Question 1

Evaluate the following integral: $\int 7 e ^ { 4 x } d x$

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Question 2

Evaluate $\int e ^ { 4 x - 6 } d x$ .

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Question 3

Evaluate $\int x \sqrt { x ^ { 2 } + 6 } d x$ .

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Question 4

Sketch the region R and then use calculus to find the area of R. R is the region between the curve $y = x ^ { 3 }$ and the line y = 20x for x $\ge$  0.

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The answer of Sketch the region R and then use...

Question 5

Records indicate that t hours past midnight, the temperature at the local airport was $f ( t ) = - 0.3 t ^ { 2 } + 8 t + 10$ degrees Fahrenheit. What was the average temperature at the airport between 3:00 A.M. and noon? Round your answer to one decimal place, if necessary.

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The answer of Records indicate that t hours past midnight,...

Question 6

An investment will generate income continuously at the constant rate of $2,300 per year for 5 years. If the prevailing annual interest rate remains fixed at 11% compounded continuously, what is the present value of the investment?

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The answer of An investment will generate income continuously at...

Question 7

Money is transferred continuously into an account at the constant rate of $1,600 per year. Assume the account earns interest at the annual rate of 5% compounded continuously. Compute the future value of the income stream over a 16 year period.

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Question 8

Evaluate $\int x ^ { 7 } \left( x ^ { 4 } - 6 \right) ^ { 7 } d x$ .

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Question 9

Evaluate $$\int \frac { \ln 3 x } { x ^ { 2 } } d x$$ .

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Question 10

After t weeks, a charity is raising money at the rate of 5,000 t ln(t + 1) dollars per week. How much money is raised during the first 10 weeks? Round to the nearest ten dollars.

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Question 11

Evaluate $\int _ { 2 } ^ { \infty } \frac { 1 } { x \ln \sqrt { x } } d x$ .

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Question 12

Evaluate the improper integral: $$\int _ { 0 } ^ { \infty } x ^ { 5 } e ^ { - x ^ { 6 } / 4 } d x$$ Round to two decimal places, if necessary.

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The answer of Evaluate the improper integral: \[\int _ {...

Question 13

A certain nuclear power plant produces radioactive waste at the rate of 500 pounds per year. The waste decays exponentially at the rate of 1.5% per year. How many pounds of radioactive waste from the plant will be present in the long run? Round to two decimal places, if necessary.

Accepted Answer

The answer of A certain nuclear power plant produces radioactive...

Question 14

$$f ( x ) = \left\{ \begin{array} { l l } 
\frac { 7 } { x ^ { 8 } } & \text { if } x \geq 1 \
0 & \text { if } x < 1
\end{array} \right.$$ is a probability density function for a particular random variable X Use integration to find $P ( X \geq 3 )$

Accepted Answer

The answer of \[f ( x ) = \left\{ \begin{array}...

Question 15

The clothes dryers at a laundromat run for 45 minutes. You arrive at the laundromat and find that all of the dryers are being used. Use an appropriate uniform density function to find the probability that a dryer chosen at random will finish its cycle within 5 minutes.

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Question 16

Compute f (1, 5) if $f ( x , y ) = 7 x y ^ { 3 }$ .

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Question 17

Compute f_x for f (x, y) = 3x⁵y - 8x +e^xy.

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Question 18

Compute $f _ { x }$ for $f ( x , y ) = 9 x y ^ { 3 }$ .

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Question 19

Let f (x, y) = x ln(1 + 2x - 5y). Find $f _ { x x } ( x , y )$ .

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Question 20

A manufacturer with exclusive rights to a sophisticated new industrial machine is planning to sell a limited number of the machines to both foreign and domestic firms. The price the manufacturer can expect to receive for the machines will depend on the number of machines made available. (For example, if only a few of the machines are placed on the market, competitive bidding among prospective purchasers will tend to drive the price up.) It is estimated that if the manufacturer supplies x machines to the domestic market and y machines to the foreign market, the machines will sell for $60 - \frac { x } { 5 } + \frac { y } { 20 }$ thousand dollars apiece at home and for $50 - \frac { y } { 10 } + \frac { x } { 20 }$ thousand dollars apiece abroad. If the manufacturer can produce the machines at a cost of $45,000 apiece, how many should be supplied to each market to generate the largest possible profit?

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Quiz 8: Appendix: Algebra Review

Evaluate the following integral: $\int 7 e ^ { 4 x } d x$

Evaluate $\int e ^ { 4 x - 6 } d x$ .

Evaluate $\int x \sqrt { x ^ { 2 } + 6 } d x$ .

Sketch the region R and then use calculus to find the area of R. R is the region between the curve $y = x ^ { 3 }$ and the line y = 20x for x $\ge$ 0.

Records indicate that t hours past midnight, the temperature at the local airport was $f ( t ) = - 0.3 t ^ { 2 } + 8 t + 10$ degrees Fahrenheit. What was the average temperature at the airport between 3:00 A.M. and noon? Round your answer to one decimal place, if necessary.

An investment will generate income continuously at the constant rate of $2,300 per year for 5 years. If the prevailing annual interest rate remains fixed at 11% compounded continuously, what is the present value of the investment?

Money is transferred continuously into an account at the constant rate of $1,600 per year. Assume the account earns interest at the annual rate of 5% compounded continuously. Compute the future value of the income stream over a 16 year period.

Evaluate $\int x ^ { 7 } \left( x ^ { 4 } - 6 \right) ^ { 7 } d x$ .

Evaluate $\int \frac { \ln 3 x } { x ^ { 2 } } d x$ .

After t weeks, a charity is raising money at the rate of 5,000 t ln(t + 1) dollars per week. How much money is raised during the first 10 weeks? Round to the nearest ten dollars.

Evaluate $\int _ { 2 } ^ { \infty } \frac { 1 } { x \ln \sqrt { x } } d x$ .

Evaluate the improper integral: $\int _ { 0 } ^ { \infty } x ^ { 5 } e ^ { - x ^ { 6 } / 4 } d x$ Round to two decimal places, if necessary.

A certain nuclear power plant produces radioactive waste at the rate of 500 pounds per year. The waste decays exponentially at the rate of 1.5% per year. How many pounds of radioactive waste from the plant will be present in the long run? Round to two decimal places, if necessary.

$f ( x ) = \left\{ \begin{array} { l l } \frac { 7 } { x ^ { 8 } } & \text { if } x \geq 1 \\0 & \text { if } x < 1\end{array} \right.$ is a probability density function for a particular random variable X Use integration to find $P ( X \geq 3 )$

The clothes dryers at a laundromat run for 45 minutes. You arrive at the laundromat and find that all of the dryers are being used. Use an appropriate uniform density function to find the probability that a dryer chosen at random will finish its cycle within 5 minutes.

Compute f (1, 5) if $f ( x , y ) = 7 x y ^ { 3 }$ .

Compute f_x for f (x, y) = 3x⁵y - 8x +e^xy.

Compute $f _ { x }$ for $f ( x , y ) = 9 x y ^ { 3 }$ .

Let f (x, y) = x ln(1 + 2x - 5y). Find $f _ { x x } ( x , y )$ .

Quiz 8: Appendix: Algebra Review

Evaluate the following integral: ∫7e4xdx\int 7 e ^ { 4 x } d x∫7e4xdx

Evaluate ∫e4x−6dx\int e ^ { 4 x - 6 } d x∫e4x−6dx .

Evaluate ∫xx2+6dx\int x \sqrt { x ^ { 2 } + 6 } d x∫xx2+6​dx .

Sketch the region R and then use calculus to find the area of R. R is the region between the curve y=x3y = x ^ { 3 }y=x3 and the line y = 20x for x ≥\ge≥ 0.

An investment will generate income continuously at the constant rate of $2,300 per year for 5 years. If the prevailing annual interest rate remains fixed at 11% compounded continuously, what is the present value of the investment?

Money is transferred continuously into an account at the constant rate of $1,600 per year. Assume the account earns interest at the annual rate of 5% compounded continuously. Compute the future value of the income stream over a 16 year period.

Evaluate ∫x7(x4−6)7dx\int x ^ { 7 } \left( x ^ { 4 } - 6 \right) ^ { 7 } d x∫x7(x4−6)7dx .

Evaluate ∫ln⁡3xx2dx\int \frac { \ln 3 x } { x ^ { 2 } } d x∫x2ln3x​dx .

After t weeks, a charity is raising money at the rate of 5,000 t ln(t + 1) dollars per week. How much money is raised during the first 10 weeks? Round to the nearest ten dollars.

Evaluate ∫2∞1xln⁡xdx\int _ { 2 } ^ { \infty } \frac { 1 } { x \ln \sqrt { x } } d x∫2∞​xlnx​1​dx .

Evaluate the improper integral: ∫0∞x5e−x6/4dx\int _ { 0 } ^ { \infty } x ^ { 5 } e ^ { - x ^ { 6 } / 4 } d x∫0∞​x5e−x6/4dx Round to two decimal places, if necessary.

A certain nuclear power plant produces radioactive waste at the rate of 500 pounds per year. The waste decays exponentially at the rate of 1.5% per year. How many pounds of radioactive waste from the plant will be present in the long run? Round to two decimal places, if necessary.

The clothes dryers at a laundromat run for 45 minutes. You arrive at the laundromat and find that all of the dryers are being used. Use an appropriate uniform density function to find the probability that a dryer chosen at random will finish its cycle within 5 minutes.

Compute f (1, 5) if f(x,y)=7xy3f ( x , y ) = 7 x y ^ { 3 }f(x,y)=7xy3 .

Compute fx for f (x, y) = 3x5y - 8x +exy.

Compute fxf _ { x }fx​ for f(x,y)=9xy3f ( x , y ) = 9 x y ^ { 3 }f(x,y)=9xy3 .

Let f (x, y) = x ln(1 + 2x - 5y). Find fxx(x,y)f _ { x x } ( x , y )fxx​(x,y) .

Evaluate the following integral: $\int 7 e ^ { 4 x } d x$

Evaluate $\int e ^ { 4 x - 6 } d x$ .

Evaluate $\int x \sqrt { x ^ { 2 } + 6 } d x$ .

Sketch the region R and then use calculus to find the area of R. R is the region between the curve $y = x ^ { 3 }$ and the line y = 20x for x $\ge$ 0.

Evaluate $\int x ^ { 7 } \left( x ^ { 4 } - 6 \right) ^ { 7 } d x$ .

Evaluate $\int \frac { \ln 3 x } { x ^ { 2 } } d x$ .

Evaluate $\int _ { 2 } ^ { \infty } \frac { 1 } { x \ln \sqrt { x } } d x$ .

Evaluate the improper integral: $\int _ { 0 } ^ { \infty } x ^ { 5 } e ^ { - x ^ { 6 } / 4 } d x$ Round to two decimal places, if necessary.

Compute f (1, 5) if $f ( x , y ) = 7 x y ^ { 3 }$ .

Compute f_x for f (x, y) = 3x⁵y - 8x +e^xy.

Compute $f _ { x }$ for $f ( x , y ) = 9 x y ^ { 3 }$ .

Let f (x, y) = x ln(1 + 2x - 5y). Find $f _ { x x } ( x , y )$ .