SAT Practice: Solving For a Variable in Terms of Another Practice 02

$D=\dfrac{C-S}{n}$

The formula above is used to find the yearly depreciation $D$ for a product in terms of its cost $C$ , its salvage value $S$ , and the number of years $n$ .

Which of the following gives $C$ in terms of $D$ , $S$ , and $n$ ?

$nD-S=C$

$C=Dn+S$

$C=\dfrac{n+S}{D}$

$c=\dfrac{-S}{D-n}$

$PV=nRT$

The formula above is the equation of a hypothetical ideal gas. $P$ is the pressure of the gas, $V$ is the volume of the gas, $n$ is the amount of substance of gas, $R$ is the ideal gas constant, and $T$ is the temperature of the gas.

Which of the following gives $n$ in terms of $P$ , $V$ , $R$ , and $T$ ?

$n=PVRT$

$n=\dfrac{1}{PVRT}$

$n=\dfrac{RT}{PV}$

$n=\dfrac{PV}{RT}$

Albert Einstein's most well-known formula $E=mc^2$ represents the correlation of energy to matter, where $E$ is energy, $m$ is the mass of the specified object, and $c$ represents the speed of light.

Which of the following gives $c$ in terms of $E$ and $m$ ?

$c=E \sqrt{m}$

$c= \dfrac{E}{m}$

$c=Em^2$

$c=\sqrt{\dfrac{E}{m}}$

$A=P(1+rt)$

The formula above represents the amount $A$ in a bank account earning simple interest with a principal amount of $P$ , interest rate of $r$ , over a time period of $t$ .

Which of the following gives $r$ in terms of $A$ , $P$ , and $t$ ?

$r=\dfrac{A-P}{Pt}$

$r=AP(1+t)$

$r=\dfrac{A}{P(1+t)}$

$r=\dfrac{A-1}{P-t}$

$V= \dfrac{1}{3} \pi r^2 h$

The formula above is used to calculate the volume, $V$ , of a cone. If the radius, $r$ , is half the length of the height, $h$ , which of the following gives $V$ in terms of $r$ ?

$V= \dfrac{1}{3} \pi r^3$

$V= \dfrac{1}{6} \pi r^2$

$V= \dfrac{2}{3} \pi r^3$

$V= \dfrac{1}{6} \pi r$