Question 1

The shape of the main cable on a suspension bridge can be described by the function  
where y is the height of the cable (in feet)above the roadbed and x is the horizontal distance (in feet)from the center of the bridge.A cross support passes by the cable,and its position can be described by the function  
Where does the cross-support intersect the cable? Use a graphing calculator to answer the question by finding the point(s)of intersection of the two equations.

Accepted Answer

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Question 2

Find the Break Even Point for a product whose Total Revenue,  
,(in $)and Total Cost,  
,(in $)are as follows:  
= (10q - 25)q  
= 2000 + 75q

Accepted Answer

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Question 3

Solve the following nonlinear system:

Accepted Answer

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Question 4

Suppose the supply and demand equations for a manufacturer's product are  
and  
respectively,where q represents number of units and p represents price per unit in dollars.Determine (a)the equilibrium quantity; (b)the equilibrium price.If a tax of $1.00 per unit is imposed on the manufacturer,(c)determine the new equilibrium quantity; (d)the new equilibrium price.

Accepted Answer

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Question 5

Suppose that the supply and demand equations for a certain product are  
and  
respectively,where p represents the price per unit in dollars and q represents the number of units per time period.
(a)Find the equilibrium price algebraically.
(b)Find the equilibrium price when a tax of 50 cents per unit is imposed.

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Question 6

Find the equilibrium point if the demand equation for a product is  
and the supply equation is

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Question 7

Solve the system

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Question 8

A manufacturer sells his product at $23 per unit,selling all he produces.His fixed cost is $18,000 and his variable cost per unit is $18.50.The level of production at which the manufacturer breaks even is
A) 3000 units.
B) 3500 units.
C) 4000 units.
D) 4500 units.
E) 5000 units.

Accepted Answer

To break even, the total revenue earned by the manufacturer must be equal to the total costs incurred. Let's first calculate the total cost for producing x units:

Total Cost = Fixed Cost + Variable Cost * Number of Units
Total Cost = $18,000 + $18.50x

Now let's calculate the revenue earned by selling x units:

Revenue = Price per Unit * Number of Units
Revenue = $23x

To break even, we need to set these two equations equal to each other and solve for x:

$18,000 + $18.50x = $23x
$4.50x = $18,000
x = 4,000 units

Therefore, the manufacturer will break even by producing and selling 4000 units.

Question 9

The supply and demand equations for a product are p =  q + 20 and p = 200 - 
Q,respectively,where q represents the number of units and p represents the price per unit in dollars.The equilibrium price is
A) $10.
B) $20.
C) $30.
D) $40.
E) $50.

Accepted Answer

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Question 10

Find the Point of Equilibrium for a product with Demand Equation and Supply Equation as follows:
Demand: p = 300 - 8q
Supply: p =  
q + 5

Accepted Answer

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Question 11

The number of solutions of the system  is
A) zero.
B) one.
C) two.
D) three.
E) four.

Accepted Answer

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Question 12

An x-value of a solution of the system  is
A) -1.
B) 1.
C) 4.
D) -4.
E) 11.

Accepted Answer

The answer of An x-value of a solution of the...

Question 13

A manufacturer sells his product at $12.50 per unit,selling all he produces.His fixed cost is $5,000 and his variable cost per unit is $8.50.(a)At what level of production will he break even? (b)At what level of production will he have a profit of $10,000?

Accepted Answer

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Question 14

Find the Equilibrium Quantity for a product with Demand Equation and Supply Equation as follows:
Demand: p = 300 - 8q
Supply: p =  
q + 5

Accepted Answer

The answer of Find the Equilibrium Quantity for a product...

Question 15

The shape of a rope bridge stretched across a ravine can be described by the function  
where y is the height of the bridge (in feet)above the bottom of the ravine and x is the horizontal distance (in feet)from the center of the ravine.A hiker traveling at night shines his flashlight across the ravine,and the path of the beam of light can be described by the function  
Where does the beam of light intersect the rope bridge? Use a graphing calculator to answer the question by finding the point(s)of intersection of the two equations.

Accepted Answer

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Question 16

Solve the system

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Question 17

Solve the following nonlinear system of equations by sketching its graph (using graphing calculator or using graph paper.)If the equations have no solutions,please say so.

Accepted Answer

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Question 18

Find the Break Even Quantity for a product whose Total Revenue,  
,(in $)and Total Cost,  
,(in $)are as follows:  
= (10q - 25)q  
= 2000 + 75q

Accepted Answer

The answer of Find the Break Even Quantity for a...

Quiz 4: Lines parabolas and Systems

Find the Break Even Point for a product whose Total Revenue, ,(in $)and Total Cost, ,(in $)are as follows: = (10q - 25)q = 2000 + 75q

Solve the following nonlinear system:

Find the equilibrium point if the demand equation for a product is and the supply equation is

Solve the system

A manufacturer sells his product at $23 per unit,selling all he produces.His fixed cost is $18,000 and his variable cost per unit is $18.50.The level of production at which the manufacturer breaks even is

The supply and demand equations for a product are p = q + 20 and p = 200 - Q,respectively,where q represents the number of units and p represents the price per unit in dollars.The equilibrium price is

Find the Point of Equilibrium for a product with Demand Equation and Supply Equation as follows: Demand: p = 300 - 8q Supply: p = q + 5

The number of solutions of the system is

An x-value of a solution of the system is

A manufacturer sells his product at $12.50 per unit,selling all he produces.His fixed cost is $5,000 and his variable cost per unit is $8.50.(a)At what level of production will he break even? (b)At what level of production will he have a profit of $10,000?

Find the Equilibrium Quantity for a product with Demand Equation and Supply Equation as follows: Demand: p = 300 - 8q Supply: p = q + 5

Solve the system

Solve the following nonlinear system of equations by sketching its graph (using graphing calculator or using graph paper.)If the equations have no solutions,please say so.

Find the Break Even Quantity for a product whose Total Revenue, ,(in $)and Total Cost, ,(in $)are as follows: = (10q - 25)q = 2000 + 75q