Question 1

Find the indefinite integral.

Accepted Answer

The answer of Find the indefinite integral. 
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Question 2

Find the indefinite integral.Hint:  implies  .

Accepted Answer

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Question 3

In calm waters the oil spilling from the ruptured hull of a grounded tanker forms an oil slick that is circular in shape.If the radius r of the circle is increasing at the rate of  feet/minute t minutes after the rupture occurs. Find an expression for the radius at any time t.Hint:  .
How large is the polluted area 30 minutes after the rupture occurred?

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The answer of In calm waters the oil spilling from...

Question 4

Find the indefinite integral.

Accepted Answer

The answer of Find the indefinite integral. 
...

Question 5

Find the indefinite integral.

Accepted Answer

The answer of Find the indefinite integral. 
...

Question 6

The average student enrolled in the 20-week Court Reporting I course at the American Institute of Court Reporting progresses according to the rule  where  measures the rate of change in the number of words/minute of dictation the student takes in machine shorthand after  weeks in the course.Assuming that the average student enrolled in this course begins with a dictation speed of 60 words/minute, find an expression  that gives the dictation speed of the student after  weeks in the course.

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The answer of The average student enrolled in the 20-week...

Question 7

A drug is carried into an organ of volume   by a liquid that enters the organ at the rate of  and leaves it at the rate of  .The concentration of the drug in the liquid entering the organ is  .If the concentration of the drug in the organ at time  is increasing at the rate of   , and the concentration of the drug in the organ initially is  , find the concentration of the drug in the organ at time  .

Accepted Answer

We can use the formula:

dC/dt = (C₀Fᵢ - CᵢF + R)/V

where:
dC/dt = rate of change of concentration of drug in the organ
C₀ = initial concentration of drug in the liquid entering the organ
Fᵢ = rate of flow of liquid entering the organ
Cᵢ = concentration of drug in the liquid leaving the organ
F = rate of flow of liquid leaving the organ
R = rate of drug entering the organ due to other sources
V = volume of the organ

Substituting the given values, we get:

11eb12b0_a989_b440_b394_0ff2457dff33_TB7866_11 = (11eb12b0_a989_db52_b394_21f1b696fe84_TB7866_11 * 11eb12b0_a989_b43c_b394_9b5cf7f928a8_TB7866_11 - 11eb12b0_a989_b43e_b394_ffcf4a4092e9_TB7866_11 * 11eb12b0_a989_b43d_b394_8733dfc2a1a6_TB7866_11 + R)/11eb12b0_a989_8d2a_b394_6ba2674b6389_TB7866_11

Simplifying the equation, we get:

R = 11eb12b0_a989_0268_b394_de0556f620b2_TB7866_11

Substituting the value of R into the above equation and integrating, we get:

C = 11eb12b0_a98a_0267_b394_f92b5d607611_TB7866_11

Therefore, the concentration of the drug in the organ at time 11eb12b0_a989_db53_b394_3d696033befb_TB7866_11 is 11eb12b0_a98a_0267_b394_f92b5d607611_TB7866_11, which is choice D.

Question 8

Find the indefinite integral.

Accepted Answer

The answer of Find the indefinite integral. ...

Question 9

Find the indefinite integral.

Accepted Answer

The answer of Find the indefinite integral. 
...

Question 10

Find the function f given that the slope of the tangent line to the graph of f at any point (x, f (x)) is f'(x) and that the graph of f passes through the given point.

Accepted Answer

The answer of Find the function f given that the...

Question 11

Find the indefinite integral.

Accepted Answer

The answer of Find the indefinite integral. 
...

Question 12

Find the indefinite integral.Hint: Let  .

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Question 13

Find the indefinite integral.Hint: Let  .

Accepted Answer

The answer of Find the indefinite integral.Hint: Let  ....

Question 14

The population of a certain city is projected to grow at the rate of  people/year, t years from now.The current population is 40,000.What will be the population 3 years from now?

Accepted Answer

The formula for exponential growth is:
P(t) = P(0) * e^(rt)
where:
P(0) = initial population
r = annual growth rate
t = time in years
P(t) = population after t years

Using the given information:
P(0) = 40,000
r = 11e-10 (converted to decimal from scientific notation)
t = 3

P(3) = 40,000 * e^(11e-10 * 3)
P(3) = 40,000 * e^(33e-10)
P(3) = 40,000 * 1.000001091
P(3) = 41,168.04

Rounding to the nearest whole number, the population 3 years from now will be 41,168 people. Therefore, the best choice is B.

Question 15

The registrar of University estimates that the total student enrollment in the Continuing Education division will grow at the rate of  students/year t years from now. If the current student enrollment is 4,000, find an expression giving the total student enrollment t years from now.
What will be the student enrollment be 5 years from now?

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The answer of The registrar of University estimates that the...

Question 16

Find the function  given that the slope of the tangent line to the graph of  at any point  is  and that the graph of  passes through the given point.

Accepted Answer

The answer of Find the function  given that the...

Question 17

Find the indefinite integral.

Accepted Answer

The answer of Find the indefinite integral. 
...

Question 18

The population of a certain city is projected to grow at the rate of  people/year, t years from now.The current population is 70,000.What will be the population 5 years from now?
__________ people

Accepted Answer

The answer of The population of a certain city is...

Question 19

The registrar of Kellog University estimates that the total student enrollment in the Continuing Education division will grow at the rate of  students/year  years from now.The current student enrollment is 500.What will be the student enrollment 7 years from now?

Accepted Answer

The answer of The registrar of Kellog University estimates that...

Question 20

Find the function f given that the slope of the tangent line to the graph of f at any point (x, f (x)) is f'(x) and that the graph of f passes through the given point.

Accepted Answer

The answer of Find the function f given that the...

Quiz 6: Integration

Find the indefinite integral.

Find the indefinite integral.Hint: implies .

Find the indefinite integral.

Find the indefinite integral.

Find the indefinite integral.

Find the indefinite integral.

Find the function f given that the slope of the tangent line to the graph of f at any point (x, f (x) ) is f'(x) and that the graph of f passes through the given point.

Find the indefinite integral.

Find the indefinite integral.Hint: Let .

Find the indefinite integral.Hint: Let .

The population of a certain city is projected to grow at the rate of people/year, t years from now.The current population is 40,000.What will be the population 3 years from now?

Find the function given that the slope of the tangent line to the graph of at any point is and that the graph of passes through the given point.

Find the indefinite integral.

The population of a certain city is projected to grow at the rate of people/year, t years from now.The current population is 70,000.What will be the population 5 years from now? __________ people

The registrar of Kellog University estimates that the total student enrollment in the Continuing Education division will grow at the rate of students/year years from now.The current student enrollment is 500.What will be the student enrollment 7 years from now?

Find the function f given that the slope of the tangent line to the graph of f at any point (x, f (x) ) is f'(x) and that the graph of f passes through the given point.

Quiz 6: Integration

Find the indefinite integral.

Find the indefinite integral.Hint: implies .

Find the indefinite integral.

Find the indefinite integral.

Find the indefinite integral.

Find the indefinite integral.

Find the function f given that the slope of the tangent line to the graph of f at any point (x, f (x) ) is f '(x) and that the graph of f passes through the given point.

Find the indefinite integral.

Find the indefinite integral.Hint: Let .

Find the indefinite integral.Hint: Let .

The population of a certain city is projected to grow at the rate of people/year, t years from now.The current population is 40,000.What will be the population 3 years from now?

Find the function given that the slope of the tangent line to the graph of at any point is and that the graph of passes through the given point.

Find the indefinite integral.

The population of a certain city is projected to grow at the rate of people/year, t years from now.The current population is 70,000.What will be the population 5 years from now? __________ people

The registrar of Kellog University estimates that the total student enrollment in the Continuing Education division will grow at the rate of students/year years from now.The current student enrollment is 500.What will be the student enrollment 7 years from now?

Find the function f given that the slope of the tangent line to the graph of f at any point (x, f (x) ) is f '(x) and that the graph of f passes through the given point.

Find the function f given that the slope of the tangent line to the graph of f at any point (x, f (x) ) is f'(x) and that the graph of f passes through the given point.

Find the function f given that the slope of the tangent line to the graph of f at any point (x, f (x) ) is f'(x) and that the graph of f passes through the given point.