Exam 19: Ratio, Proportion, and Variation

If $y$ is directly proportional to the square of $x$ and has a value of 22 when $x$ is 3 , find $y$ when $x$ is 5 .

Assume $y$ is directly proportional to $x$ and $y$ is 22.3 when $x$ is 22.9 . (a) Find the constant of proportionality. (b) Write the equation $y=\mathrm{f}(x)$ . (c) Find $y$ when $x=3210$ . (d) Find $x$ when $y=4321$ .

If $y$ varies directly as the cube of $x$ and $y$ is 15.6 when $x$ is 1.07 , find $y$ when $x$ is 6.88 .

Find the mean proportional between 16 and 64 .

Find the missing quantity: $\frac{5}{3 a}: \frac{?}{5 a}$

If $y$ varies inversely as $x$ and $y$ is 72 when $x$ is 32 , find $y$ when $x$ is 96 .

If $y$ varies directly as the cube of $w$ and inversely as the square root of $x$ , by what factor will $y$ change if $x$ and $w$ are both increased by $15 \%$ ?

If $y$ varies directly as the square of $x$ and $y$ is 616 when $x$ is 34.0 , find $y$ when $x$ is 99.0 .

The force of gravity between two objects is inversely proportional to the square of the distance between them. If the force of gravity between two objects is $3.27 \times 10^{-7} \mathrm{~N}$ when the distance is $1.00 \mathrm{~m}$ , what is the force when the distance is $0.200 \mathrm{~m}$ ?

Find two numbers that are to each other as $4: 7$ and whose sum is 66 .

A car uses $6.9 \mathrm{~L}$ of fuel to travel go $10 \overline{0} \mathrm{~km}$ . How far can the car go on $32 \mathrm{~L}$ of fuel?

If $y$ varies jointly as $w$ and $x$ , and $y$ is 32.1 when $x$ is 92.3 and $w$ is 2.37 , evaluate the constant of proportionality and write the expression for $y$ in terms of $x$ and $w$ .

If $y$ varies directly as $x$ and $y$ is 45 when $x$ is 3 , find $y$ when $x$ is 6 .

If $y$ varies directly as $x$ and $y$ is 54 when $x$ is 3 , find $y$ when $x$ is 2.5 .

If $y$ is inversely proportional to the square of $x$ and $y$ is 153 when $x$ is 28.0 , find $y$ when $x$ is 100 .

Assume $y$ is directly proportional to $x$ and $y$ is 33.11 when $x$ is 15.05 . (a) Find the constant of proportionality. (b) Write the equation $y=\mathrm{f}(x)$ . (c) Find $y$ when $x=562.5$ . (d) Find $x$ when $y=152.46$ .

The area of a rectangle varies jointly as its length and width. By what percent will the area of a rectangle change if its length is increased by $10 \%$ and its width is decreased by $8 \%$ ?

If $y$ varies directly as $x$ and $y$ is 17 when $x$ is 59.5 , find $y$ when $x$ is 8.75 .

If $x$ is directly proportional to $y$ and $x$ is 3.24 when $y$ is 923 , find $x$ when $y$ is 323 .

Find the missing quantity: $\frac{?}{9 x}: \frac{14}{63 x}$