Find the point(s) at which the function f(x) = 5 - 2x equals its average value on the interval [0,4]. The function equals its average value at x=

Answers

Answer 1

Thus, the point(s) at which f(x) = 5 - 2x equals its average value on the interval [0,4] is x=5/2.

To find the point(s) at which the function f(x) = 5 - 2x equals its average value on the interval [0,4], we first need to find the average value of the function on this interval. The formula for the average value of a function f(x) on an interval [a,b] is:

average value = (1/(b-a)) * ∫[a,b] f(x) dx

In this case, a=0 and b=4, so the average value of f(x) on [0,4] is:

average value = (1/(4-0)) * ∫[0,4] (5-2x) dx
average value = (1/4) * [5x - x^2] from 0 to 4
average value = (1/4) * [(5(4) - 4^2) - (5(0) - 0^2)]
average value = (1/4) * (0)
average value = 0

So the average value of f(x) on [0,4] is 0. Now we need to find the point(s) where f(x) equals 0. We can set the function equal to 0 and solve for x:

5 - 2x = 0
2x = 5
x = 5/2

So the function f(x) equals its average value of 0 at x=5/2. Therefore, the point(s) at which f(x) = 5 - 2x equals its average value on the interval [0,4] is x=5/2.

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Related Questions

A cone has a volume of 47.1 cm³ and a radius of 3 cm what is its height?

Answers

Radius of cone ( r ) = 3 cm,

Curved surface area of a cone= 47.1 cm²

Curved surface area of a cone= πrl

47.1 = πrl

47.1 = 3.14 × 3 × l

l = 47.1 / (3.14 × 3)

l = 15.7 / 3.14= 1570/314= 5 cm

slant height (l) = 5 cm

Height of a cone (h) = √(l²) - (r²)

h = √ 5² -3²

h = √ 25 - 9 = √ 16 = 4 cm

h = 4 cm

Volume of cone= ⅓(πr²h)

= ⅓(3.14 × 3 × 3 × 4)

= 3.14 × 12= 37.68 cm³

Hence, the volume of a cone is 37.68 cm³.

On a certain hot summer's day, 234 people used the public swimming pool. The
daily prices are $1.25 for children and $2.00 for adults. The receipts for admission totaled
$435.00. How many children and how many adults swam at the public pool that day?

Answers

Answer44 children and 190 adults

Step-by-step explanation:

Find the missing length indicated.

Pls Help

Answers

none of them are correct

Santino pays $36.85 for eleven 10-count boxes of granola bars. How much does 1 box of granola bars cost?

Answers

Answer:

One box of granola bars costs $3.35.

Step-by-step explanation:

36.85/11=3.35

It took Hank 3.4 hours to travel 124 miles. At that rate, how long will it take Hank to travel 310 miles?

Answers

Answer: Time = 8.5 hours

Step-by-step explanation:

Step 1

Speed = distance / time

Distance traveled by Hank = 124 miles

Time = 3.4 hrs

Speed= Distance / Time

= 124/ 3.4 = 36.47 miles per hour

Step 2

At this same rate of speed =36.47 miles per hour, if he travels 310 miles, he will spend=

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Time = 310/ 36.47

Time =8.5 hours

I need help plz......I'll give brainliest:
The sum of two numbers is 44. The smaller number is 12 less than the larger number. What are the numbers?

Answers

x+(12+x)=44

2x+12=44

2x=32

x=32/2

x=16

The two numbers are 16, 28

Hope I helped :)

Write the linear equation in slope-intercept form given the following:
(-3, 7) and (6, -8)

Answers

Answer:

y = - [tex]\frac{5}{3}[/tex] x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 7) and (x₂, y₂ ) = (6, - 8)

m = [tex]\frac{-8-7}{6+3}[/tex] = [tex]\frac{-15}{9}[/tex] = - [tex]\frac{5}{3}[/tex] , then

y = - [tex]\frac{5}{3}[/tex] x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (6, - 8) , then

- 8 = - 10 + c ⇒ c = - 8 + 10 = 2

y = - [tex]\frac{5}{3}[/tex] x + 2 ← equation of line

if 2x + 16 = -6x what is x

Answers

Answer:

x = -2

Step-by-step explanation:

Answer:

x is -2

Step-by-step explanation:

8x+16=0

subtract 16 from both sides

8x=-16

Divide each term by 8 and simplify

x=-2

Susan graphed a system of equations for the lines y = 3x + 1 and y = 3x - 10. Which statement is true about Susan's lines?
The lines intersect once at a right angle because they are perpendicular.
The lines intersect at all points because they are the same line.
The lines intersect three times because each has a slope of three.
The lines do not intersect because they are parallel and have different y-intercepts.

Answers

Answer: The lines do not intersect because they are parallel and have different y-intercepts.

Step-by-step explanation:

Which represents the solution(s) of the graphed system of equations, y = x2 – 2x and y = –2x – 1?

(1, –1)
(0, 0) and (0, –1)
(0, 0) and (2, 0)
no solutions

Answers

Hopefully someone comes along and helps, 0,0 - 732 + 3

Answer:

D) no solutions :D

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Hank's age is 5 more than three times John's age. Hank
is 29 years old. How old is John?

Answers

8. Because 29-5 =24 and 24/3 =8

choose the answer that represents the product below as an exponential expression*

Answers

Answer:

Step-by-step explanation:

the bases are the same and according to exponential laws exponents of the same base are added

Answer:

2/3z=-6

Help please!!

Answers

Answer:

z = -9

Step-by-step explanation:

what are all the sums and differences of 3/4?

Answers

Answer:

1/2 + 2/4

11/12 - 1/6

3/5 + 3/20

7/8 - 1/2

Step-by-step explanation:

If the cos 90° = 0, then the sin 0° = _____.

pls help

Answers

Answer:

I think its 0

Step-by-step explanation:

Answer:

This one too clicked by me

What is the multiplicative rate of change for the exponential function f(x)= 3 (2/3)^-x
A. 0.4
B. 2.5
C. 0.6
D. 1.5

Answers

Answer:

C basta Yan ang sagot HAHAHA dko mapicturan solution ko e

Step-by-step explanation:

ano ba yan arte nyo sabing yan ang sagot e

Answer:

c 0.6

Step-by-step explanation:

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Answers

Answer:

Désolé mec mais je n'ai pas compris ta question

Solve for n:
1-5|n-9|=-74

I need answer by 12:10, please help!!!

Answers

Answer:

[tex]n=-6, 24[/tex]

Step-by-step explanation:

We are given:

[tex]1-5|n-9|=-74[/tex]

Subtract 1 from both sides:

[tex]-5|n-9|=-75[/tex]

Divide both sides by -5:

[tex]|n-9|=15[/tex]

By definition of absolute value:

[tex](n-9)=15\text{ or } -(n-9)=15[/tex]

Solve for each case:

[tex]n=24\text{ or } n=-15+9=-6[/tex]

Therefore, our two solutions are:

[tex]n=-6, 24[/tex]

A spinner has 3 sections of different sizes. The sections are orange, purple, and green. 1/4 of the spinner is orange. 7/12 of the spinner is purple. Which fraction of the spinner is green?

Answers

Answer: it would be 2/3

Step-by-step explanation:

Radium-226 has a half-life of 1660 years. How many years does it take a radium sample to decay to 55% of the original amount? Round your answer to the nearest year.

Answers

Answer:

1432 years

Step-by-step explanation:

A(t) = I(0.5)^t/t1/2

Where t1/2 = half life = 1660

Final amount, A(t) = 0.55 of its original amount =. 0.55I

Hence, we have

0.55I = I(0.5)^t/1660

Take the log of both sides

Log(0.55) = log(0.5)^t/1660

t/1660 = log(0.55) / log(0.5)

t/1660 = 0.8624964

t = 0.8624964 * 1660

t = 1431.7441

t = 1432(nearest whole number)

There are three rows of VIP seats in each section. Each row
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are there in all?

Answers

Answer:

The answer is 576 seats

Step-by-step explanation:

3 rows x 12 seats = 36 seats in one section

36 seats in one section x 16 sections = 576 seats

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Using the given equation find the missing coordinates of the points and then find the slope of the line for the equation.
y=3.5x+4; A(...;5), B(10;...)

Answers

Okay so,

A (0.2875; 5), B (10; 39)

THE SLOPE IS 3.5

Are 0.34 and 3/4 equivalent? Please explain your answer In complete sentences.

Answers

no

when 3 divided by 4 is converted into a decimal, it is 0.75 which does not equal 0.34

0.34 can also be written as 34/100
and 3/4 can be written as 75/100

therefore 0.34 and 3/4 are not equivalent

broooo plzzz helpppp

Answers

Answer:

3 3/5 + 1 1/4 = 4 17/20

7/8 + 1/12 = 23/24

8/9 - 2/5 = 22/45

5 1/4 - 2 2/3 = 2 7/12

Step-by-step explanation:

3 3/5 + 1 1/4

First convert into improper fractions

= 18/5 + 5/4

Now find the common denominator

72/20 + 25/20 =

97/20

Now simplify

4 17/20

Next problem:

7/8 + 1/12

find the common denominator

21/24 + 2/24 =

23/24

Next problem:

8/9 - 2/5

find the common denominator

40/45 - 18/45 =

22/45

Next problem:

5 1/4 - 2 2/3

First convert into improper fractions

21/4 - 8/3

find the common denominator

63/12 - 32/12 =

31/12

Now simplify

2 7/12

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