Question 1

A car rental company charges a fee that varies directly with the number of days rented. If the cost is $$120 for 3 days, what is the equation relating cost C$ to days d$?

Accepted Answer

$$C = 40d$$

Question 2

The pressure $$P of a $$gas in a container varies inversely as its volume $$V. If$$ $$P = 200$$ kPa when $$V = 2 L$$, what is the pressure when the volume is $$5 L$$?

Accepted Answer

$$P = 80$$ kPa

Question 3

Which of the following best describes the graph of $$y = kx$$, where $$k \u003e 0$$?

Accepted Answer

A straight line passing through the origin with positive slope

Question 4

The time $$t$$ required to travel a fixed distance varies inversely as the speed $$s. If it $$takes 4 hours at 60 km/h, how long will it take at 80 km/h?

Accepted Answer

$$t = 3$$ hours

Question 5

If $$y$$ varies directly as the square of $$x$$, and $$y = 20$$ when $$x = 2$$, what is the equation relating $$y$$ and $$x$$?

Accepted Answer

$$y = 5x^2$

Question 6

A chemical reaction rate $$R$$ varies jointly as the concentration $$C$$ and temperature $$T$$, and inversely as the pressure $$P. If$$ $$R = 24$$ when $$C = 2$$ mol/L, $$T = 300 K$$, and $$P = 25$$ atm, what is the equation for $$R$$?

Accepted Answer

$$R = 1.0 \dfrac{CT}{P}$$

Question 7

The volume $$V of a $$tree varies jointly as its height $$h$$ and the square of its girth $$g. If$$ $$V = 200 m$^3$$ when $$h = 25 m $$and $$g = 2 m$$, what is the variation constant $$k$$?

Accepted Answer

$$k = 2$$

Question 8

Which of the following situations is best modeled by inverse variation?

Accepted Answer

The time to complete a job with more workers

Question 9

If $$y$$ varies inversely as $$x$$, and $$y = 10$$ when $$x = 4$$, what is $$y$$ when $$x = 8$$?

Accepted Answer

$$y = 5$$

Question 10

A medication's effectiveness $$E$$ varies directly as the dosage $$d$$ and inversely as the patient's weight $$w. If$$ $$E = 50$$ when $$d = 100 mg $$and $$w = 80 kg$$, what is the effectiveness for $$d = 150 mg $$and $$w = 60 kg$$?

Accepted Answer

$$E = 93.75$$

Question 11

Which equation represents a combined variation where $$y$$ varies directly as $$x$$ and inversely as the square of $$z$$?

Accepted Answer

$$y = k \dfrac{x}{z^2$}$$

Question 12

A factory produces widgets, and the number of widgets $$N$$ produced varies directly as the number of hours $$h$$ worked and the number of machines $$m$$ used. If $$N = 600$$ when $$h = 5$$ and $$m = 4$$, what is the equation for $$N$$?

Accepted Answer

$$N = 30hm$$

Question 13

If $$y$$ varies directly as $$x$$ and inversely as $$z$$, and $$y = 12$$ when $$x = 6$$ and $$z = 3$$, what is $$y$$ when $$x = 10$$ and $$z = 5$$?

Accepted Answer

$$y = 8$$

Question 14

Which of the following is NOT a property of the graph $$y = k/x$$ for $$k \u003e 0$$?

Accepted Answer

It passes through the origin

Question 15

A tank is being filled with water. The time $$t to $$fill the tank varies inversely as the rate of flow $$r. If it $$takes 120 minutes at 500 L/min, how long will it take at 750 L/min?

Accepted Answer

$$t = 80$$ minutes

Question 16

If $$y$$ varies directly as $$x$$ and $$y = 24$$ when $$x = 8$$, what is the value of $$y$$ when $$x = 15$$?

Accepted Answer

$$y = 45$$

Question 17

The gravitational force $$F$$ between two masses varies inversely as the square of the distance $$d$$ between them. If $$F = 100 N $$when $$d = 2 m$$, what is $$F$$ when $$d = 5 m$$?

Accepted Answer

$$F = 16 N$$

Question 18

Which of the following is a correct step in solving a variation problem?

Accepted Answer

Substitute known values into the variation equation to solve for $$k$$

Question 19

A population $$P of $$bacteria varies directly as the amount of nutrients $$N$$ and inversely as the temperature $$T. If$$ $$P = 600$$ when $$N = 30$$ and $$T = 5$$, what is $$P$$ when $$N = 40$$ and $$T = 8$$?

Accepted Answer

$$P = 480$$

Section 2.6: Variation and Applications – Precalculus Study Notes

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