Question 1

Find an equation of variation in which the following are true.
-y varies jointly as x and w and inversely as z, and y =  when x = 2, w = 5, and z = 50.
A) 
B) 
C) y = 4xwz
D)

Accepted Answer

The answer of Find an equation of variation in which...

Question 2

Solve.
-The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of illumination on a screen 5 ft from a light is 2 foot candles, find the intensity on a screen 20 ft from the light.
Express the answer as a fraction.
A) 
B) 
C) 2 foot-candles
D) 8 foot-candles

Accepted Answer

The answer of Solve.
-The intensity I of light varies inversely...

Question 3

Write the word or phrase that best completes each statement or answers the question.
 
-If 4 is substituted for x in the rational expression  , the result is  . Mathematicians have been known to say "Any number divided by itself is 1." Does this mean that this expression is equal to 1 for x = 4 ? Explain why or why not.

Accepted Answer

The answer of Write the word or phrase that best...

Question 4

Solve.
-At a fixed temperature, the resistance R of a wire varies directly as the length l and inversely as the square of its diameter d. If the resistance is 0.84 ohm when the diameter is 1 mm and the length is 210 cm, what is the
Resistance when the diameter is 2 mm and the length is 530 cm?
A) 0.53 ohm
B) 111.3 ohm
C) 1.06 ohm
D) 132.5 ohm

Accepted Answer

The resistance R is given by the formula R = k * (l/d^2), where k is a constant. First, find k using the given values: 0.84 = k * (210/1^2). Solving gives k = 0.004. Then, use this k to find the new resistance: R = 0.004 * (530/2^2) = 0.53 ohm.

Question 5

Write the word or phrase that best completes each statement or answers the question.
 
-Explain in your own words how to divide rational expressions. (How would you explain this to a student in this  class who was absent from class?).

Accepted Answer

The answer of Write the word or phrase that best...

Question 6

Solve.
-The volume of wood in a tree varies jointly as the height of the tree and the square of the distance around the tree trunk. If the volume of wood is 15.84 cubic feet when the height is 22 feet and the distance around the trunk Is 3 feet, what is the volume of wood obtained from a tree that is 33 feet tall having a measurement of 5 feet Around the trunk?
A) 75 cubic feet
B) 70 cubic feet
C) 58 cubic feet
D) 66 cubic feet

Accepted Answer

The volume of wood in a tree $V$ varies jointly as the height $h$ of the tree and the square of the distance $d$ around the tree trunk, which can be represented by the equation $V = k \cdot h \cdot d^2$, where $k$ is the constant of variation. Given $V = 15.84$ cubic feet when $h = 22$ feet and $d = 3$ feet, we can find $k$ by substituting these values into the equation: $15.84 = k \cdot 22 \cdot 3^2$. Solving for $k$ gives $k = 0.08$. To find the volume of wood from a tree that is 33 feet tall with a 5 feet circumference, substitute $h = 33$, $d = 5$, and $k = 0.08$ into the equation: $V = 0.08 \cdot 33 \cdot 5^2 = 66$ cubic feet.

Question 7

Solve.
-The force needed to keep a car from skidding on a curve varies jointly as the weight of the car and the square of the car's speed, and inversely as the radius of the curve. If a force of 3600 pounds is needed to keep an 1800 pound car traveling at 20 mph from skidding on a curve of radius 600 feet, what force would be required To keep the same car from skidding on a curve of radius 550 feet at 30 mph? Round your answer to the nearest Pound of force?
A) 9406 pounds
B) 8704 pounds
C) 8836 pounds
D) 8868 pounds

Accepted Answer

The answer of Solve.
-The force needed to keep a car...

Question 8

Find an equation of variation in which the following are true.
-y varies jointly as x and p and inversely as the square of s, and  .
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find an equation of variation in which...

Question 9

Find an equation of variation in which the following are true.
-y varies jointly as x and z, and y = 120 when x = 8 and z = 3
A) 
B) y = 7xz
C) y = 5xz
D) y = 15x

Accepted Answer

The answer of Find an equation of variation in which...

Question 10

Solve.
-The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 4 lb when the masses are 3 ft apart, what is the attraction when the masses are 6 ft
Apart?
A) 3 lb
B) 1 lb
C) 2 lb
D) 4 lb

Accepted Answer

The gravitational attraction varies inversely as the square of the distance, so if the distance doubles, the attraction becomes 1/4 of the original. Since the original force is 4 lb at 3 ft, at 6 ft (double the distance), the force is 4 lb * (1/4) = 1 lb.

Question 11

Solve.
-Wind resistance or atmospheric drag tends to slow down moving objects. Atmospheric drag varies jointly as an object's surface area A and velocity v. If a car traveling at a speed of 40 mph with a surface area of 38  experiences a drag of 182.4 N (Newtons), how fast must a car with 35  of surface area travel in order to Experience a drag force of 281.4 N?
A) 64 mph
B) 72 mph
C) 67 mph
D) 69 mph

Accepted Answer

The answer of Solve.
-Wind resistance or atmospheric drag tends to...

Question 12

Write the word or phrase that best completes each statement or answers the question.
 
-Explain in your own words how to multiply rational expressions. (How would you explain this to a student in this class who was absent from class?).

Accepted Answer

The answer of Write the word or phrase that best...

Question 13

Solve.
-The weight of a body above the surface of the earth varies inversely as the square of its distance from the center of the earth. What is the effect on the weight when the distance is multiplied by 2?
A) The weight is divided by 2.
B) The weight is divided by 4.
C) The weight is multiplied by 4.
D) The weight is multiplied by 2.

Accepted Answer

The weight varies inversely as the square of the distance, so if the distance is multiplied by 2, the weight is divided by $2^2 = 4$.

Question 14

Find an equation of variation in which the following are true.
-y varies directly as x and inversely as z, and y = 18 when x = 2 and z = 9.
A) 
B) 
C) y = 84xz
D)

Accepted Answer

The answer of Find an equation of variation in which...

Question 15

Write the word or phrase that best completes each statement or answers the question.
 
-For  , the rational expression  is equal to 9 . Can the same be said for  ? Explain why or why not.

Accepted Answer

The answer of Write the word or phrase that best...

Question 16

Solve.
-The period of vibration P for a pendulum varies directly as the square root of the length L. If the period of vibration is 3.5 sec when the length is 49 inches, what is the period when L = 1.5625 inches?
A) 3.75 sec
B) 0.625 sec
C) 4.25 sec
D) 4.5 sec

Accepted Answer

The period of vibration $P$ is directly proportional to the square root of the length $L$, so $P = k\sqrt{L}$ for some constant $k$. Given $P = 3.5$ sec when $L = 49$ inches, we find $k$ by substituting these values: $3.5 = k\sqrt{49}$, which simplifies to $3.5 = 7k$, so $k = 0.5$. For $L = 1.5625$ inches, $P = 0.5\sqrt{1.5625} = 0.5 \times 1.25 = 0.625$ sec.

Question 17

Find an equation of variation in which the following are true.
-y varies jointly as x and z and inversely as the product of w and p, and y =  when x = 5, z = 9, w = 8, and p = 5.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find an equation of variation in which...

Question 18

Solve.
-The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P. If  , what is the volume when 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve.
-The volume V of a given mass...

Question 19

Find an equation of variation in which the following are true.
-f varies jointly as  and h, and f = 144 when q = 4 and h = 3.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find an equation of variation in which...

Question 20

Solve.
-The cost of stainless steel tubing varies jointly as the length and the diameter of the tubing. If a 5 foot length with diameter 2 inches costs $48.00 , how much will a 9 foot length with diameter 4 inches cost?
A) $172.80
B) $170.40
C) $178.10
D) $178.37

Accepted Answer

The cost of the tubing is directly proportional to both the length and the diameter. So, if the length and diameter both double, the cost would quadruple. Since the new length is 9/5 times the original length and the new diameter is 4/2 times the original diameter, the new cost is $48.00 * (9/5) * (4/2) = $172.80.

Quiz 7: Rational Expressions and Equations

Find an equation of variation in which the following are true. -y varies jointly as x and w and inversely as z, and y = when x = 2, w = 5, and z = 50.

Solve. -The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of illumination on a screen 5 ft from a light is 2 foot candles, find the intensity on a screen 20 ft from the light. Express the answer as a fraction.

Solve. -At a fixed temperature, the resistance R of a wire varies directly as the length l and inversely as the square of its diameter d. If the resistance is 0.84 ohm when the diameter is 1 mm and the length is 210 cm, what is the Resistance when the diameter is 2 mm and the length is 530 cm?

Write the word or phrase that best completes each statement or answers the question. -Explain in your own words how to divide rational expressions. (How would you explain this to a student in this class who was absent from class?).

Find an equation of variation in which the following are true. -y varies jointly as x and p and inversely as the square of s, and .

Find an equation of variation in which the following are true. -y varies jointly as x and z, and y = 120 when x = 8 and z = 3

Solve. -The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 4 lb when the masses are 3 ft apart, what is the attraction when the masses are 6 ft Apart?

Write the word or phrase that best completes each statement or answers the question. -Explain in your own words how to multiply rational expressions. (How would you explain this to a student in this class who was absent from class?).

Solve. -The weight of a body above the surface of the earth varies inversely as the square of its distance from the center of the earth. What is the effect on the weight when the distance is multiplied by 2?

Find an equation of variation in which the following are true. -y varies directly as x and inversely as z, and y = 18 when x = 2 and z = 9.

Write the word or phrase that best completes each statement or answers the question. -For , the rational expression is equal to 9 . Can the same be said for ? Explain why or why not.

Solve. -The period of vibration P for a pendulum varies directly as the square root of the length L. If the period of vibration is 3.5 sec when the length is 49 inches, what is the period when L = 1.5625 inches?

Find an equation of variation in which the following are true. -y varies jointly as x and z and inversely as the product of w and p, and y = when x = 5, z = 9, w = 8, and p = 5.

Solve. -The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P. If , what is the volume when

Find an equation of variation in which the following are true. -f varies jointly as and h, and f = 144 when q = 4 and h = 3.

Solve. -The cost of stainless steel tubing varies jointly as the length and the diameter of the tubing. If a 5 foot length with diameter 2 inches costs $48.00 , how much will a 9 foot length with diameter 4 inches cost?