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stellarik [79]
3 years ago
14

Consider the given function and the given interval. f\(x\) = 2 sin\(x\) - sin\(2 x\) text(, ) [0 text(, ) pi] (a) Find the avera

ge value fave of f on the given interval. fave = Correct: Your answer is correct. (b) Find c such that fave = f(c). (Enter solutions from smallest to largest. If there are any unused answer boxes, enter NONE in the last boxes. Round the answers to three decimal places.)
Mathematics
1 answer:
Finger [1]3 years ago
4 0

a. The average value of f on the given interval is

\displaystyle f_{\rm ave}=\frac1{\pi-0}\int_0^\pi(2\sin x-\sin2x)\,\mathrm dx=\boxed{\frac4\pi}

b. Solve for c:

\dfrac4\pi=2\sin c-\sin2c\implies\boxed{c\approx1.238\text{ or }c\approx2.808}

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What is the solution to the inequality? 4x−5>19−8x
Nostrana [21]

Answer:

x>1.16

Step-by-step explanation:

Subtract 5 from each side to get 4x>14-8x

change the symbol from +8 to -8

4x> 14+ (-8x)

than add 8x to both sides

12x > 14

which would mean that x has to be greater than 1.16

x>1.16

7 0
3 years ago
The sum of three numbers is 95. The first number is 5 more than the third. The second number is 4 times the third. What are the
kotykmax [81]

Answer:

20, 60, 15

Step-by-step explanation:

Let the third number be n, then

The first number is n + 5 and the second number is 4n

Sum the 3 numbers and equate to 95, that is

n + 5 + 4n + n = 95 ← collect like terms on left side

6n + 5 = 95 ( subtract 5 from both sides )

6n = 90 ( divide both sides by 6 )

n = 15

Thus

The first number is 15 + 5 = 20

The second number is 4 × 15 = 60

The third number is 15

4 0
3 years ago
Wyatt is going to a carnival that has games and rides. Each game costs $1. 25 and each ride costs $2. 75. Wyatt spent $20. 25 al
Nonamiya [84]

In the carnival the number of games number of rides Wyatt went on is 3 and 6 respectively.

<h3>What is system of equation?</h3>

A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.

The number of unknown objects can be find using the system of solution.

Given information-

The cost of each game is $1.25.

The cost of each ride is $2.75.

Total amount of money spent by the Wyatt is $20.25.

The number of rides he went on is twice the number of games he played.

Suppose the number of games Wyatt played is x and the number of rides he went in the carnival is <em>y. </em>

As, the number of rides he went on is twice the number of games he played. Thus,

y=2x

Let the above equation as equation one.

As total amount of money spent by the Wyatt is $20.25 and The cost of each game is $1.25 and the cost of each ride is $2.75. Thus,

1.25x+2.75y=20.25\\

Put the value of y in the above equation from the equation one as,

1.25x+2.75(2x)=20.25\\1.25x+5.5x=20.25\\6.75x=20.25\\x=3

Thus the number of games he played is 3.

Put this value of <em>x </em>in the equation one as,

y=2\times3\\y=6

Thus the number rides Wyatt went on is 6.

Hence, In the carnival the number of games number of rides, Wyatt went on is 3 and 6 respectively.

Learn more about the system of equations here;

brainly.com/question/13729904

5 0
2 years ago
A driver travelled a distance of 864 km in 12 hours what is the speed of car
Elanso [62]

answer:

speed= 72 km - per • hour

8 0
3 years ago
Read 2 more answers
Consider the sphere enclosed by the cylinder. If the diameter of the sphere is 12 cm, what is the volume of the cylinder? A) 36π
kogti [31]
To find the volume of a cylinder , you will use the formula
V = Bh, where B is the area of the circular base.
Pi x r^2 x h
pi x 6^2 x 12
V = 432
The volume of the cylinder is 432pi cm³.
6 0
3 years ago
Read 2 more answers
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