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SOVA2 [1]
2 years ago
14

Find the numbers b such that the average value of f(x) = 4 + 10x − 6x2 on the interval [0, b] is equal to 5.

Mathematics
1 answer:
Tju [1.3M]2 years ago
6 0

Answer:

  b = (5±√17)/4 ≈ {0.2192, 2.2808}

Step-by-step explanation:

The average on the interval is found from the integral ...

  \frac{1}{b}\int\limits^b_0 {(4+10x-6x^2)} \, dx =\frac{1}{b}(4b+5b^2-2b^3)\\\\=-2b^2+5b+4

We want the value of this integral to be 5, so we want to find b such that ...

  5 = -2b^2 +5b +4

  2b^2 -5b +1 = 0

  b^2 -5/2b = -1/2

  b^2 -5/2b +25/16 = -1/2 +25/16

  (b -5/4)^2 = 17/16

  b = (5±√17)/4

The average value of f(x) is 5 on the intervals ...

  [0, (5-√17)/4] and [0, (5+√17)/4]

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The city of Anville is currently home to 16000 people, and the population has been growing at a continuous rate of 4% per year.
Nesterboy [21]

Answer

After 13.15 years the population of both towns will become equal.

Step-by-step explanation:

Population of the city Anville is given by using the compound interest formula  

The formula of compound interest

A = p( 1+r/n)^n*t

using this we get

P1 = 16000 (1 +\frac{0.04}{1}) ^1*t

Population of the city of Brinker will be

P2 = 11000( 1  + \frac{0.07}{1}) ^1*t

now to make equal population in both towns

P1=P2

16000 (1 +\frac{0.04}{1}) ^1*t = 11000( 1  + \frac{0.07}{1}) ^1*t

(\frac{1.04}{1.07} )^t = \frac{11}{16}

t = 13.15 years

5 0
3 years ago
Find the two square roots of 81
pishuonlain [190]
9 is one of them I think
3 0
3 years ago
Suppose you are putting up a tent for a camping trip.
SSSSS [86.1K]

The length of the rope needed is 15 feet

Given the following parameters;

  • Height of the pole = 9 foot
  • The distance from the <u>rope away from the base </u>of the pole is 12 feet

Required

  • Length of the rope.

To get the length of the rope, you will use the pythagoras theorem expressed as:

  • c² = a² + b²

Substituting the given parameters:

c² = 9² + 12²

c² =81 + 144

c² = 225

c = √225

c = 15 feet

Therefore the length of the rope needed is 15 feet

Learn more on Pythagoras theorem here: brainly.com/question/231802

7 0
2 years ago
The ratio of yellow blue and red balloons is 2:3:2 respectively. If the total number is 28 is many yellow balloons are there
Phoenix [80]

Answer:

8

Step-by-step explanation:

The ratio of yellow balloons to the total is ...

... 2:(2+3+2) = 2/7

This fraction of 28 balloons is ...

... (2/7)·28 = 56/7 = 8 . . . . yellow balloons

8 0
2 years ago
PLEASE HELP!!!!!!!!<br> a2 - 10ab + 3b^2
Zielflug [23.3K]
Let's simplify step-by-step.

<span><span><span>a2</span>−<span><span>10a</span>b</span></span>+<span>3<span>b2

</span></span></span>There are no like terms.

Answer:

<span>=<span><span><span>a2</span>−<span><span>10a</span>b</span></span>+<span>3<span>b<span>2</span></span></span></span></span>
5 0
3 years ago
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