Exam 19: Ratio, Proportion, and Variation

If $(m+n):(m-n)=11: 3$ , determine the ratio $m: n$ .

A certain photograph will be correctly exposed at a shutter speed of $0.01 \mathrm{~s}$ at a lens opening of $\mathrm{f2.8}$ . What lens opening is needed for a shutter speed of $0.04 \mathrm{~s}$ ?

If $y$ varies jointly as $w$ and $x$ , by what factor will $w$ change if $x$ is tripled and $y$ is halved?

If $y$ varies jointly as $w$ and $x$ , and $y$ is 42 when $x$ is 0.10 and $w$ is 15 , find $x$ when $y$ is 5.0 and $w$ is 1.5 .

If a body falls $270 \mathrm{ft}$ in $4 \mathrm{~s}$ , how far will it fall in $11 \mathrm{~s}$ ?

Find the value of $x$ where $5: 7=x: 42$ .

If $y$ varies directly as the square of $w$ and inversely as the cube of $x$ , by what factor will $y$ change if $w$ is doubled and $x$ is tripled?

If $y$ varies jointly as $w$ and $x$ , by what percent will $y$ change if $w$ is decreased by $44 \%$ and $x$ is increased by $26 \%$ .

If the gravitational force between two objects is $1.05 \times 10^{-9} \mathrm{~N}$ when the objects are $9.39 \mathrm{~cm}$ apart, how far apart should the objects be placed to make the force between them equal $4.32 \times 10^{-9} \mathrm{~N}$ ?

If $(m-n):(m+n)=2: 5$ , determine the ratio $m: n$ .

Find the mean proportional between 10 and 40 .

Determine the values of $x, y$ , and $z$ given that $x: y: z=3: 5: 7$ and $5 x+2 y+3 z=598$ .

Assume $y$ is inversely proportional to the square root of $x$ and has a value of 15.4 when $x$ is 1.25 . (a) Find the constant of proportionality. (b) Write the equation $y=\mathrm{f}(x)$ . (c) Find $y$ when $x=7.25$ . (d) Find $x$ when $y=9.50$ .

The frequency of a sound wave travelling through a medium varies inversely as the wavelength. If the frequency is $243 \mathrm{~Hz}$ when the wavelength is $0.500 \mathrm{~m}$ , what is the wavelength when the frequency is $320 \mathrm{~Hz}$ ?

Assume $y$ is inversely proportional to the square of $x$ and has a value of 2200 when $x$ is 30.9 . (a) Find the constant of proportionality. (b) Write the equation $y=\mathrm{f}(x)$ . (c) Find $y$ when $x=132$ . (d) Find $x$ when $y=36.2$ .

Assume $y$ is directly proportional to the 5th power of $x$ and has a value of 20.42 when $x$ is 2.10 . (a) Find the constant of proportionality. (b) Write the equation $y=\mathrm{f}(x)$ . (c) Find $y$ when $x=1.48$ . (d) Find $x$ when $y=5.22$ .

If $y$ varies jointly as $w$ and $x$ , and $y$ is 419 when $x$ is 0.155 and $w$ is 21.6 , find $x$ when $y$ is 13.3 and $w$ is 17.5 .

The difference of two numbers is 54 and the smaller is to the larger as one is to three. What are the numbers?