Question 1

Write an equation that describes the variation.
A is directly proportional to the cube of L. A = 2 when L = 1.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Write an equation that describes the variation.
A...

Question 2

Write an equation that describes the variation.
F is inversely proportional to the square of t. f = 8 when t = 1.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Write an equation that describes the variation.
F...

Question 3

Write an equation that describes the variation. Use k as the constant of variation.
V varies is directly proportional to both  and  . V = 32 when x = 1 and t = 4.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Write an equation that describes the variation....

Question 4

Write an equation that describes the variation.
F is inversely proportional to both ? and L. F =  when ? = 7?m and L = 200 km.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Write an equation that describes the variation.
F...

Question 5

Hooke's Law in physics states that if a spring at rest (equilibrium position ) has a weight attached to it, then the distance the spring stretches is directly proportional to the force (weight).
F = kx
Where F is the force in Newtons(N), x is the distance stretched in meters (m), and k is the spring constant (N/m).A force of 352 N will stretch the spring 22 cm. How far will a force of 288 stretch the spring? Round to two decimal places.
A) 0.27 m
B) 26.89 m
C) 0.18 m
D) 18.00 m

Accepted Answer

To find the distance the spring stretches with a different force, we first find the spring constant k using F = kx with the given values: 352 N = k * 0.22 m, so k = 352 / 0.22. Then, use this k to find the new distance x with F = 288 N: 288 = k * x. Solving for x gives approximately 0.18 m.

Question 6

Hooke's Law in physics states that if a spring at rest (equilibrium position ) has a weight attached to it, then the distance the spring stretches is directly proportional to the force (weight).
F = kxwhere
F is the force in Newtons(N), x is the distance stretched in meters (m), and k is the spring constant (N/m).A force of 429 N will stretch the spring 33 cm. How much force to the nearest Newtons is required to stretch the spring 72 cm?
A) 196.63 N
B) 936.00 N
C) 1,019,304.00 N
D) 9.36 N

Accepted Answer

To find the force required to stretch the spring 72 cm, first calculate the spring constant k using the given force and stretch: k = F/x = 429 N / 0.33 m. Then use this k to find the new force for 72 cm (0.72 m): F = k * 0.72 m. The calculated force is approximately 936 N.

Question 7

In physics, the inverse square law states that any physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity. In particular, the intensity of light radiating from a point source is inversely proportional to the square of the distance from the source. Below is a table of average distances from the Sun:

The solar radiation on the Earth is approximately 1560 watts per square meter. How much solar radiation is there on Mercury? Round to the nearest hundred watts per square meter.
A) 605,172,413.79 watts per square meter
B) 4034.48 watts per square meter
C) 10,434.01 watts per square meter
D) 0.07 watts per square meter

Accepted Answer

The answer of In physics, the inverse square law states...

Question 8

A gas contained in a 3 mL container at a temperature of 340 K has a pressure of 1.5 atm. If the temperature decreases to 325 K, what is the resulting pressure?
A) 165,750.0 atm
B) 1.6 atm
C) 170.0 atm
D) 1.4 atm

Accepted Answer

Using the ideal gas law and assuming the volume and amount of gas remain constant, the pressure is directly proportional to the temperature. Therefore, P1/T1 = P2/T2. Solving for P2 gives P2 = P1 * (T2/T1) = 1.5 atm * (325 K / 340 K) = 1.4 atm.

Question 9

A gas contained in a 3 mL container at a temperature of 340 K has a pressure of 1 atm. If the container changes to a volume of 2 mL, what is the resulting pressure?
A) 113.3 atm
B) 0.7 atm
C) 1.5 atm
D) 6.0 atm

Accepted Answer

The answer of A gas contained in a 3 mL...

Question 10

Levi's makes jeans in a variety of price ranges for juniors. The Flare 519 jeans sell for about $19, whereas the 646 Vintage Flare jeans sell for $150. The demand for Levi's jeans is inversely proportional to the price. If 200,000 pairs of the Flare 519 jeans were bought, approximately how many of the 646 Vintage Flare were bought? Round to the nearest integer.
A) 1,578,947 pairs of the 646 Vintage Flare
B) 25,333 pairs of the 646 Vintage Flare
C) 1333 pairs of the 646 Vintage Flare
D) 10,526 pairs of the 646 Vintage Flare

Accepted Answer

The answer of Levi's makes jeans in a variety of...

Question 11

Determine if the relationship f = {(18, 12), (2, 1), (-8, 1), (-20, -3)} is a one-to-one function.
A) not a function
B) a one-to-one function
C) a function, but not one-to-one

Accepted Answer

The answer of Determine if the relationship f = {(18,...

Question 12

Determine if the relationship f = {(9, -3), (-17, 12), (5, -6), (-15, -18)} is a one-to-one function.
A) not a function
B) a one-to-one function
C) a function, but not one-to-one

Accepted Answer

A one-to-one function means each input has a unique output and each output is paired with a unique input. In the given set, each input (9, -17, 5, -15) is paired with a unique output (-3, 12, -6, -18), and each output is also unique. Thus, it is a one-to-one function.

Question 13

Determine if the relationship f = {(-1, 6), (-1, -7), (15, -7), (5, 3)} is a one-to-one function.
A) not a function
B) a one-to-one function
C) a function, but not one-to-one

Accepted Answer

For a relation to be a function, each input (first element of the ordered pairs) must map to exactly one output (second element). Here, the input -1 maps to both 6 and -7, so it is not a function.

Question 14

Determine if the relationship y =  is a function. If it is a function, determine if it is a one-to-one function.
A) not a function
B) a one-to-one function
C) a function, but not one-to-one

Accepted Answer

The answer of Determine if the relationship y = ...

Question 15

Determine if the relationship x =  + 20 is a function. If it is a function, determine if it is a one-to-one function.
A) not a function
B) a one-to-one function
C) a function, but not one-to-one

Accepted Answer

The answer of Determine if the relationship x = ...

Question 16

Determine if the relationship y = -9  is a function. If it is a function, determine if it is one-to-one function.
A) not a function
B) a one-to-one function
C) a function, but not one-to-one

Accepted Answer

The answer of Determine if the relationship y = -9...

Question 17

Determine if the relationship y =  , x > 0 is a function. If it is a function, determine if it is one-to-one.
A) not a function
B) a one-to-one function
C) a function, but not one-to-one

Accepted Answer

The answer of Determine if the relationship y = ...

Question 18

The function y = 9 - 2x is a one-to-one function. Find its inverse.
A) 
B) 
C) 
D)

Accepted Answer

The answer of The function y = 9 - 2x...

Question 19

The function f (x) =  + 3, x ? 0 is a one-to-one function. Find its inverse.
A) y = x + 3
B) y = 
C) y = 
D) y =

Accepted Answer

The answer of The function f (x) =  +...

Question 20

The function f (x) =  + 8, x ? 3 is a one-to-one function. Find its inverse.
A) 
B) 
C) 
D)

Accepted Answer

The answer of The function f (x) =  +...

Quiz 3: Functions and Their Graphs

Write an equation that describes the variation. A is directly proportional to the cube of L. A = 2 when L = 1.

Write an equation that describes the variation. F is inversely proportional to the square of t. f = 8 when t = 1.

Write an equation that describes the variation. Use k as the constant of variation. V varies is directly proportional to both and . V = 32 when x = 1 and t = 4.

Write an equation that describes the variation. F is inversely proportional to both ? and L. F = when ? = 7?m and L = 200 km.

A gas contained in a 3 mL container at a temperature of 340 K has a pressure of 1.5 atm. If the temperature decreases to 325 K, what is the resulting pressure?

A gas contained in a 3 mL container at a temperature of 340 K has a pressure of 1 atm. If the container changes to a volume of 2 mL, what is the resulting pressure?

Determine if the relationship f = {(18, 12) , (2, 1) , (-8, 1) , (-20, -3) } is a one-to-one function.

Determine if the relationship f = {(9, -3) , (-17, 12) , (5, -6) , (-15, -18) } is a one-to-one function.

Determine if the relationship f = {(-1, 6) , (-1, -7) , (15, -7) , (5, 3) } is a one-to-one function.

Determine if the relationship y = is a function. If it is a function, determine if it is a one-to-one function.

Determine if the relationship x = + 20 is a function. If it is a function, determine if it is a one-to-one function.

Determine if the relationship y = -9 is a function. If it is a function, determine if it is one-to-one function.

Determine if the relationship y = , x > 0 is a function. If it is a function, determine if it is one-to-one.

The function y = 9 - 2x is a one-to-one function. Find its inverse.

The function f (x) = + 3, x ? 0 is a one-to-one function. Find its inverse.

The function f (x) = + 8, x ? 3 is a one-to-one function. Find its inverse.