12.3 Homework Problems: Variations

1. Find the constant of variation (k) for each problem, if no variation put N/a

a.  [latex]\ 6x=\frac{12}{y}[/latex]

b.  18x + 6y = 0

c.  -5x + 4y = 9

2. Find the direct variation constant (k) for the tables

a.

b.

3. Find the inverse variation constant (k) for the tables

a.

b.

4.  Rewrite each equation to solve for the requested variable, then determine if the relationship of the requested variable

a.  [latex]4x=5y[/latex];  solve for y

is y directly, inversely or not proportional to x?

b. [latex]2x=y\ – 1[/latex] ; solve for x

is x directly, inversely or not proportional to y?

c.  [latex]\frac{V_1}{n_1}=\frac{V_2}{n_2}[/latex]; Solve for V₂

is V­₂ directly, inversely or not proportional to n₂?

d. P₁V₁ = P₂V₂ ; Solve for V₁

is V_­1 directly, inversely or not proportional to P₁?

e.  [latex]\frac{N_P}{N_S}=\frac{I_S}{I_P}[/latex]; solve for I_s

is I­_S directly, inversely or not proportional to I_P?

5.  If y varies directly as x, and y = 3 when x = 9, find y if x = 7.

6.  If y varies inversely as x, and y = 5 when x = 8, find y if x = 20.

7.  If y varies inversely as x², and y = −8 when x = 2, find y if x= 3.

8.  z varies jointly as x and y, and z = 60 when x = 2 and y = 3. Find z if x = 3 and y = 4

9.  z varies jointly as x and y², and z = 63 when x = 5 and y = 3. Find z if x = [latex]\frac{10}{3}[/latex] and y = 2.

10.  z varies directly as x and inversely as y². If z = 5 when x = 1 and y = 2, find z if x = 2 and y =1

11.  The extension of a spring is proportional to the load (force) applied to it. If the spring stretches 5 inches with a weight of 10 lbs at the end, how far will the spring stretch if the weight is increased to 12 lbs?

12.  The resistance of a wire is directly proportional to the length of wire and inversely proportional to the square of the diameter. The resistance of a wire that is 500 ft long with a diameter of 0.01 inches is 20 Ω. If the wire is replaced with a wire that is 1500 ft long and has a diameter of 0.02 in instead, what is the new resistance?

13.  The temperature of a gas (T) is directly proportional to the pressure (P) times the volume (V) and inversely proportional to the number of moles (n) times the universal gas constant (R). If P = 1.95 atm, V = 12.30 L, n = 0.654 mol and R = 0.08206 L atm/mol K find the temperature of the gas in Kelvins

14.  Your car stereo uses a 5 ft audio wire with a diameter of 0.025 in and a resistance of 1.6 ohms. What is the resistance of a piece of the same audio wire if it is 8 ft long instead?

Unit 12.3 Homework Printable Copy