Question 1

Each unit of a certain commodity costs p = 11x + 12 cents when x units of the commodity are produced. If all units are sold at this price, express the revenue derived from the sales as a function of x.
A) x(11x + 12) cents
B) 10x + 12 cents
C) $11 x ^ { 2 } + 12$ cents
D) 12x + 12 cents

Accepted Answer

Revenue is calculated by multiplying the price per unit by the number of units sold. Here, the price per unit is $p = 11x + 12$ cents, and the number of units sold is $x$, so the revenue is $x(11x + 12)$ cents.

Question 2

A manufacturer's total cost consists of a fixed overhead of $250 plus production costs of $70 per unit. Express the total cost in dollars as a function of the number of units produced.

Accepted Answer

The answer of A manufacturer's total cost consists of a...

Question 3

A manufacturer's total cost consists of a fixed overhead of $350 plus production costs of $60 per unit. Express the total cost in dollars as a function of the number of units produced.

Accepted Answer

The answer of A manufacturer's total cost consists of a...

Question 4

A farmer is planning to plant a rectangular garden with an area of 4,000 square yards. The garden is to be fenced on all four sides. Express the number of yards of fencing required as a function of x, the long side of the fence.

Accepted Answer

The answer of A farmer is planning to plant a...

Question 5

A farmer is planning to plant a rectangular garden with an area of 400 square yards. The garden is to be fenced on all four sides. Express the number of yards of fencing required as a function of x, the long side of the fence.

Accepted Answer

The answer of A farmer is planning to plant a...

Question 6

A rectangle is constructed inside a circle of radius r with the corners of the rectangle lying on the circle. Express the area A of the rectangle as a function of the radius r if the width of one side of the rectangle is 2.

Accepted Answer

The answer of A rectangle is constructed inside a circle...

Question 7

A cylindrical can is to have a volume of 36 $\pi$cubic inches. The cost of the material used for the top and bottom of the can is 4 cents per square inch, and the cost of the material used for the curved side is 3 cents per square inch. Express the cost in cents of constructing the can as a function of its radius.

Accepted Answer

The answer of A cylindrical can is to have a...

Question 8

A cylindrical can is to have a volume of 45 $\pi$ cubic inches. The cost of the material used for the top and bottom of the can is 4 cents per square inch, and the cost of the material used for the curved side is 5 cents per square inch. Express the cost of constructing the can as a function of its radius.

Accepted Answer

The answer of A cylindrical can is to have a...

Question 9

A closed box with a square base is to have a volume of 20 cubic meters. The material for the top and bottom of the box costs $3 per square meter, and the material for the sides costs $1 per square meter. Express the construction cost of the box as a function of the length of its base, x.
A) $C ( x ) = x ^ { 2 } + 80 x + 2$ dollars
B) $C ( x ) = 2 x ^ { 2 } + \frac { 2 } { x } + 6$ dollars
C) $C ( x ) = 2 x ^ { 2 } + \frac { 20 } { x }$ dollars
D) $C ( x ) = 6 x ^ { 2 } + \frac { 80 } { x }$ dollars

Accepted Answer

The cost function is derived by considering the cost of the top and bottom, which is $6x^2$ (since both top and bottom cost $3 per square meter), and the sides, which cost $\frac{80}{x}$ (since the volume constraint gives height as $\frac{20}{x^2}$ and the total side area is $4x \times \frac{20}{x^2}$).

Question 10

The supply and demand functions, S(x) and D(x), respectively, for a certain commodity are given in terms of the level of production x. S(x) = 2x + 30, D(x) = 360 - x. Find the value of x_e for which equilibrium occurs.

Accepted Answer

The answer of The supply and demand functions, S(x) and...

Question 11

Two car rental agencies are competing. One agency rents cars for 35 dollars per day and 35 cents a mile; the other agency rents cars for 30 dollars per day and 50 cents a mile. For a 9 day trip, how many miles must you travel to have the total cost be the same with each agency? Round to the nearest whole mile , if necessary.
A) 300 miles
B) 33 miles
C) 14 miles
D) 10 miles

Accepted Answer

To find the number of miles where the total cost is the same for both agencies, set up an equation where the total cost of each agency is equal. Let $x$ be the number of miles driven.Agency 1: $35 \times 9 + 0.35x$Agency 2: $30 \times 9 + 0.50x$Setting them equal to each other:$$35 \times 9 + 0.35x = 30 \times 9 + 0.50x$$Solving for $x$:$$315 + 0.35x = 270 + 0.50x$$$$45 = 0.15x$$$$x = 300$$ miles.

Question 12

Two jets bound for San Diego leave Boston 20 minutes apart. The first travels at 450 miles per hour, while the second goes 500 miles per hour. How how many hours after the second plane departs will the second plane pass the first?

Accepted Answer

The answer of Two jets bound for San Diego leave...

Question 13

Two jets bound for San Diego leave Boston 20 minutes apart. The first plane travels at 300 miles per hour, while the second plane goes 320 miles per hour. At what time will the second plane pass the first?

Accepted Answer

The answer of Two jets bound for San Diego leave...

Question 14

An appliance manufacturer can sell refrigerators for $600 apiece. The manufacturer's total cost consists of a fixed overhead of $12,000 plus production cost of $400 per refrigerator. How many refrigerators must be sold for the manufacturer to break even?

Accepted Answer

The answer of An appliance manufacturer can sell refrigerators for...

Question 15

An appliance manufacturer can sell refrigerators for $600 apiece. The manufacturer's total cost consists of a fixed overhead of $12,000 plus production cost of $400 per refrigerator. How many refrigerators must be sold for the manufacturer to break even?

Accepted Answer

The answer of An appliance manufacturer can sell refrigerators for...

Question 16

If f (x) is graphed below, find $\lim _ { x \rightarrow 1 } f ( x )$ if it exists.

Accepted Answer

The answer of If f (x) is graphed below, find...

Question 17

If f (x) is graphed below, find $\lim _ { x \rightarrow 1 } f ( x )$ if it exists.

Accepted Answer

The answer of If f (x) is graphed below, find...

Question 18

Find the indicated limit if it exists. $\lim _ { x \rightarrow 1 } \left( 2 x ^ { 2 } - 3 x + 1 \right)$

Accepted Answer

The answer of Find the indicated limit if it exists....

Question 19

Find the indicated limit if it exists. $\lim _ { x \rightarrow 1 } \left( 3 x ^ { 2 } - 8 x + 1 \right)$

Accepted Answer

The answer of Find the indicated limit if it exists....

Question 20

Find the indicated limit if it exists. $\lim _ { x \rightarrow 3 } ( x + 4 )$
A) 7
B) 3
C) Does not exist
D) -1

Accepted Answer

The limit of a linear function as x approaches a value is simply the function evaluated at that value. Here, substituting $x = 3$ into $x + 4$ gives $3 + 4 = 7$.

Quiz 1: Functions, Graphs, and Limits

Each unit of a certain commodity costs p = 11x + 12 cents when x units of the commodity are produced. If all units are sold at this price, express the revenue derived from the sales as a function of x.

A manufacturer's total cost consists of a fixed overhead of $250 plus production costs of $70 per unit. Express the total cost in dollars as a function of the number of units produced.

A manufacturer's total cost consists of a fixed overhead of $350 plus production costs of $60 per unit. Express the total cost in dollars as a function of the number of units produced.

A farmer is planning to plant a rectangular garden with an area of 4,000 square yards. The garden is to be fenced on all four sides. Express the number of yards of fencing required as a function of x, the long side of the fence.

A farmer is planning to plant a rectangular garden with an area of 400 square yards. The garden is to be fenced on all four sides. Express the number of yards of fencing required as a function of x, the long side of the fence.

A rectangle is constructed inside a circle of radius r with the corners of the rectangle lying on the circle. Express the area A of the rectangle as a function of the radius r if the width of one side of the rectangle is 2.

A closed box with a square base is to have a volume of 20 cubic meters. The material for the top and bottom of the box costs $3 per square meter, and the material for the sides costs $1 per square meter. Express the construction cost of the box as a function of the length of its base, x.

The supply and demand functions, S(x) and D(x), respectively, for a certain commodity are given in terms of the level of production x. S(x) = 2x + 30, D(x) = 360 - x. Find the value of x_e for which equilibrium occurs.

Two jets bound for San Diego leave Boston 20 minutes apart. The first travels at 450 miles per hour, while the second goes 500 miles per hour. How how many hours after the second plane departs will the second plane pass the first?

Two jets bound for San Diego leave Boston 20 minutes apart. The first plane travels at 300 miles per hour, while the second plane goes 320 miles per hour. At what time will the second plane pass the first?

An appliance manufacturer can sell refrigerators for $600 apiece. The manufacturer's total cost consists of a fixed overhead of $12,000 plus production cost of $400 per refrigerator. How many refrigerators must be sold for the manufacturer to break even?

An appliance manufacturer can sell refrigerators for $600 apiece. The manufacturer's total cost consists of a fixed overhead of $12,000 plus production cost of $400 per refrigerator. How many refrigerators must be sold for the manufacturer to break even?

If f (x) is graphed below, find $\lim _ { x \rightarrow 1 } f ( x )$ if it exists. $If f (x) is graphed below, find \lim _ { x \rightarrow 1 } f ( x ) if it exists.$

If f (x) is graphed below, find $\lim _ { x \rightarrow 1 } f ( x )$ if it exists. $If f (x) is graphed below, find \lim _ { x \rightarrow 1 } f ( x ) if it exists.$

Find the indicated limit if it exists. $\lim _ { x \rightarrow 1 } \left( 2 x ^ { 2 } - 3 x + 1 \right)$

Find the indicated limit if it exists. $\lim _ { x \rightarrow 1 } \left( 3 x ^ { 2 } - 8 x + 1 \right)$

Find the indicated limit if it exists. $\lim _ { x \rightarrow 3 } ( x + 4 )$

Quiz 1: Functions, Graphs, and Limits

Each unit of a certain commodity costs p = 11x + 12 cents when x units of the commodity are produced. If all units are sold at this price, express the revenue derived from the sales as a function of x.

A manufacturer's total cost consists of a fixed overhead of $250 plus production costs of $70 per unit. Express the total cost in dollars as a function of the number of units produced.

A manufacturer's total cost consists of a fixed overhead of $350 plus production costs of $60 per unit. Express the total cost in dollars as a function of the number of units produced.

A farmer is planning to plant a rectangular garden with an area of 4,000 square yards. The garden is to be fenced on all four sides. Express the number of yards of fencing required as a function of x, the long side of the fence.

A farmer is planning to plant a rectangular garden with an area of 400 square yards. The garden is to be fenced on all four sides. Express the number of yards of fencing required as a function of x, the long side of the fence.

A rectangle is constructed inside a circle of radius r with the corners of the rectangle lying on the circle. Express the area A of the rectangle as a function of the radius r if the width of one side of the rectangle is 2.

A closed box with a square base is to have a volume of 20 cubic meters. The material for the top and bottom of the box costs $3 per square meter, and the material for the sides costs $1 per square meter. Express the construction cost of the box as a function of the length of its base, x.

The supply and demand functions, S(x) and D(x), respectively, for a certain commodity are given in terms of the level of production x. S(x) = 2x + 30, D(x) = 360 - x. Find the value of xe for which equilibrium occurs.

Two jets bound for San Diego leave Boston 20 minutes apart. The first travels at 450 miles per hour, while the second goes 500 miles per hour. How how many hours after the second plane departs will the second plane pass the first?

Two jets bound for San Diego leave Boston 20 minutes apart. The first plane travels at 300 miles per hour, while the second plane goes 320 miles per hour. At what time will the second plane pass the first?

An appliance manufacturer can sell refrigerators for $600 apiece. The manufacturer's total cost consists of a fixed overhead of $12,000 plus production cost of $400 per refrigerator. How many refrigerators must be sold for the manufacturer to break even?

An appliance manufacturer can sell refrigerators for $600 apiece. The manufacturer's total cost consists of a fixed overhead of $12,000 plus production cost of $400 per refrigerator. How many refrigerators must be sold for the manufacturer to break even?

If f (x) is graphed below, find lim⁡x→1f(x)\lim _ { x \rightarrow 1 } f ( x )limx→1​f(x) if it exists.

If f (x) is graphed below, find lim⁡x→1f(x)\lim _ { x \rightarrow 1 } f ( x )limx→1​f(x) if it exists.

Find the indicated limit if it exists. lim⁡x→1(2x2−3x+1)\lim _ { x \rightarrow 1 } \left( 2 x ^ { 2 } - 3 x + 1 \right)limx→1​(2x2−3x+1)

Find the indicated limit if it exists. lim⁡x→1(3x2−8x+1)\lim _ { x \rightarrow 1 } \left( 3 x ^ { 2 } - 8 x + 1 \right)limx→1​(3x2−8x+1)

Find the indicated limit if it exists. lim⁡x→3(x+4) \lim _ { x \rightarrow 3 } ( x + 4 ) limx→3​(x+4)

The supply and demand functions, S(x) and D(x), respectively, for a certain commodity are given in terms of the level of production x. S(x) = 2x + 30, D(x) = 360 - x. Find the value of x_e for which equilibrium occurs.

If f (x) is graphed below, find $\lim _ { x \rightarrow 1 } f ( x )$ if it exists. $If f (x) is graphed below, find \lim _ { x \rightarrow 1 } f ( x ) if it exists.$

If f (x) is graphed below, find $\lim _ { x \rightarrow 1 } f ( x )$ if it exists. $If f (x) is graphed below, find \lim _ { x \rightarrow 1 } f ( x ) if it exists.$

Find the indicated limit if it exists. $\lim _ { x \rightarrow 1 } \left( 2 x ^ { 2 } - 3 x + 1 \right)$

Find the indicated limit if it exists. $\lim _ { x \rightarrow 1 } \left( 3 x ^ { 2 } - 8 x + 1 \right)$

Find the indicated limit if it exists. $\lim _ { x \rightarrow 3 } ( x + 4 )$