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Yakvenalex [24]
3 years ago
13

What is the average rate of change of the function on the interval from x = 0 to x = 5?

Mathematics
2 answers:
Bumek [7]3 years ago
6 0

Answer:

from 0 to 7.5

Step-by-step explanation:

Just plug in (x)

f(5)=1/2(3)5

1 and 1/2*5

>>7.5<<

mamaluj [8]3 years ago
3 0

Answer:

m = 24.2

Step-by-step explanation:

The value of each extreme is presented below:

f(0) = \frac{1}{2}\cdot 3^{0}

f(0) = 0.5

f(5) = \frac{1}{2}\cdot 3^{5}

f(5) = 121.5

The average rate of change of the function is:

m = \frac{121.5 - 0.5}{5-0}

m = 24.2

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A cylindrical tank with radius 3 m is being filled with water at a rate of 4 m3/min. How fast is the height of the water increas
Fittoniya [83]

Height of the water increasing is at rate of  #(dh)/(dt)=3/(25 pi)m/(min)#

<h3>How to solve?</h3>

With related rates, we need a function to relate the 2 variables, in this case it is clearly volume and height. The formula is:

#V=pi r^2 h#

There is radius in the formula, but in this problem, radius is constant so it is not a variable. We can substitute the value in:

#V=pi (5m)^2 h#

Since the rate in this problem is time related, we need to implicitly differentiate wrt (with respect to) time:

#(dV)/(dt)=(25 m^2) pi (dh)/(dt)#

In the problem, we are given #3(m^3)/min# which is #(dV)/(dt)#.

So we need to substitute this in:

#(dh)/(dt)=(3m^3)/(min (25m^2) pi)=3/(25 pi)m/(min)#

Hence,  Height of the water increasing is at rate of  #(dh)/(dt)=3/(25 pi)m/(min)#

<h3>Formula used: </h3>

#V=pi r^2 h#

To Learn more visit:

brainly.com/question/4313883

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2 years ago
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Part A: Create a system of linear equations with no solution. In two or more complete sentences, explain the specific characteri
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y = 2x + 2

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