함수 전체 문제

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

The rate of vibration of a string under constant tension varies inversely with the length of the string. If a string is 24 inches long and vibrates 128 times per second, what is the length of a string that vibrates 64 times per second?

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

The volume of a gas held at constant temperature varies indirectly as the pressure of the gas. If the volume of a gas is 1200 cubic centimeters when the pressure is 200 millimeters of mercury, what is the volume when the pressure is 300 millimeters of mercury?

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

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 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 intensity of light measured in foot-candles varies inversely with the square of the distance from the light source. Suppose the intensity of a light bulb is 0.08 foot-candles at a distance of 3 meters. Find the intensity level at 8 meters.

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, use the given information to answer the questions.

The force exerted by the wind on a plane surface varies jointly with the square of the velocity of the wind and with the area of the plane surface. If the area of the surface is 40 square feet surface and the wind velocity is 20 miles per hour, the resulting force is 15 pounds. Find the force on a surface of 65 square feet with a velocity of 30 miles per hour.

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

The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute (rpm)) and the cube of the diameter. If the shaft of a certain material 3 inches in diameter can transmit 45 hp at 100 rpm, what must the diameter be in order to transmit 60 hp at 150 rpm?

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

The kinetic energy $K$ of a moving object varies jointly with its mass $m$ and the square of its velocity $v.$ If an object weighing 40 kilograms with a velocity of 15 meters per second has a kinetic energy of 1000 joules, find the kinetic energy if the velocity is increased to 20 meters per second.

For the following exercises, write the quadratic function in standard form. Then, give the vertex and axes intercepts. Finally, graph the function.

$f(x)={x}^{2}-4x-5$

For the following exercises, write the quadratic function in standard form. Then, give the vertex and axes intercepts. Finally, graph the function.

$f(x)=-2{x}^{2}-4x$

For the following problems, find the equation of the quadratic function using the given information.

The vertex is $(-2,3)$ and a point on the graph is $(3,6).$

For the following problems, find the equation of the quadratic function using the given information.

The vertex is $(-3,6.5)$ and a point on the graph is $(2,6).$

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.

For the following exercises, solve the application problem.

The volume $V$ of an ideal gas varies directly with the temperature $T$ and inversely with the pressure $P$. A cylinder contains oxygen at a temperature of 310 degrees K and a pressure of 18 atmospheres in a volume of 120 liters. Find the pressure if the volume is decreased to 100 liters and the temperature is increased to 320 degrees K.