Question

1. the formula for the volume of a rectangular solid is v = lwh where l is the length, w is the width, and h is the height. which equations are equivalent to the formula for the volume of a rectangular solid?

□\\(\frac{v}{l}=wh\\)
□\\(\frac{v}{wl}=h\\)
□\\(\frac{v}{h}=lw\\)
□vl = wh
□vwh = l

1. since 1990, the average price, d, in dollars, of a gallon of milk can be modeled by the function d(x)=0.08x + 1.01, where x represents the number of years since 1990. what does the value 0.08 mean in terms of the price of a gallon of milk?

a. years since 1990.
b. cost of a gallon of milk in 1990.
c. the rate the price of a gallon of milk increases each year.
d. the amount of milk purchased in gallons.

Explanation:

Step1: Analyze equivalent volume equations

Given $V = lwh$. Divide both sides by $l$: $\frac{V}{l}=\frac{lwh}{l}=wh$.

Step2: Another equivalent - divide by $wl$

Divide both sides of $V = lwh$ by $wl$: $\frac{V}{wl}=\frac{lwh}{wl}=h$.

Step3: Third equivalent - divide by $h$

Divide both sides of $V = lwh$ by $h$: $\frac{V}{h}=\frac{lwh}{h}=lw$.

Step4: Analyze the linear - function coefficient

The function $D(x)=0.08x + 1.01$ is in the form of a linear function $y=mx + b$, where $m$ is the slope. Here, $x$ is the number of years since 1990, and $D(x)$ is the price of a gallon of milk. The slope $m = 0.08$ represents the rate of change of the price of a gallon of milk per year.

Answer:

1. $\frac{V}{l}=wh$, $\frac{V}{wl}=h$, $\frac{V}{h}=lw$
2. C. the rate the price of a gallon of milk increases each year.