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Yuri [45]
3 years ago
8

Find the average value of f over region

Mathematics
1 answer:
yan [13]3 years ago
3 0
The area of D is given by:

\int\limits \int\limits {1} \, dA = \int\limits_0^7 \int\limits_0^{x^2} {1} \, dydx  \\  \\ = \int\limits^7_0 {x^2} \, dx =\left. \frac{x^3}{3} \right|_0^7= \frac{343}{3}

The average value of f over D is given by:

\frac{1}{ \frac{343}{3} }  \int\limits^7_0  \int\limits^{x^2}_0 {4x\sin(y)} \, dydx  = -\frac{3}{343}  \int\limits^7_0 {4x\cos(x^2)} \, dx  \\  \\ =-\frac{3}{343} \int\limits^{49}_0 {2\cos(t)} \, dt=-\frac{6}{343} \left[\sin(t)\right]_0^{49} \, dt=-\frac{6}{343}\sin49
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What is the average rate of change of the function over the interval x = 0 to x = 8?<br>​
serious [3.7K]

Answer:

The average rate of change is:

\frac{13}{161}

Step-by-step explanation:

The rational function given to us is;

f(x)=\frac{3x+4}{2x+7}

f(0)=\frac{3(0)+4}{2(0)+7}

f(0)=\frac{4}{7}

f(8)=\frac{3(8)+4}{2(8)+7}

f(0)=\frac{28}{23}=1

The average rate of change of this function from x=0 to x=8  is the slope of the secant line connecting:

(0,f(0)) and (8,f(8))

Average rate of change ==\frac{f(8)-f(0)}{8-0}

=\frac{\frac{28}{23}-\frac{4}{7} }{8}

=\frac{13}{161}

7 0
3 years ago
Given the pay rate and hours worked, determine the gross earnings, Federal taxes (assuming 18% of gross earnings), state taxes (
ella [17]

Answer:

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no. of hours worked = n

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Federal taxes = 18% of gross earnings

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State taxes = 4% of gross earnings

= 0.04(x*n)

Social security deduction = 7.05% of gross earnings

= 0.0705(x*n)

Total deductions = Federal taxes + State taxes +SSD

= 0.18(x*n) + 0.04(x*n) + 0.0705(x*n)

= 0.2905(x*n)

Net pay = Gross earnings - Total Deduction

Net pay = x*n - 0.2905(x*n)

Net pay = 0.7095(x*n)

3 0
3 years ago
Plz help me w this !!
larisa [96]

Answer:

sum of angles in atriangle=180°

Step-by-step explanation:

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3w=243°

w=81°

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3 years ago
Mr grain left for work at 7:15 am. twenty five mintutes later he aririved at his work. what time did mr giarmo arrive at his
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25 minutes (0:25) added to 7:15.

7:15 + 0:25 = 7:40
Also expressible as 15+25

He arrived at 7:40AM.
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3 years ago
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Answer:

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Step-by-step explanation:

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