Lesson 11.1 Inverse Variation

Last updated almost 2 years ago

9 questions

Note from the author:

Instructions

Untitled Section

Is this a wrench in the system?

Are we getting strung along?

We will have to labor over this one.

Have we reached a Boyle-ing Point?

Lesson 11.1 Inverse Variation

Last updated almost 2 years ago

9 questions

Note from the author:

I can recognize when two quantities show inverse variation and write an equation to model the relationship between the quantities.

Instructions

I can recognize when two quantities show inverse variation and write an equation to model the relationship between the quantities.

Untitled Section

Is this a wrench in the system?

The table shows the force needed to loosen a bolt using wrenches with handles of various lengths.
Does force vary inversely with handle length? Explain.

Predict the force required to loosen the bolt using a wrench with a handle length of 18 in.

Are we getting strung along?

The frequency (in vibrations per second) of a vibrating violin string varies inversely with the string’s length (in centimeters). Suppose a violin string that is 30 cm long vibrates 280 times per second.

Write an equation that gives the frequency f as a function of the string length ℓ.

What is the frequency for a violin string 25 cm long?

We will have to labor over this one.

For a certain carpentry project, the time t (in hours) needed to finish the project depends on the number of carpenters c assigned to it, as shown in the table.

Does the time to finish the project vary inversely with the number of carpenters? Explain.

Write an equation that gives t as a function of c.

If the project needs to be finished in at most 3 days and the carpenters work 8 hours per day, what is the minimum number of carpenters that must be assigned to the project?

Have we reached a Boyle-ing Point?

Desmos Time!

Boyle’s Law states that for a given mass of confined gas at a constant temperature, the pressure P the gas exerts varies inversely with the volume V the gas occupies. At 100 °F, a given mass of gas exerts a pressure of 125 lb/in^2 when placed in a tank with a volume of 2 ft^3. If the same mass of gas at the same temperature is placed in a tank with a volume of 5 ft^3, what pressure will the gas exert? Graph the function and use the graph to justify your answer.

Lesson 11.1 Inverse Variation

Lesson 11.1 Inverse Variation

The table shows the force needed to loosen a bolt using wrenches with handles of various lengths.Does force vary inversely with handle length? Explain.

Predict the force required to loosen the bolt using a wrench with a handle length of 18 in.

The frequency (in vibrations per second) of a vibrating violin string varies inversely with the string’s length (in centimeters). Suppose a violin string that is 30 cm long vibrates 280 times per second. Write an equation that gives the frequency f as a function of the string length ℓ.

What is the frequency for a violin string 25 cm long?

Does the time to finish the project vary inversely with the number of carpenters? Explain.

Write an equation that gives t as a function of c.

If the project needs to be finished in at most 3 days and the carpenters work 8 hours per day, what is the minimum number of carpenters that must be assigned to the project?

Which equation below represent inverse variation?

The table shows the force needed to loosen a bolt using wrenches with handles of various lengths.Does force vary inversely with handle length? Explain.

Predict the force required to loosen the bolt using a wrench with a handle length of 18 in.

The frequency (in vibrations per second) of a vibrating violin string varies inversely with the string’s length (in centimeters). Suppose a violin string that is 30 cm long vibrates 280 times per second. Write an equation that gives the frequency f as a function of the string length ℓ.

What is the frequency for a violin string 25 cm long?

Does the time to finish the project vary inversely with the number of carpenters? Explain.

Write an equation that gives t as a function of c.

If the project needs to be finished in at most 3 days and the carpenters work 8 hours per day, what is the minimum number of carpenters that must be assigned to the project?

The table shows the force needed to loosen a bolt using wrenches with handles of various lengths.
Does force vary inversely with handle length? Explain.

The frequency (in vibrations per second) of a vibrating violin string varies inversely with the string’s length (in centimeters). Suppose a violin string that is 30 cm long vibrates 280 times per second.

Write an equation that gives the frequency f as a function of the string length ℓ.

The table shows the force needed to loosen a bolt using wrenches with handles of various lengths.
Does force vary inversely with handle length? Explain.

The frequency (in vibrations per second) of a vibrating violin string varies inversely with the string’s length (in centimeters). Suppose a violin string that is 30 cm long vibrates 280 times per second.

Write an equation that gives the frequency f as a function of the string length ℓ.