $-\frac{1}{3}$? (c) what is the product of any nonzero real number and its multiplicative inverse? 3. what is another name for the multiplicative inverse of a number? 4. which real number does not have a multiplicative inverse and why? 5. use two unit multipliers to convert 112 feet to centimeters. 6. use two unit multipliers to convert 60 square kilometers to square meters. 7. the area of a rectangle is 72 square centimeters. the length of one side is 6 centimeters. what is the length of the other side? 8. the length of the base of a right triangle is 12 meters. the height of the right triangle is 9 meters. find the area of the right triangle. 9. the diameter of a circle is 16 kilometers. find the area of the circle.

Question

Accepted Answer

### 2. (a)
# Explanation:
## Step1: Recall multiplicative - inverse definition
The multiplicative inverse of a non - zero number $a$ is $\frac{1}{a}$ such that $a	imes\frac{1}{a}=1$. For the number $\frac{1}{3}$, if we let $a = \frac{1}{3}$, then its multiplicative inverse is $3$ since $\frac{1}{3}	imes3 = 1$.
# Answer:
$3$

### 2. (b)
# Explanation:
## Step1: Apply multiplicative - inverse rule
The multiplicative inverse of a non - zero number $a$ is $\frac{1}{a}$. For $a=-\frac{1}{3}$, its multiplicative inverse is $- 3$ because $-\frac{1}{3}	imes(-3)=1$.
# Answer:
$-3$

### 2. (c)
# Explanation:
## Step1: Use the property of multiplicative inverses
By the definition of multiplicative inverses, for any non - zero real number $x$, its multiplicative inverse is $\frac{1}{x}$, and $x	imes\frac{1}{x}=1$.
# Answer:
$1$

### 3.
# Explanation:
## Step1: Recall alternative name
The multiplicative inverse of a number is also called the reciprocal of the number.
# Answer:
Reciprocal

### 4.
# Explanation:
## Step1: Consider the multiplicative - inverse formula
The multiplicative inverse of a non - zero real number $a$ is $\frac{1}{a}$. Division by zero is undefined. So, the real number $0$ does not have a multiplicative inverse because $\frac{1}{0}$ is undefined.
# Answer:
The real number $0$; because division by zero is undefined.

### 5.
# Explanation:
## Step1: Know the conversion factors
We know that $1$ foot $ = 12$ inches and $1$ inch $=2.54$ centimeters.
## Step2: Set up the unit - multiplier conversion
$112$ feet $	imes\frac{12	ext{ inches}}{1	ext{ foot}}	imes\frac{2.54	ext{ centimeters}}{1	ext{ inch}}=112	imes12	imes2.54$ centimeters.
## Step3: Calculate the result
$112	imes12	imes2.54 = 112	imes30.48=3413.76$ centimeters.
# Answer:
$3413.76$ centimeters

### 6.
# Explanation:
## Step1: Recall the conversion factors for area
We know that $1$ kilometer $ = 1000$ meters, so $1$ square kilometer $=(1000	ext{ m})	imes(1000	ext{ m}) = 1000000$ square meters.
## Step2: Set up the unit - multiplier conversion
$60$ square kilometers $	imes\frac{1000	ext{ m}}{1	ext{ km}}	imes\frac{1000	ext{ m}}{1	ext{ km}}=60	imes1000	imes1000$ square meters.
## Step3: Calculate the result
$60	imes1000	imes1000=60000000$ square meters.
# Answer:
$60000000$ square meters

### 7.
# Explanation:
## Step1: Use the rectangle area formula
The area of a rectangle is $A = l	imes w$, where $A$ is the area, $l$ is the length, and $w$ is the width. Given $A = 72$ square centimeters and $l = 6$ centimeters.
## Step2: Solve for the other side
We can find the other side $w=\frac{A}{l}=\frac{72}{6}=12$ centimeters.
# Answer:
$12$ centimeters

### 8.
# Explanation:
## Step1: Recall the area formula for a right - triangle
The area of a right - triangle is $A=\frac{1}{2}	imes b	imes h$, where $b$ is the base and $h$ is the height.
## Step2: Substitute the given values
Given $b = 12$ meters and $h = 9$ meters, then $A=\frac{1}{2}	imes12	imes9$.
## Step3: Calculate the area
$\frac{1}{2}	imes12	imes9=6	imes9 = 54$ square meters.
# Answer:
$54$ square meters

### 9.
# Explanation:
## Step1: Find the radius
The radius $r$ of a circle is half of the diameter $d$. Given $d = 16$ kilometers, so $r=\frac{d}{2}=\frac{16}{2}=8$ kilometers.
## Step2: Use the area formula for a circle
The area of a circle is $A=\pi r^{2}$, substituting $r = 8$ kilometers, we get $A=\pi	imes(8)^{2}=64\pi$ square kilometers. Using $\pi\approx3.14$, $A\approx64	imes3.14 = 200.96$ square kilometers.
# Answer:
$64\pi$ square kilometers (or approximately $200.96$ square kilometers)

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QUESTION IMAGE

Question

Explanation:

2. (a)

Step1: Recall multiplicative - inverse definition

Step1: Apply multiplicative - inverse rule

Step1: Use the property of multiplicative inverses

Answer:

2. (b)