Question 1

A division of Ditton Industries manufactures a deluxe toaster oven. Management has determined that the daily marginal cost function associated with producing these toaster ovens is given by  where  is measured in dollars/unit and  denotes the number of units produced. Management has also determined that the daily fixed cost incurred in the production is $800. Find the total cost incurred by Ditton in producing the first 700 units of these toaster ovens per day. What is the total cost incurred by Ditton in producing the 601st through 700th units/day?

Accepted Answer

The answer of A division of Ditton Industries manufactures a...

Question 2

Tempco Electronics, a division of Tempco Toys, manufactures an electronic football game. An efficiency study showed that the rate at which the games are assembled by the average worker t hours after starting work at 8 a.m. is  units/hour. How many units can the average worker be expected to assemble in the third hour of the morning shift? Answers are rounded to the nearest whole unit.

Accepted Answer

To find the number of units the average worker can be expected to assemble in the third hour of the morning shift, we need to plug in t=3 in the given equation:

Rate of assembling = 11e^(0.01t) units/hour 
= 11e^(0.01*3) units/hour 
= 11e^(0.03) units/hour

Using a calculator, we get: 
Rate of assembling = 11.34 units/hour (rounded to the nearest whole unit)

Therefore, the best choice is C, which gives the closest rounded value of 11.34 as 11eaa8b1_da99_78e5_b1b6_87fe5540eb42_TB6026_11 units.

Question 3

Evaluate the definite integral.

Accepted Answer

The answer of Evaluate the definite integral. 
...

Question 4

Evaluate the definite integral.

Accepted Answer

The answer of Evaluate the definite integral. 
...

Question 5

Find the area of the region under the graph of the function  on the interval  , using the fundamental theorem of calculus. Then verify your result using geometry.

Accepted Answer

The answer of Find the area of the region under...

Question 6

Evaluate the definite integral.

Accepted Answer

The answer of Evaluate the definite integral. 
...

Question 7

Annual sales (in millions of units) of hand-held computers are expected to grow in accordance with the function  where t is measured in years, with t = 0 corresponding to 1997. How many hand-held computers will be sold over the 6-year period between the beginning of 1997 and the end of 2002? Round your answer to two decimal places, if necessary.

Accepted Answer

The answer of Annual sales (in millions of units) of...

Question 8

U.S. Internet advertising revenue grew at the rate of  billion dollars/year between 2002 (t = 0) and 2006 (t = 4). The advertising revenue in 2002 was $6.3 billion.Find an expression giving the advertising revenue in year t.If the trend continued, what was the Internet advertising revenue in 2007?

Accepted Answer

The answer of U.S. Internet advertising revenue grew at the...

Question 9

Evaluate the definite integral.

Accepted Answer

The answer of Evaluate the definite integral. 
...

Question 10

Find the area of the region under the graph of the function  on the interval  .

Accepted Answer

The answer of Find the area of the region under...

Question 11

Annual sales (in millions of units) of hand-held computers are expected to grow in accordance with the function  where t is measured in years, with t = 0 corresponding to 1997. How many hand-held computers will be sold over the 6-year period between the beginning of 1997 and the end of 2002?

Accepted Answer

The function given is:

11eaa8b1_da9a_634e_b1b6_7366975d5052_TB6026_11

We need to find out the sales of handheld computers between 1997 to 2002, which is a 6-year period.

Let's put t=6 years in the given function:

11eaa8b1_da9a_8961_b1b6_c1ec07a1b437_TB6026_11

This gives us the expected sales for 6 years.

So, the answer is (C) 11eaa8b1_da9a_8961_b1b6_c1ec07a1b437_TB6026_11.

Question 12

In a recent pretrial run for the world water speed record, the velocity of the Sea Falcon II t seconds after firing the booster rocket was given by  ft/sec. Find the distance covered by the boat over the 20-second period after the booster rocket was activated. Hint: The distance is given by  .

Accepted Answer

The distance covered by the boat over the 20-second period after the booster rocket was activated is given by the definite integral of the velocity function from 0 to 20:

∫[0,20] 11e^(t/5) dt

Using integration by substitution (u = t/5, du = (1/5) dt), we get:

(55)∫[0,4] e^u du

= (55)(e^u)|[0,4]

= (55)(e^4 - e^0)

= 11eaa8b1_da9a_152c_b1b6_8fbf460044c1_TB6026_11

Therefore, the answer is C.

Question 13

Evaluate the definite integral.

Accepted Answer

The answer of Evaluate the definite integral. ...

Question 14

Find the area of the region under the graph of the function  on the interval  , using the fundamental theorem of calculus. Then verify your result using geometry.

Accepted Answer

The answer of Find the area of the region under...

Question 15

The number of Americans aged 45 to 54 (which stood at 25 million at the beginning of 1990) grew at the rate of  million people/year, t years from the beginning of 1990. How many Americans aged 45 to 54 were added to the population between 1990 and the year 1995? Give your answer to one decimal place.

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Question 16

Evaluate the definite integral.

Accepted Answer

The answer of Evaluate the definite integral. ...

Question 17

The population aged 65 years old and older (in millions) from 2000 to 2050 is projected to be  where t is measured in decades, with  corresponding to 2000. What will be the average population aged 65 years and older over the years from 2000 to 2050? (Hint: The average population is given by  . Multiply the integrand by  and then use the method of substitution.) Round your answer to one decimal place.

Accepted Answer

The answer of The population aged 65 years old and...

Question 18

The number of Americans aged 45 to 54 (which stood at 25 million at the beginning of 1990) grew at the rate of  million people/year, t years from the beginning of 1990. How many Americans aged 45 to 54 were added to the population between 1990 and the year 1999? Please give your answer to one decimal place.

Accepted Answer

The answer of The number of Americans aged 45 to...

Question 19

Evaluate the definite integral.

Accepted Answer

The answer of Evaluate the definite integral. 
...

Question 20

The population aged 65 years old and older (in millions) from 2000 to 2050 is projected to be  where t is measured in decades, with  corresponding to 2000. What will be the average population aged 65 years and older over the years from 2000 to 2050?
(Hint: The average population is given by  . Multiply the integrand by  and then use the method of substitution.) Please round your answer to one decimal place.
__________ million

Accepted Answer

The answer of The population aged 65 years old and...

Quiz 6: Integration

Evaluate the definite integral.

Evaluate the definite integral.

Find the area of the region under the graph of the function on the interval , using the fundamental theorem of calculus. Then verify your result using geometry.

Evaluate the definite integral.

U.S. Internet advertising revenue grew at the rate of billion dollars/year between 2002 (t = 0) and 2006 (t = 4) . The advertising revenue in 2002 was $6.3 billion.Find an expression giving the advertising revenue in year t.If the trend continued, what was the Internet advertising revenue in 2007?

Evaluate the definite integral.

Find the area of the region under the graph of the function on the interval .

Annual sales (in millions of units) of hand-held computers are expected to grow in accordance with the function where t is measured in years, with t = 0 corresponding to 1997. How many hand-held computers will be sold over the 6-year period between the beginning of 1997 and the end of 2002?

In a recent pretrial run for the world water speed record, the velocity of the Sea Falcon II t seconds after firing the booster rocket was given by ft/sec. Find the distance covered by the boat over the 20-second period after the booster rocket was activated. Hint: The distance is given by .

Evaluate the definite integral.

Find the area of the region under the graph of the function on the interval , using the fundamental theorem of calculus. Then verify your result using geometry.

The number of Americans aged 45 to 54 (which stood at 25 million at the beginning of 1990) grew at the rate of million people/year, t years from the beginning of 1990. How many Americans aged 45 to 54 were added to the population between 1990 and the year 1995? Give your answer to one decimal place.

Evaluate the definite integral.

Evaluate the definite integral.