Question 1

If y' = 6x - 3 and y(2)= 4,then y =
A) 6.
B) 3  - 3x.
C) 3  - 3x + 2.
D) 3  - 3x - 2.
E) 6  - 3x + 2.

Accepted Answer

Using the given initial condition, we can find the constant of integration:

y' = 6x - 3

Integrating with respect to x:

y = 3x^2 - 3x + C

Using y(2) = 4 to solve for C:

4 = 3(2)^2 - 3(2) + C
C = -2

Therefore, the solution to the differential equation is:

y = 3x^2 - 3x - 2

which matches choice D.

Question 2

A manufacturer of a product has a marginal cost function given by  where c is the total cost (in dollars)of producing q units of a product.If fixed costs are $30,000,then the total cost of producing 30 units is
A) $66,600.
B) $66,700.
C) $66,800.
D) $66,900.
E) $67,000.

Accepted Answer

The answer of A manufacturer of a product has a...

Question 3

If the marginal revenue for a manufacturer's product is  
= 700 - 6q - 8  
,find the demand function.

Accepted Answer

The answer of If the marginal revenue for a manufacturer's...

Question 4

If  = 3 
- 3 and y(0)= 8,then y(1)=
A) 6.
B) 0.
C) 12.
D) 8.
E) 4.

Accepted Answer

The answer of If  = 3 
- 3 and...

Question 5

The marginal cost function for a manufacturer's product is given by  
where c is in dollars.Find the cost function if fixed costs are $100.

Accepted Answer

The answer of The marginal cost function for a manufacturer's...

Question 6

Determine:

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The answer of Determine: ...

Question 7

If the marginal cost for a company is f(x)= 6,find

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The answer of If the marginal cost for a company...

Question 8

Determine:

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The answer of Determine: ...

Question 9

A manufacturer of a product has a marginal revenue function given by  =200 + 70q - 3 
)The demand function for the product is given by
A) p =  - 6.
B) p = 70 - 6q.
C) p = 200q + 35  - 
D) p = 200 + 35q - 
E) p = 200q + 35  -

Accepted Answer

Marginal revenue (MR) is given by the derivative of the total revenue function (TR). 
Here, MR = 70 - 6q
Demand (D) is given by the inverse of the total revenue function (TR). 
Therefore, D = (TR)^(-1) -> p = TR/q
From the given marginal revenue function, we can obtain the total revenue function as follows:
MR = d(TR)/dq = 70 - 6q
Integrating both sides with respect to q, we get:
TR = 70q - 3q^2 + C
Using the demand equation p = TR/q, and given that at quantity 0, the price is 20, we can find the constant C as follows:
20 = TR(0)/0 -> C = 20
Therefore, the total revenue function is: TR = 70q - 3q^2 + 20
Substituting this in the demand equation, we get:
p = (70q - 3q^2 + 20)/q
Simplifying, we get:
p = 200/3 - (100/q) + 35q
This matches the form p = 200 + 35q - 10q^(-1), which is option D.

Question 10

For a group of rats that were fed a particular diet,the rate of change of the average weight gain G (in grams)of a rat with respect to the percent P of yeast in the diet is  
If G = 36 when P = 8,find G.

Accepted Answer

The answer of For a group of rats that were...

Question 11

If y'' =  
- 2,and y'(0)= 3 and y(0)= 4,find y.

Accepted Answer

The answer of If y'' =  
- 2,and y'(0)=...

Question 12

Determine

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The answer of Determine ...

Question 13

Find y subject to the given conditions: y'' = 6x - 2; y'(1)= 2; y(1)= 2.

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The answer of Find y subject to the given conditions:...

Question 14

Determine:

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The answer of Determine: ...

Question 15

The marginal cost function for a manufacturer's product is  
= 0.0003  
- 0.03q + 4,where c is in dollars.If fixed costs are $5000,determine: (a)the manufacturer's total cost function; (b)the manufacturer's average cost function.

Accepted Answer

The answer of The marginal cost function for a manufacturer's...

Question 16

If the marginal revenue function for a manufacturer's product is  
= 1000 - 10q - 6  
,find the demand function.

Accepted Answer

The answer of If the marginal revenue function for a...

Question 17

If  
=  
- 4x + 1 and y(3)= 8,find y.

Accepted Answer

The answer of If  
=  
- 4x +...

Question 18

If y' = 6  
- 4x - 3 and y(1)= 2,find y.

Accepted Answer

The answer of If y' = 6  
- 4x...

Question 19

Find y subject to the given conditions: y'' =  
  
+ 5; y'(0)= 1; y(0)= 5

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The answer of Find y subject to the given conditions:...

Question 20

If y'' = 6x + 2 and y'(1)= 2 and y(1)= 2,find y.

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The answer of If y'' = 6x + 2 and...

Quiz 15: Integration

If y' = 6x - 3 and y(2) = 4,then y =

A manufacturer of a product has a marginal cost function given by where c is the total cost (in dollars) of producing q units of a product.If fixed costs are $30,000,then the total cost of producing 30 units is

If the marginal revenue for a manufacturer's product is = 700 - 6q - 8 ,find the demand function.

If = 3 - 3 and y(0) = 8,then y(1) =

The marginal cost function for a manufacturer's product is given by where c is in dollars.Find the cost function if fixed costs are $100.

Determine:

If the marginal cost for a company is f(x)= 6,find

Determine:

A manufacturer of a product has a marginal revenue function given by =200 + 70q - 3 ) The demand function for the product is given by

For a group of rats that were fed a particular diet,the rate of change of the average weight gain G (in grams)of a rat with respect to the percent P of yeast in the diet is If G = 36 when P = 8,find G.

If y'' = - 2,and y'(0)= 3 and y(0)= 4,find y.

Determine

Find y subject to the given conditions: y'' = 6x - 2; y'(1)= 2; y(1)= 2.

Determine:

The marginal cost function for a manufacturer's product is = 0.0003 - 0.03q + 4,where c is in dollars.If fixed costs are $5000,determine: (a)the manufacturer's total cost function; (b)the manufacturer's average cost function.

If the marginal revenue function for a manufacturer's product is = 1000 - 10q - 6 ,find the demand function.

If = - 4x + 1 and y(3)= 8,find y.

If y' = 6 - 4x - 3 and y(1)= 2,find y.

Find y subject to the given conditions: y'' = + 5; y'(0)= 1; y(0)= 5

If y'' = 6x + 2 and y'(1)= 2 and y(1)= 2,find y.