유리함수

Find the actual distance from Chicago to Memphis.

Find the actual distance from New Orleans to Miami.

Find the actual distance from Atlanta to Miami.

A 2-foot-tall dog casts a 3-foot shadow at the same time a cat casts a one foot shadow. How tall is the cat ?

If $y$ varies directly as $x$ and $y=14,$ when $x=3.$ find the equation that relates $x$ and $y.$

If $a$ varies directly as $b$ and $a=16,$ when $b=4.$ find the equation that relates $a$ and $b.$

If $p$ varies directly as $q$ and $p=9.6,$ when $q=3.$ find the equation that relates $p$ and $q.$

If $v$ varies directly as $w$ and $v=8,$ when $w=\frac{1}{2}.$ find the equation that relates $v$ and $w.$

The length that a spring stretches varies directly with a weight placed at the end of the spring. When Sarah placed a 10-pound watermelon on a hanging scale, the spring stretched 5 inches.

ⓐ Write the equation that relates the length of the spring to the weight. ⓑ What weight of watermelon would stretch the spring 6 inches?

The maximum load a beam will support varies directly with the square of the diagonal of the beam’s cross-section. A beam with diagonal 6 inch will support a maximum load of 108 pounds.

ⓐ Write the equation that relates the load to the diagonal of the cross-section. ⓑ What load will a beam with a 10-inch diagonal support?

If $y$ varies inversely with $x$ and $y=5$ when $x=4,$ find the equation that relates $x$ and $y.$

If $p$ varies inversely with $q$ and $p=2$ when $q=1$, find the equation that relates $p$ and $q.$

If $v$ varies inversely with $w$ and $v=6$ when $w=\frac{1}{2},$ find the equation that relates $v$ and $w.$

If $a$ varies inversely with $b$ and $a=12$ when $b=\frac{1}{3},$ find the equation that relates $a$ and $b.$

The fuel consumption (mpg) of a car varies inversely with its weight. A Toyota Corolla weighs 2800 pounds getting 33 mpg on the highway.

ⓐ Write the equation that relates the mpg to the car’s weight. ⓑ What would the fuel consumption be for a Toyota Sequoia that weighs 5500 pounds?

A car’s value varies inversely with its age. Jackie bought a 10-year-old car for $2,400.

ⓐ Write the equation that relates the car’s value to its age. ⓑ What will be the value of Jackie’s car when it is 15 years old?

Marisol solves the proportion $\frac{144}{a}=\frac{9}{4}$ by ‘cross multiplying,’ so her first step looks like $4\cdot 144=9\cdot a.$ Explain how this differs from the method of solution shown in (see text).

Make up an example from your life experience of inverse variation.

How can you use factoring to simplify rational expressions?

How do you use the LCD to combine two rational expressions?