함수 전체 문제

For the following exercises, use Kepler’s Law, which states that the square of the time, $T,$ required for a planet to orbit the Sun varies directly with the cube of the mean distance, $a,$ that the planet is from the Sun.

Using Earth’s distance of 1 astronomical unit (A.U.), determine the time for Saturn to orbit the Sun if its mean distance is 9.54 A.U.

For the following exercises, use the given information to answer the questions.

The weight of an object above the surface of Earth varies inversely with the square of the distance from the center of Earth. If a body weighs 50 pounds when it is 3960 miles from Earth’s center, what would it weigh it were 3970 miles from Earth’s center?

For the following exercises, use the given information to answer the questions.

The current in a circuit varies inversely with its resistance measured in ohms. When the current in a circuit is 40 amperes, the resistance is 10 ohms. Find the current if the resistance is 12 ohms.

For the following exercises, find the unknown value.

$y$ varies directly as the square of $x.$ If when $x=3,\,y=36,$ find $y$ if $x=4.$

For the following exercises, find the unknown value.

$y$ varies inversely as the square root of $x$ If when $x=25,\,y=2,$ find $y$ if $x=4.$

For the following exercises, find the unknown value.

$y$ varies jointly as the cube of $x$ and as $z.$ If when $x=1$ and $z=2,$ $y=6,$ find $y$ if $x=2$ and $z=3.$

For the following exercises, find the unknown value.

$y$ varies jointly as $x$ and the square of $z$ and inversely as the cube of $w.$ If when $x=3,$ $z=4,$ and $w=2,$ $y=48,$ find $y$ if $x=4,$ $z=5,$ and $w=3.$

For the following exercises, solve the application problem.

The weight of an object above the surface of the earth varies inversely with the square of the distance from the center of the earth. If a person weighs 150 pounds when he is on the surface of the earth (3,960 miles from center), find the weight of the person if he is 20 miles above the surface.

Timmy goes to the fair with $40. Each ride costs $2. How much money will he have left after riding $n$ rides?

For the following exercises, determine whether the equation of the curve can be written as a linear function.

$y=\frac{1}{4}x+6$

For the following exercises, determine whether the equation of the curve can be written as a linear function.

$y=3x-5$

For the following exercises, determine whether the equation of the curve can be written as a linear function.

$y=3{x}^{2}-2$

For the following exercises, determine whether the equation of the curve can be written as a linear function.

$3x+5y=15$

For the following exercises, determine whether the equation of the curve can be written as a linear function.

$3{x}^{2}+5y=15$

For the following exercises, determine whether the equation of the curve can be written as a linear function.

$3x+5{y}^{2}=15$

For the following exercises, determine whether the equation of the curve can be written as a linear function.

$-2{x}^{2}+3{y}^{2}=6$

For the following exercises, determine whether the equation of the curve can be written as a linear function.

$-\frac{x-3}{5}=2y$

For the following exercises, determine whether each function is increasing or decreasing.

$f(x)=4x+3$

For the following exercises, determine whether each function is increasing or decreasing.

$g(x)=5x+6$

For the following exercises, determine whether each function is increasing or decreasing.

$a(x)=5-2x$