WeBWorK : mathprep : Section09SettingUpFunctionsTest : v8

Problem 1.

(1 point)

A right circular cone with height $h$ and radius $r$ has volume $V = {1\over 3}\pi r^2 h$ . Write a formula for $V(h)$ if its radius is half as long as its height.
$V(h) =$

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Problem 2.

(1 point)

You are told that the difference between two functions is constant, $f(x) - g(x) = C$ . Which of the following is true?

A. All of $f, g, x$ are names of functions and $C$ is a constant.
B. $f$ and $g$ are names of functions, and $x$ and $C$ both represent variables.
C. All of $f, g, x$ are names of functions and $C$ is a variable.
D. $x$ is the name of a function, $f, g$ are variables, and $C$ is a constant.
E. $f$ and $g$ are names of functions, $x$ represents a variable, and $C$ is a constant.

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Problem 3.

(1 point)

If $g(x) = 3\sin(2x)$ and $x = 4\cos(2t)$ , find a formula for the function $g(t)$ .
$g(t) =$

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Problem 4.

(1 point)

In the height function $H(t) = AB^t$ , which of the following is true?

A. $H$ , $A$ and $t$ represent variables, and $B$ is a constant.
B. $B$ and $t$ represent variables, and $H, A$ are constants.
C. $H$ is the name of a function, $t$ represents a variable, and $A, B$ are constants.
D. $H$ is the name of a function, $A,B$ represent variables, and $t$ is a constant.
E. All of $A$ , $B$ , $H$ and $t$ are variables.

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Problem 5.

(1 point)

If $P = {nRT\over V}$ , what is the coefficient of $R$ ?

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Problem 6.

(1 point)

The rate at which an ice tray in a freezer cools, $R$ is given as a function of time to be $R(T) = k ( T - T_0 )$ , where $k$ is a constant of proportionality, $T$ is the temperature of the ice tray and $T_0$ the temperature of the freezer. Which of the following is true?

A. $R$ and $k$ are variables, and $T$ and $T_0$ are constants.
B. $R$ and $k$ are names of functions, $T$ is a variable and $T_0$ is a constant.
C. $R$ is the name of a function, $T$ and $T_0$ are variables, and $k$ is a constant.
D. $R$ , $T$ , and $T_0$ are variables, and $k$ is a constant.
E. $R$ is the name of a function, $T$ is a variable, and $k$ and $T_0$ are constants.

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