WeBWorK : mathprep : Section09SettingUpFunctionsTest : v7

Problem 1.

(1 point)

If $V={4\over3}\pi r^3$ , what is the coefficient of $r^3$ ?

Problem 2.

(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 $V(r)$ if its height is four times as long as its radius.
$V(r) =$

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Problem 3.

(1 point)

The bank balance resulting from an initial deposit of $P_0$ dollars is given as a function of time $t$ (in years) by $B(t) = P_0(1 + {r\over12})^{12 t}$ , where $r$ is a fixed annual interest rate compounded monthly. Which of the following is true?

A. $B$ and $P_0$ are names of functions, $t$ represents a variable, and $r$ is constant.
B. $B$ is the name of a function, $t$ represents a variable, and $P_0, r$ are constants.
C. $B$ , $t$ and $r$ represent variables, and $P_0$ is constant.
D. $B$ is the name of a function, $r$ and $t$ represent variables, and $P_0$ is constant.
E. All of $B$ , $t$ and $P_0$ are variables, and $r$ is constant.

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Problem 4.

(1 point)

The $y$ -coordinate of the lower half of a circle is given by $y = y_0 - \sqrt{r^2 - (x - x_0)^2}$ , where the center of the circle is at $(x_0, y_0)$ and its radius is $r$ . Which of the following is true?

A. $x$ , $y$ , and $r$ are variables, and $x_0$ and $y_0$ are constants.
B. $x$ and $y$ are variables, and $r$ , $x_0$ and $y_0$ are constants.
C. $y$ is the name of a function, $x$ and $r$ are variables, and $x_0$ and $y_0$ are constants.
D. $x$ and $y$ are names of functions, $r$ is a constant, and $x_0$ and $y_0$ are variables.
E. $y$ and $r$ are variables, and $x$ , $x_0$ and $y_0$ are constants.

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Problem 5.

(1 point)

If $g(\varphi) = 3\cos(\pi(\varphi - {1\over3}))$ , what is the coefficient of $\varphi$ ?

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Problem 6.

(1 point)

If $y = 3x + 5$ and $x = {\pi t^3\over 3}$ , write a formula for $y$ in terms of $t$ .
$y(t) =$

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Problem 7.

(1 point)

A refrigerator has a square base that is 4 units on each side. Express its height $h$ as a function of its volume $V$ .
$h(V) =$

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Problem 8.

(1 point)

If $s=-16t^2-2t+1$ , what is the coefficient of $t$ ?

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Problem 9.

(1 point)

An interval on the $y$ axis is specified by $c \le y \le d$ . Which of the following is true?

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

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Problem 10.

(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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Test Section09SettingUpFunctionsTest

Problem 1.

Problem 2.

Problem 3.

Problem 4.

Problem 5.

Problem 6.

Problem 7.

Problem 8.

Problem 9.

Problem 10.