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Anit [1.1K]
3 years ago
5

Find the average value of f(x)=e2x over the interval [2, 4].

Mathematics
1 answer:
shusha [124]3 years ago
5 0
<h2>Option B is the correct answer.</h2>

Step-by-step explanation:

We need to find average value of e^{2x} in [2,4]

Area of e^{2x} in [2,4] is given by

                  \int_{2}^{4}e^{2x}dx=\frac{1}{2}\times \left [ e^{2x}\right ]^4_2\\\\\int_{2}^{4}e^{2x}dx=\frac{1}{2}\times(e^8-e^4)=1463.18

Area of e^{2x} in [2,4] = 1463.18

Difference = 4 - 2 = 2

Average value = Area of e^{2x} in [2,4] ÷ Difference

Average value = 1463.18 ÷ 2

Average value = 731.59

Option B is the correct answer.

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The length of a rectangle is 5 inches more than twice a number.The width is 4 inches less than the same number.If the area of th
umka2103 [35]

Answer:

n = 5, n = -7/2

Step-by-step explanation:

2n + 5 = l

n - 4 = w

A = l × w = 15

(2n + 5)(n-4) = 15

2n^2 - 8n + 5n - 20 = 15

2n^2 -3n - 35 = 0

(2n + 7)(n - 5) = 0

2n + 7 = 0      or       n - 5 = 0

n = -7/2          or       n = 5

6 0
3 years ago
Ashton used 12.6 gallons of gasoline to drive his car on a weekend trip. he averaged 21.5 miles per gallon. about how many miles
7nadin3 [17]

Answer: 270.9 miles.

Step-by-step explanation:

The formula  we use here is :

\text{Distance=Speed * Number of gallons of gasoline}

Given : Ashton used 12.6 gallons of gasoline to drive his car on a weekend trip. he averaged 21.5 miles per gallon.

Then \text{Distance traveled }=12.6\times21.5=270.9\text{ miles}

Hence, he traveled 270.9 miles.

4 0
3 years ago
The problem is in the picture
Nitella [24]
The problem is the number by the side
7 0
3 years ago
Which statement is correct?
quester [9]

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Step-by-step explanation:

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3 0
3 years ago
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The position of a particle on the x-axis at time t, t &gt; 0, is s(t) = ln(t) with t measured in seconds and s(t) measured in fe
Mrrafil [7]

Answer:

C.<em> </em><em>The quotient of the natural logarithm of 2 and e.</em>

Step-by-step explanation:

The position of a particle on the x-axis at time t, t > 0, is given by

s(t) = \ln(t)

with t is in seconds and s(t) is in feet.

The rate of change is,

=\dfrac{f(b)-f(a)}{b-a}

So rate of change of position or average velocity, for e ≤ t ≤ 2e will be,

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=\dfrac{\ln2e-\ln e}{e}

=\dfrac{\ln\frac{2e}{e}}{e}

=\dfrac{\ln2}{e}

Therefore, option C is the correct answer.

8 0
3 years ago
Read 2 more answers
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