Chapter 17

If \(y\) varies jointly as \(w\) and \(x,\) and \(y\) is 483 when \(x\) is 742 and \(w\) is \(383,\) find \(y\) when \(x\) is 274 and \(w\) is 756.

If \(y\) varies directly as \(x,\) and \(y\) is 56 when \(x\) is \(21,\) find \(y\) when \(x\) is 74.

If \(y\) varies directly as the square of \(x,\) and \(y\) is 726 when \(x\) is \(163,\) find \(y\) when \(x\) is 274

If \(y\) varies inversely as \(x,\) and \(y\) is 385 when \(x\) is \(832,\) find \(y\) when \(x\) is 226.

Find the value of \(x.\) $$3: x=4: 6$$

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

If \(y\) is directly proportional to the square of \(x,\) and \(y\) is 5570 when \(x\) is 172 find \(y\) when \(x\) is 382

If \(w\) is directly proportional to \(z\), and \(w\) has a value of 136 when \(z\) is \(10.8,\) find \(w\) when \(z\) is 37.3.

If \(y\) is inversely proportional to the square of \(x,\) and \(y\) has the value 1.55 when \(x\) is \(7.38,\) find \(y\) when \(x\) is 44.2.

A certain wood stove has a firebox volume of \(4.25 \mathrm{ft}^{3} .\) What firebox volume would be expected if all dimensions of the stove were increased by a factor of \(1.25 ?\)

If \(p\) varies directly as \(q,\) and \(p\) is 846 when \(q\) is \(135,\) find \(q\) when \(p\) is \(448 .\)

If \(y\) varies jointly as \(w\) and \(x,\) by what percent will \(y\) change if \(w\) is increased by \(12 \%\) and \(x\) is decreased by \(7.0 \% ?\)

If \(y\) varies directly as the cube of \(x,\) and \(y\) is 4.83 when \(x\) is \(1.33,\) find \(y\) when \(x\) is 3.38

If \(y\) is inversely proportional to \(x,\) how does \(y\) change when \(x\) is doubled?

Find the value of \(x.\) $$4: 6=x: 4$$

If \(y\) is directly proportional to \(x,\) and \(y\) has a value of 88.4 when \(x\) is 23.8 (a) Find the constant of proportionality. (b) Write the cquation \(y=f(x)\). (c) Find \(y\) when \(x=68.3\). (d) Find \(x\) when \(y=164\).

If \(y\) varies jointly as \(w\) and \(x,\) and \(y\) is 3.85 when \(w\) is 8.36 and \(x\) is \(11.6,\) evaluate the constant of proportionality, and write the complete expression for \(y\) in terms of \(w\) and \(x\).

If \(y\) is directly proportional to the cube of \(x,\) and \(y\) is 27.2 when \(x\) is \(11.4,\) find \(y\) when \(x\) is 24.9

Evaluate each trigonometric expression to three significant digits. If \(y\) varies inversely as \(x,\) and \(y\) has the value 104 when \(x\) is 532. (a) Find the constant of proportionality. (b) Write the equation \(y=f(x)\) (c) Find \(y\) when \(x\) is 668 (d) Find \(x\) when \(y\) is 226

A certain solar house stores heat in 155 metric tons of stone which are in a chamber beneath the house. Another solar house is to have a chamber of similar shape but with all dimensions increased by \(15 \% .\) How many metric tons of stone will it hold?

Find the value of \(x.\) $$3: x=x: 12$$

Assuming that \(y\) varies directly as \(x,\) fill in the missing values in each table of 1 pairs. $$\begin{array}{l|r|r|r} x & 9 & 11 & \\ \hline y & 45 & & 75 \end{array}$$

If \(y\) varies directly as the square of \(x,\) and \(y\) is 285.0 when \(x\) is \(112.0,\) find \(y\) when \(x\) is 351.0

Find the value of \(x.\) $$x:(14-x)=4: 3$$

If \(y\) is directly proportional to the square of \(x\) and inversely proportional to the cube of \(w,\) and \(y\) is 11.6 when \(x\) is 84.2 and \(w\) is \(28.4,\) find \(y\) when \(x\) is 5.38 and \(w\) is 2.28.

If \(y\) varies directly as the square root of \(x,\) and \(y\) is 11.8 when \(x\) is \(342,\) find \(y\) when \(x\) is 288

The floor plan of a certain building has a scale of \(\frac{1}{4}\) in. \(=1 \mathrm{ft}\) and shows a room having an area of 40 in. \(^{2}\). What is the actual room area in square feet?

Find the value of \(x.\) $$x: 12=(x-12): 3$$

If \(y\) varies directly as the square root of \(w\) and inversely as the cube of \(x,\) by what factor will \(y\) change if \(w\) is tripled and \(x\) is halved?

If \(y\) is directly proportional to the cube of \(x,\) and \(y\) is 638 when \(x\) is \(145,\) find \(y\) when \(x\) is 68.3

Find the value of \(x.\) $$x: 6=(x+6): 10 \frac{1}{2}$$

The distance between two cities is \(828 \mathrm{km},\) and they are \(29.5 \mathrm{cm}\) apart on a map. Find the distance between two points \(15.6 \mathrm{cm}\) apart on the same map.

If \(y\) is directly proportional to the cube root of \(x\) and to the square root of \(w,\) by what percent will \(y\) change if \(x\) and \(w\) are both increased by \(7.0 \% ?\)

If \(y\) is directly proportional to the five-halves power of \(x,\) and \(y\) has the value 55.3 when \(x\) is 17.3 (a) Find the constant of proportionality. (b) Write the equation \(y=f(x)\) (c) Find \(y\) when \(x=27.4\) (d) Find \(x\) when \(y=83.6\)

If \(y\) is inversely proportional to the cube root of \(x,\) by what factor will \(y\) change when \(x\) is tripled?

A pipe 3.00 inches in diameter discharges 500 gal of water in a certain time. What must be the diameter of a pipe that will discharge 750 gal in the same time? Assume that the amount of flow through a pipe is proportional to its cross-sectional area.

Find the value of \(x.\) $$(x-7):(x+7)=2: 9$$

If the weight of 2500 steel balls is \(3.65 \mathrm{kg},\) find the number of balls in \(10.0 \mathrm{kg}\).

If \(y\) is directly proportional to the \(\frac{3}{2}\) power of \(x\) and inversely proportional to \(w\) and \(y\) is 284 when \(x\) is 858 and \(w\) is \(361,\) evaluate the constant of proportional. ity, and write the complete equation for \(y\) in terms of \(x\) and \(w\).

If \(y\) is inversely proportional to the square root of \(x,\) by what percentage will \(y\) change when \(x\) is decreased by \(50.0 \% ?\)

Insert the missing quantity. $$\frac{x}{3}=\frac{?}{9}$$

If 80 transformer laminations make a stack \(1.75 \mathrm{cm}\) thick, how many laminations are contained in a stack \(3.00 \mathrm{cm}\) thick?

A triangular field whose base is 215 m contains \(12,400 \mathrm{m}^{2} .\) Find the area of a field of similar shape whose base is \(328 \mathrm{m}\).

Insert the missing quantity. $$\frac{?}{4 x}=\frac{7}{16 x}$$

If your car now gets \(21.0 \mathrm{mi} / \mathrm{gal}\) of gas, and if you can go \(251 \mathrm{mi}\) on a tank of gasoline, how far could you drive with the same amount of gasoline with a car that gets \(35.0 \mathrm{mi} / \mathrm{gal} ?\)

The area of a triangle varics jointly as its base and altitude. By what percent will the area change if the base is increased by \(15 \%\) and the altitude decreased by \(25 \% ?\)

Insert the missing quantity. $$\frac{5 a}{7 b}=\frac{?}{-7 b}$$

A certain automobile engine delivers 53 hp and has a displacement (the total volume swept out by the pistons) of 3.0 liters. If the power is directly proportional to the displacement, what horsepower would you expect from a similar engine that has a displacement of 3.8 liters?

If the base and the altitude of a triangle are both halved, by what factor will the area change?

Graph the power function \(y=1.04 x^{2}\) for \(x=-5\) to 5