Question 1

Round your answer to two decimal places.
-The pitch P of a musical tone varies inversely as its wavelength W. One tone has a pitch of 463 vibrations per second and a wavelength of 14.4 ft. Find the wavelength of another tone that has a
Pitch of 370 vibrations per second. Round to the nearest tenth.

Accepted Answer

The relationship between pitch $P$ and wavelength $W$ is inversely proportional, so $P = k/W$, where $k$ is a constant. For the first tone, $P = 463$ when $W = 14.4$. We can find $k$ by rearranging the formula to $k = P \times W$, so $k = 463 \times 14.4$. For the second tone with $P = 370$, we use the same constant $k$ to find the new wavelength $W$, using $W = k / P$. Substituting the values, we find the wavelength for the second tone, which rounds to 18 ft when calculated correctly.

Question 2

Round your answer to two decimal places.
-The weight that a horizontal beam can support varies inversely as the length of the beam. Suppose that a 5-m beam can support 760 kg. How many kilograms can a 1-m beam support?

Accepted Answer

The weight a beam can support varies inversely with its length, meaning weight = k/length, where k is a constant. For a 5-m beam supporting 760 kg, k = 760*5. For a 1-m beam, weight = k/1 = 760*5 = 3800 kg.

Question 3

Round your answer to two decimal places.
-The amount of tread left on a tire varies inversely as the number of miles the tire has traveled. A tire that has traveled $66,000 \mathrm { mi }$ has $\frac { 1 } { 32 } \mathrm { in }$. of tread left. How much tread will be left on a tire that has traveled 21,000 mi?

Accepted Answer

The relationship between tread left (T) and miles traveled (M) is inversely proportional, so $T = \frac{k}{M}$, where $k$ is a constant. With $66,000 \, \mathrm{mi}$ and $\frac{1}{32} \, \mathrm{in}$ of tread, we find $k = 66,000 \times \frac{1}{32}$. For $21,000 \, \mathrm{mi}$, $T = \frac{66,000 \times \frac{1}{32}}{21,000} = \frac{11}{112} \, \mathrm{in}$.

Question 4

Round your answer to two decimal places.
-The current I in an electrical conductor varies inversely as the resistance R of the conductor. The current is 8 amperes when the resistance is 727 ohms. What is the current when the resistance is 899
Ohms? Round to the nearest tenth.

Accepted Answer

The relationship between current (I) and resistance (R) is given by $I = \frac{k}{R}$, where $k$ is a constant. When $I = 8$ amperes and $R = 727$ ohms, we can find $k = I \times R = 8 \times 727 = 5824$. To find the current when $R = 899$ ohms, we use $I = \frac{5824}{899}$, which gives $I \approx 6.48$ amperes, rounded to the nearest tenth as 6.5 amperes.

Question 5

Round your answer to two decimal places.
-If $\mathrm { f }$ varies jointly as $\mathrm { q } ^ { 2 }$ and $\mathrm { h }$, and $\mathrm { f } = 96$ when $\mathrm { q } = 4$ and $\mathrm { h } = 3$, find $\mathrm { q }$ when $\mathrm { f } = 40$ and $\mathrm { h } = 5$

Accepted Answer

The equation for joint variation is $f = kq^2h$. Using the given values, solve for $k$ and then use it to find $q$ for the new conditions.

Question 6

Round your answer to two decimal places.
-The weight of a person on or above the surface of the earth varies inversely as the square of the distance the person is from the center of the earth. If a person weighs 180 pounds on the surface of
The earth and the radius of the earth is 3900 miles, what will the person weigh if he or she is 125
Miles above the earth's surface? Round your answer to the nearest hundredth of a pound.

Accepted Answer

The answer of Round your answer to two decimal places.
-The...

Question 7

Round to the nearest tenth unless indicated otherwise.
-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 19 foot length with diameter 4 inches cost? Round to the nearest cent.

Accepted Answer

The answer of Round to the nearest tenth unless indicated...

Question 8

Round your answer to two decimal places.
-The time it takes to complete a certain job varies inversely to the number of people working on that job. If it takes 20 hours for 13 carpenters to frame a house, then how long will it take 25 carpenters
To do the same job?

Accepted Answer

The time it takes to complete a job varies inversely with the number of people, so $T = \frac{k}{n}$, where $T$ is time, $n$ is the number of people, and $k$ is a constant. Given $T = 20$ hours for $n = 13$ carpenters, we find $k = 20 \times 13 = 260$. For $n = 25$ carpenters, $T = \frac{260}{25} = 10.4$ hours.

Question 9

Round to the nearest tenth unless indicated otherwise.
-The volume $\mathrm { V }$ of a given mass of gas varies directly as the temperature $\mathrm { T }$ and inversely as the pressure $\mathrm { P }$. If $\mathrm { V } = 400.0 \mathrm { in } ^ { 3 }$ when $\mathrm { T } = 400 ^ { \circ }$ and $\mathrm { P } = 15 \mathrm { lb } / \mathrm { in } ^ { 2 }$, what is the volume when $\mathrm { T } = 100 ^ { \circ }$ and $\mathrm { P } = 15 \mathrm { lb } / \mathrm { in } ^ { 2 } ?$

Accepted Answer

The volume of gas varies directly with temperature and inversely with pressure, so when the temperature is reduced to a quarter (from 400 to 100 degrees) and the pressure remains constant, the volume also reduces to a quarter of its original value, making it 100.0 in$^3$.

Question 10

Round your answer to two decimal places.
-If $\mathrm { f }$ varies jointly as $\mathrm { q } ^ { 2 }$ and $\mathrm { h }$, and $\mathrm { f } = 81$ when $\mathrm { q } = 3$ and $\mathrm { h } = 3$, find $\mathrm { f }$ when $\mathrm { q } = 4$ and $\mathrm { h } = 2$.

Accepted Answer

The formula for joint variation is $f = kq^2h$, where $k$ is the constant of variation. Given $f = 81$, $q = 3$, and $h = 3$, we can solve for $k$. Substituting these values into the formula gives $81 = k(3)^2(3)$, leading to $k = 3$. To find $f$ when $q = 4$ and $h = 2$, substitute these values and $k = 3$ into the formula: $f = 3(4)^2(2) = 96$.

Question 11

Round your answer to two decimal places.
-The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 2.25 lb when the masses are 4 ft apart, what is the attraction
When the masses are 6 ft apart?

Accepted Answer

The gravitational force varies inversely with the square of the distance, so A = k/d^2. Given A = 2.25 lb at d = 4 ft, k = 2.25 * 4^2 = 36. For d = 6 ft, A = 36/6^2 = 1 lb.

Question 12

Round to the nearest tenth unless indicated otherwise.
-The resistance of a wire varies directly as the length of the wire and inversely as the square of the diameter of the wire. A 20 foot length of wire with a diameter of $0.1$ inch has a resistance of 3 ohms What would the resistance be for a 21 foot length, with diameter $0.01$ inch, of the same kind of wire ?

Accepted Answer

The resistance of a wire varies directly as the length of the wire and inversely as the square of the diameter of the wire.$$R = \frac{kL}{d^2}$$where:* R is the resistance in ohms* k is a constant* L is the length of the wire in feet* d is the diameter of the wire in inchesWe are given that a 20 foot length of wire with a diameter of 0.1 inch has a resistance of 3 ohms. We can use this information to find the value of k:$$3 = \frac{k(20)}{(0.1)^2}$$$$k = 0.015$$Now we can use the value of k to find the resistance of a 21 foot length of wire with a diameter of 0.01 inch:$$R = \frac{kL}{d^2}$$$$R = \frac{0.015(21)}{(0.01)^2}$$$$R = 315 \mathrm { ohms }$$

Question 13

Round to the nearest tenth unless indicated otherwise.
-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 $50 \mathrm { mph }$ with a surface area of $36 \mathrm { ft } ^ { 2 }$ experiences a drag of $270 \mathrm {~N}$ (Newtons), how fast must a car with $35 \mathrm { ft } ^ { 2 }$ of surface area travel in order to experience a drag force of $231 \mathrm {~N}$ ?

Accepted Answer

The drag force formula can be expressed as $D = kAv^2$, where $D$ is the drag force, $A$ is the surface area, $v$ is the velocity, and $k$ is a constant. Given that a car with a surface area of $36 \mathrm{ft}^2$ and velocity of $50 \mathrm{mph}$ experiences a drag of $270 \mathrm{N}$, we can find the constant $k$ and then use it to find the required velocity for a car with a surface area of $35 \mathrm{ft}^2$ to experience a drag of $231 \mathrm{N}$. The calculation involves setting up a proportion based on the given and required conditions and solving for the unknown velocity. The correct answer, after performing the calculations and rounding to the nearest tenth, is $44 \mathrm{mph}$.

Question 14

Round your answer to two decimal places.
-The intensity of a radio signal from the radio station varies inversely as the square of the distance from the station. Suppose the the intensity is 8000 units at a distance of 2 miles. What will the
Intensity be at a distance of 13 miles? Round your answer to the nearest unit.

Accepted Answer

The answer of Round your answer to two decimal places.
-The...

Question 15

Provide an appropriate response.
-How many positive real zeros does this graph have?

Accepted Answer

The answer of Provide an appropriate response.
-How many positive real...

Question 16

Round to the nearest tenth unless indicated otherwise.
-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 30 feet tall having a measurement of 5 feet around the trunk?

Accepted Answer

The answer of Round to the nearest tenth unless indicated...

Question 17

Round to the nearest tenth unless indicated otherwise.
-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 0.48 ohm when the diameter is 1 mm and the length is
240 cm, what is the resistance when the diameter is 3 mm and the length is 430 cm?

Accepted Answer

The answer of Round to the nearest tenth unless indicated...

Question 18

Round to the nearest tenth unless indicated otherwise.
-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 590 feet at
60 mph? Round your answer to the nearest pound of force.

Accepted Answer

The force needed to keep a car from skidding on a curve is given by $F = k \cdot \frac{Wv^2}{r}$, where $F$ is the force, $W$ is the weight of the car, $v$ is the speed of the car, $r$ is the radius of the curve, and $k$ is a constant of proportionality. Given $F = 3600$ pounds for a 1800 pound car at 20 mph and a radius of 600 feet, we can find $k$ and then use it to calculate the force required for the same car at 60 mph on a curve of radius 590 feet. The calculation shows that the force required is approximately 32,949 pounds, rounding to the nearest pound.

Question 19

Round to the nearest tenth unless indicated otherwise.
-The volume of a gas varies inversely as the pressure and directly as the temperature (in degrees Kelvin). If a certain gas occupies a volume of $2.1$ liters at a temperature of $340 \mathrm {~K}$ and a pressure of 22 newtons per square centimeter, find the volume when the temperature is $442 \mathrm {~K}$ and the pressure is 11 newtons per square centimeter.

Accepted Answer

The volume of a gas varies inversely with pressure and directly with temperature, which can be represented by the formula $V = k \frac{T}{P}$, where $V$ is volume, $T$ is temperature, $P$ is pressure, and $k$ is a constant. Given the initial conditions, we can solve for $k$ and then use it to find the new volume under the new conditions. The new volume, when calculated, is $5.5 \mathrm {~L}$.

Question 20

Provide an appropriate response.
-How many real zeros does this graph have?

Accepted Answer

The answer of Provide an appropriate response.
-How many real zeros...

Quiz 4: Polynomial and Rational Functions

Round your answer to two decimal places. -The pitch P of a musical tone varies inversely as its wavelength W. One tone has a pitch of 463 vibrations per second and a wavelength of 14.4 ft. Find the wavelength of another tone that has a Pitch of 370 vibrations per second. Round to the nearest tenth.

Round your answer to two decimal places. -The weight that a horizontal beam can support varies inversely as the length of the beam. Suppose that a 5-m beam can support 760 kg. How many kilograms can a 1-m beam support?

Round your answer to two decimal places. -The current I in an electrical conductor varies inversely as the resistance R of the conductor. The current is 8 amperes when the resistance is 727 ohms. What is the current when the resistance is 899 Ohms? Round to the nearest tenth.

Round your answer to two decimal places. -If $\mathrm { f }$ varies jointly as $\mathrm { q } ^ { 2 }$ and $\mathrm { h }$ , and $\mathrm { f } = 96$ when $\mathrm { q } = 4$ and $\mathrm { h } = 3$ , find $\mathrm { q }$ when $\mathrm { f } = 40$ and $\mathrm { h } = 5$

Round to the nearest tenth unless indicated otherwise. -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 19 foot length with diameter 4 inches cost? Round to the nearest cent.

Round your answer to two decimal places. -The time it takes to complete a certain job varies inversely to the number of people working on that job. If it takes 20 hours for 13 carpenters to frame a house, then how long will it take 25 carpenters To do the same job?

Round your answer to two decimal places. -If $\mathrm { f }$ varies jointly as $\mathrm { q } ^ { 2 }$ and $\mathrm { h }$ , and $\mathrm { f } = 81$ when $\mathrm { q } = 3$ and $\mathrm { h } = 3$ , find $\mathrm { f }$ when $\mathrm { q } = 4$ and $\mathrm { h } = 2$ .

Round your answer to two decimal places. -The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 2.25 lb when the masses are 4 ft apart, what is the attraction When the masses are 6 ft apart?

Provide an appropriate response. -How many positive real zeros does this graph have?

Provide an appropriate response. -How many real zeros does this graph have?

Quiz 4: Polynomial and Rational Functions

Round your answer to two decimal places. -The pitch P of a musical tone varies inversely as its wavelength W. One tone has a pitch of 463 vibrations per second and a wavelength of 14.4 ft. Find the wavelength of another tone that has a Pitch of 370 vibrations per second. Round to the nearest tenth.

Round your answer to two decimal places. -The weight that a horizontal beam can support varies inversely as the length of the beam. Suppose that a 5-m beam can support 760 kg. How many kilograms can a 1-m beam support?

Round your answer to two decimal places. -The current I in an electrical conductor varies inversely as the resistance R of the conductor. The current is 8 amperes when the resistance is 727 ohms. What is the current when the resistance is 899 Ohms? Round to the nearest tenth.

Round your answer to two decimal places. -If f\mathrm { f }f varies jointly as q2\mathrm { q } ^ { 2 }q2 and h\mathrm { h }h , and f=96\mathrm { f } = 96f=96 when q=4\mathrm { q } = 4q=4 and h=3\mathrm { h } = 3h=3 , find q\mathrm { q }q when f=40\mathrm { f } = 40f=40 and h=5\mathrm { h } = 5h=5

Round your answer to two decimal places. -The time it takes to complete a certain job varies inversely to the number of people working on that job. If it takes 20 hours for 13 carpenters to frame a house, then how long will it take 25 carpenters To do the same job?

Round your answer to two decimal places. -If f\mathrm { f }f varies jointly as q2\mathrm { q } ^ { 2 }q2 and h\mathrm { h }h , and f=81\mathrm { f } = 81f=81 when q=3\mathrm { q } = 3q=3 and h=3\mathrm { h } = 3h=3 , find f\mathrm { f }f when q=4\mathrm { q } = 4q=4 and h=2\mathrm { h } = 2h=2 .

Round your answer to two decimal places. -The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 2.25 lb when the masses are 4 ft apart, what is the attraction When the masses are 6 ft apart?

Provide an appropriate response. -How many positive real zeros does this graph have?

Provide an appropriate response. -How many real zeros does this graph have?

Round your answer to two decimal places. -If $\mathrm { f }$ varies jointly as $\mathrm { q } ^ { 2 }$ and $\mathrm { h }$ , and $\mathrm { f } = 96$ when $\mathrm { q } = 4$ and $\mathrm { h } = 3$ , find $\mathrm { q }$ when $\mathrm { f } = 40$ and $\mathrm { h } = 5$

Round your answer to two decimal places. -If $\mathrm { f }$ varies jointly as $\mathrm { q } ^ { 2 }$ and $\mathrm { h }$ , and $\mathrm { f } = 81$ when $\mathrm { q } = 3$ and $\mathrm { h } = 3$ , find $\mathrm { f }$ when $\mathrm { q } = 4$ and $\mathrm { h } = 2$ .