WeBWorK : mathprep : Section09SettingUpFunctionsTest : v8

Problem 1.

(1 point)

Express the volume, $V$ , of a cube as a function of the area, $A$ , of its base.
$V(A) =$

Problem 2.

(1 point)

The height $s$ of an object under the effect of gravity, $g$ , is given at time $t$ by $s = {1\over2}gt^2 + v_0 t + s_0$ . Which of the following is true?

A. $s$ and $t$ represent variables, and $g, v_0$ , and $s_0$ are constants.
B. $s$ is the name of a function, $t$ and $v_0$ represent variables, and $g$ and $s_0$ are constants
C. $s$ is the name of a function, $t$ and $s_0$ represent variables, and $g$ and $v_0$ are constants.
D. $s, t$ , and $v_0$ are variables, and $g$ and $s_0$ are constants
E. All of $s, t, v_0$ , and $s_0$ are variables, and $g$ is constant

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Problem 3.

(1 point)

If $y = \ln({x+4\over 5})$ , what is the coefficient of $x$ ?

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Problem 4.

(1 point)

If $P=3l+2w+6d$ , what is the coefficient of $w$ ?

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Problem 5.

(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 6.

(1 point)

A cylindrical water tank drains through a hole in its bottom. The water level $y$ in the tank after $t$ seconds is $y = (\sqrt{y_0} - \alpha \sqrt{2g}t)^2$ , where $y_0$ is the initial water-level, $\alpha$ a measure of the size of the hole, and $g$ the acceleration due to gravity. Which of the following is true?

A. $y$ is the name of a function, $\alpha$ represents a variable, and $t$ , $y_0$ and $g$ are constants.
B. $y$ and $t$ represent variables and $y_0$ , $\alpha$ and $g$ are constants.
C. $y$ is the name of a function, $t$ and $\alpha$ represent variables, and $y_0$ and $g$ are constants.
D. $y$ , $t$ and $\alpha$ represent variables, and $y_0$ and $g$ are constants.
E. $y$ , $t$ and $y_0$ represent variables, and $\alpha$ and $g$ are constants.

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Problem 7.

(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 8.

(1 point)

The function giving the amount of medicine remaining in the bloodstream $t$ hours after it has been administered is $M(t) = M_0 e^{-8.3t/h}$ , where $h$ is the medicine's half-life and $M_0$ is the initial dose. Which of the following is true?

A. $M$ and $M_0$ are names of functions, $t$ represents a variable, and $h$ is constant.
B. $M$ is the name of a function, $t$ represents a variable, and $M_0$ and $h$ are constants.
C. $M$ , $t$ and $h$ represent variables, and $M_0$ is a constant.
D. $M$ is the name of a function, $h$ represents a variable, and $M_0$ and $t$ are constants.
E. All of $M$ , $M_0$ , $t$ and $h$ represent variables.

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Problem 9.

(1 point)

If $B(t) = P_0(1 + {r\over12})^{12t}$ , what is the coefficient of $t$ ?

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Problem 10.

(1 point)

If $s = 3p - 2q$ and ${p\over q} = 6$ , write $s$ in terms of $q$ .
$s(q) =$

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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.