Find the average value fave of the function f on the given interval.f(x) = x2/(x3 + 7)2, [−1, 1]

Answers

Answer 1

The average value of the function f(x) = x2/(x3 + 7)2 on the interval [-1,1] is 0.

To find the average value of the function f(x) = x2/(x3 + 7)2 on the interval [-1,1], first we need to calculate the integral of f(x) from -1 to 1. The integral of f(x) is

∫[-1,1]f(x)dx = ∫[-1,1] (x2/(x3 + 7)2) dx.

Using the substitution method, we can break down this integral into the integral of two easier expressions.

Let u = x3 + 7, then du = 3x2 dx

Therefore, the integral is equal to

∫[-1,1] (x2/(x3 + 7)2) dx = ∫[-1,1] (x2/u2)du = (1/3)∫[7,8] (u-7) du

This integral can be solved by integrating by parts. Let v = u-7 and dv = du

Therefore,

(1/3)∫[7,8] (u-7) du = (1/3)[uv - ∫[7,8] vdu]

= (1/3)[(u-7)u - ∫[7,8] (1/3)x2 dx]

= (1/3)[(u-7)u - (1/3)[x3/3]|[7,8]]

= (1/3)[(u-7)u - (1/3)(8/3 - 7/3)]

= (1/3)(7/2 - 7/2)

= 0

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Related Questions

Last week Miss Karen had 50 dollars. She went to clean a couple houses and now has
76 dollars. How much money did Miss Karen make cleaning houses?|

This has to be converted into an algebraic expression.
Please help!

Answers

50 + x = 76
x = 76 - 50
x = 26
She made 26$ cleaning houses.

Some of the steps in the derivation of the quadratic formula are shown.

Step 4: StartFraction negative 4 a c + b squared Over 4 a EndFraction = a ( x + StartFraction b Over 2 a EndFraction) squared

Step 5: (StartFraction 1 Over a EndFraction) StartFraction b squared minus 4 a c Over 4 a EndFraction = (StartFraction 1 Over a EndFraction) a (x + StartFraction b Over 2 a EndFraction) squared

Step 6: StartFraction b squared minus 4 a c Over 4 a squared EndFraction = ( x + StartFraction b Over 2 a EndFraction) squared

Step 7: StartFraction plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction = x + StartFraction b Over 2 a EndFraction

Answers

A statement which best explains why the expression cannot be rewritten as during the next step include the following: C. the square root of terms separated by addition and subtraction cannot be calculated individually.

What is a quadratic equation?

In Mathematics, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph. In Mathematics, the standard form of a quadratic equation is given by;

ax² + bx + c = 0

Mathematically, the quadratic formula is modeled or represented by this mathematical expression:

\(x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\)

In conclusion, it is very important to note that the square root of x-terms that are separated by addition and subtraction should not be calculated individually when solving a quadratic equation by using the quadratic formula.

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Complete Question:

Which best explains why the expression cannot be rewritten as during the next step?

Negative values, like −4ac, do not have a square root.

The ± symbol prevents the square root from being evaluated.

The square root of terms separated by addition and subtraction cannot be calculated individually.

The entire term b2 − 4ac must be divided by 2a before its square root can be determined.

Answer:

it is C

Step-by-step explanation:

i did it on e2020

why is the term ""arc"" used to describe units of measure for angular distance

Answers

The term "arc" is used to describe units of measure for angular distance because it refers to the length of an arc on a circle.

Angular distance is the measure of the separation between two points on a circle or an arc. The term "arc" is used to describe this measure because it refers to the length of the arc connecting the two points on the circle.

This length is a fraction of the circumference of the circle and is proportional to the angle between the two points. The use of the term "arc" in this context is a nod to the geometric origins of angular measurement, which is based on the properties of circles and their angles.

The most common units of angular measurement are degrees, minutes, and seconds, which are all based on the division of a circle into 360 equal parts (degrees) and further subdivisions (minutes and seconds).

Other units of angular measurement, such as radians and gradians, are also based on the properties of circles and their angles.

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Can someone please help me im giving 30 points

Can someone please help me im giving 30 points

Answers

Answer:

46m

Step-by-step explanation:

set river width=x,

x/23.7=56/29

x=56÷29x23.7 ≈ 46 m

PLEASE HELP
A boutique in Hampton specializes in leather goods for men. Last month, the company sold 36 wallets and 11 belts, for a total of $3,295. This month, they sold 91 wallets and 10 belts, for a total of $7,599. How much does the boutique charge for each item?


Wallets: $__


Belts: $__

Answers

The amount charged by the boutique for each item is given as follows:

Wallet: $79.Belt: $41.

How to obtain the price of each item?

The price of each item is obtained considering a system of equations, for which the variables are given as follows:

Variable x: cost of a wallet.Variable y: cost of a belt.

From the description, the equations are given as follows:

36x + 11y = 3295.91x + 10y = 7599.

Simplifying the first equation by 11, we have that:

3.272727x + y = 299.5454

y = 299.5454 - 3.272727x

Replacing on the second equation, the cost of a wallet is given as follows:

91x + 10(299.5454 - 3.272727x) = 7599

58.2728x = 4603.5455

x = 4603.5455/58.2728

x = 79.

Then the cost of a belt is obtained as follows:

y = 299.5454 - 3.272727(79)

y = $41.

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is the integer k divisible by 4 ? (1) 8k is divisible by 16. (2) 9k is divisible by 12.

Answers

Yes , the integer k is divisible by 4 and statement (1) alone is sufficient to determine that k is divisible by 4.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

To determine if the integer k is divisible by 4, let's analyze the given statements:

Statement (1): 8k is divisible by 16.

This means that 8k is a multiple of 16. Since 16 is divisible by 4, we can conclude that k must be divisible by 4 as well. Therefore, statement (1) alone is sufficient to determine that k is divisible by 4.

8k = 16

k = 2

b)

This statement does not provide direct information about the divisibility of k by 4. While 12 is divisible by 4, the fact that 9k is divisible by 12 does not guarantee that k itself is divisible by 4.

9k = 12

k = 12/9

k = 4/3

So , it is not an integer

In conclusion, statement (1) alone is sufficient to determine that k is divisible by 4. Statement (2) is not sufficient on its own.

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Find the radius of the circle below. Round your answer to the nearest tenth. You mustshow work for full credit.A= 31.2 cm 2.256A

Find the radius of the circle below. Round your answer to the nearest tenth. You mustshow work for full

Answers

The given information is:

- The area of the sector of the circle is 31.2 cm^2.

- The exterior of the sector angle is 256°.

The area of the sector is given by the formula:

\(A=(\frac{\theta}{360\degree})*\pi r^2\)

Where theta is the sector angle and r is the radius of the circle.

The whole circle measures 360°, so the sector angle can be found as follows:

\(\begin{gathered} \theta+256\degree=360\degree \\ \theta=360\degree-256\degree \\ \theta=104\degree \end{gathered}\)

Now, replace theta and the area value in the formula to solve for r:

\(\begin{gathered} 31.2=\frac{104}{360}*\pi r^2 \\ \\ 31.2*\frac{360}{104}=\pi r^2 \\ \\ 108=\pi r^2 \\ \\ r^2=\frac{108}{\pi} \\ \\ r^2=34.4 \\ \\ r=\sqrt{34.4} \\ \\ r=5.9 \end{gathered}\)

The radius of the circle is 5.9 cm.

the cell phone bill recorded that Jeremiah sent 532 text messages last week. On average how many text messages did he send each day?​

Answers

Answer:

76 messages

Step-by-step explanation:

532 divided by 7 = 76

Answer:

76 Texts

Step-by-step explanation:

Amount of texts/Days = 532/7 = 76

Please help I need it in a hurry

Please help I need it in a hurry

Answers

Answer:

Option D: Thse two matrices cannot be added

Step-by-step explanation:

Two matrices can be added (or subtracted) only if they have the same dimensions

The dimension of a matrix is expressed as m x n where m = number of rows and n = number of columns

Dimension of the left matrix in the expression is 3 rows x 3 columns or
3 x 3

Dimension of the right matrix is 3 rows and 2 columns or 3 x 2

Since the dimensions are different addition is not possible

Correct Answer:

Option D: Thse two matrices cannot be added

$3.79 per pound for chicken wings OR $20.25 for a 5-pound bag

Answers

Answer:29.04

Step-by-step explanation:

3.79+20.25=24.04

24.04+5=29.04

Jeff can paint 28 square feet every 15 minutes. Angela can paint 115 square feet every hour. Who can paint faster, and by how many square feet per hour?

Answers

Answer:

Angela by 3 sf per hour

Step-by-step explanation:

60÷15=4

28×4=112

115-112=3

Which number is larger? (1 mark)

0.67 or
2/3

Answers

Answer:

0.67

Step-by-step explanation:

2/3= to 0.66 which means 0.67 would be technally larger than 0.66

How can 26n - 7m + 4 (10m—6m) be rewritten

Answers

Answer:

26m - (11m) 4m

Step-by-step explanation:

Margo ran a stop sign and crashed into another car as they were crossing the intersection. margo had two other passengers in her car. in the car that she hit there were 3 passengers. two sued margo for damages and medical expenses. they were awarded $250,000 each. the third person did not sue but had $54,000 in medical expenses from the accident. todd in margo's car always was hurt and had $36,000 in medical expenses. there was also damage to a fence, the other car, and a lawn for a total of $24,000. margo pays for the following car insurance: 200/500/20, pip: 40,000. what is the total cost the insurance company will pay and what is the total cost to margo?

Answers

The total cost that the insurance company will pay is $584,000.

What is insurance?

Insurance is an agreement between two parties, an insurer and an insured, wherein the insurer agrees to provide financial protection to the insured in exchange for a payment of a premium. Insurance is a form of risk management and helps provide peace of mind. It helps protect individuals, businesses, and organizations from unexpected losses or damages and can be used to cover the costs of medical expenses, property damage, and other financial losses. Insurance can also provide coverage for damage caused by natural disasters and other catastrophic events.

This amount is made up of the two awards to the passengers in the other car ($500,000) plus the medical expenses of the third person in the other car and Todd in Margo's car ($54,000 + $36,000). The remaining $24,000 in damages is not covered by Margo's insurance policy and will thus have to be paid by Margo herself.

The total cost to Margo is therefore $608,000. This is the sum of the insurance company's payout ($584,000) and the remaining $24,000 in damages which Margo will have to pay out of pocket.

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WHOEVER ANSWERS FIRST AND CORRECTLY GETS BRAINLIEST!

9y + 2 = 58; {4,5,6}
Please show your work.

A, Y=4
B, Y=5
C, Y=6

Answers

Answer:

Im pretty sure c Y=6

Step-by-step explanation:

9y+2=58

Subtract 2 from both sides.

9y=58−2

Subtract 2 from 58 to get 56.

9y=56

Divide both sides by 9.

y= 56/ 9  Which is Also 6.2

The first term of a sequence is 13 The term -to-term rule is take away 5 work out the 4th term

Answers

Answer:

a₄ = - 2

Step-by-step explanation:

to calculate a term in the sequence subtract 5 from the previous term

give first term a₁  = 13 , then

a₂ = a₁ - 5 = 13 - 5 = 8

a₃ = a₂ - 5 = 8 - 5 = 3

a₄ = a₃ - 5 = 3 - 5 = - 2

i need to spend my points so

i need to spend my points so

Answers

Answer:

Its 3 but why spend points?

Answer:

thanks hebehebebe Urdu itching frisk OCD bi ixixixixixiwjsnsbdbbddbbdbdbsbsjjzuhzhndj

what shape in this lesson can be used to prove statements about triangles?

Answers

Answer: parallelograms

cosec4A-1/cot4a=1+2tan2a​

Answers

Answer:

See image for answer.

cosec4A-1/cot4a=1+2tan2a

Oak street and elm street run parallel to each other when Main Street intersects them it forms interior <6 measuring70 what is the measure of <4

Answers

IfIf it forms interior <6 measuring70. The measure of <4 is: B. 110°.

Measure of <4

Using this interior angle theorem

Measure of <4=180° - <6

Where:

<6 measure 70

Hence:

Measure of <4=180°-70°

Measure of <4=110°

Therefore the measure of <4 is: B. 110°.

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Oak street and elm street run parallel to each other when Main Street intersects them it forms interior

Solve the following eqation
34 + 12x =3x - 22

Answers

Answer:

x = - 6.22 or - 56/9

Step-by-step explanation:

Step 1:

34 + 12x = 3x - 22             Equation

Step 2:

12x = 3x - 56            Subtract 34 on both sides

Step 3:

9x = - 56          Subtract 3x on both sides

Step 4:

x = - 56 ÷ 9           Divide

Answer:

x = - 6.22

Hope This Helps :)

Linda had 90 fliers to post around town. Last week, she posted 1/5 of them. This week, she posted 1/3 of the remaining fliers. How many fliers has she still not posted?

Answers

The number of fliers that she has still not broadcasted will be 48 fliers.

What is Algebra?

Algebra is the study of ideational characters, while logic is the manipulation of all those opinions.

Linda had 90 fliers to post around town. Last week, she posted 1/5 of them. Then the number of fliers staying is given as,

⇒ (1 - 1/5) x 90

⇒ (4/5) x 90

⇒ 72 fliers

This week, she posted 1/3 of the remaining fliers. Then the number of fliers that she has still not broadcasted is given as,

⇒ (1 - 1/3) x 72

⇒ (2/3) x 72

⇒ 48 fliers

The number of fliers that she has still not broadcasted will be 48 fliers.

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Which expression has the same value as -18+(-9)?
-18-2
-12+(-3)
-10-5
O-8(-4)

Answers

Answer:

None

Step-by-step explanation:

-18-2 would be equal to -20

-12+(-3) would be equal to -15

-10-5 would be equal to -15

0-8(-4) would be equal to 32

Is that the letter "O" or the number "0"?

Is all of this information given to you for this question here?

Impaired brain function as a result of drug use involves all of the following except: a. increased confusion b. errors in judgment c. memory loss d. increased concentration

Answers

Increased concentration is the answer as drug impairs our ability to control ourselves.

Hope it helps!

Impaired brain function as a result of drug use doesn't involve: Option D: Increased concentration.

What is impaired brain function?

A significant deterioration in one or more domains of conscious mental activity, such as language, learning, and memory, that interferes with everyday function and independence are some of the traits of impairment of brain.

Thus, as we see, first three options are showing acts of impaired brain but the fourth option contradicts, as impairment from drug use isn't going to increase concentration and if it somehow does, then it isn't impairment.

Thus, impaired brain function as a result of drug use doesn't involve: Option D: Increased concentration.

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URGENTTT PLEASEE HELPP!!!!

URGENTTT PLEASEE HELPP!!!!

Answers

Answer: y = 3/5x + 1

The y-intercept or the value for y when x is at 0 is 1. The slope is 3/5 because you can take two points and see the rise and run between them. If you count, you can see that each point is 3 up, and 5 to the right between each other.

6. A motorcycle is moving at a constant speed of 40 miles/hour. How long does it take to travel
a distance of 65 miles?

Answers

Answer:

1.625 hours

Step-by-step explanation:

The equation is

d = rt  where d is distance  r is rate and t is time

65 = 40 *t

Divide each side by 40

65/40 = t

1.625 hours = time

Explain why a+b+c=240degrees

Answers

Answer: The equation a+b+c=240 degrees is not true for any triangle, since the sum of the angles of a triangle is always 180 degrees. However, it could be true for a quadrilateral, which has four angles. One way to explain why a+b+c=240 degrees is to use the fact that opposite angles of a cyclic quadrilateral (a quadrilateral that can be inscribed in a circle) are supplementary, meaning they add up to 180 degrees. If we label the opposite angle of c as d, then we have c+d=180 degrees. Subtracting c from both sides, we get d=180-c. Then, adding a+b to both sides, we get a+b+d=240-c+c, which simplifies to a+b+c=240 degrees. Another way to explain why a+b+c=240 degrees is to use the fact that an exterior angle of a triangle is equal to the sum of the opposite interior angles. If we extend one side of the triangle and label the exterior angle as e, then we have e=a+b. Then, adding c to both sides, we get e+c=a+b+c. Since e+c is an exterior angle of another triangle formed by extending the side, it is equal to 180 degrees. Therefore, we have 180=a+b+c, which implies that a+b+c=240 degrees.

WILL GIVE BRAINLIEST IF CORRECT PLEASE ANSWER!!!!

Solve for x to the nearest tenth.

WILL GIVE BRAINLIEST IF CORRECT PLEASE ANSWER!!!!Solve for x to the nearest tenth.

Answers

Answer:

5.8

Step-by-step explanation:

Pythagorean Theorem:

You have the side 6 and 3. To find x you must make the right triangle.

6-1=5. So the longer side of the tri is 5. Now we will solve:

3^2+5^2=9+25=34. Now we have to square root 34.

\(\sqrt{34}\) is approximately = 5.8

Find the range of the graphed function.

Find the range of the graphed function.

Answers

Range is set of all y-values. To find a range of graphed function, we need to know that range starts from the minimum value of graph to maximum value. That's because the minimum value is the least value that you can get by substituting the domain and the maximum value is the largest value that you can get by substituting the domain as well.

Now we don't talk about domain here, we talk about range. See the attachment! You are supposed to focus on y-axis, plane or vertical line. See how the minimum value of function is the negative value while the maximum value is positive.

That means any ranges that don't contain the negative values are cleared out. (Hence A and C choices are wrong.)

Next, range being set of all real numbers mean that graphed functions don't have maximum value or minimum value (We can say that both max and min are infinite.)

Take a look at line graph as an example of range being set of all real numbers, or cubic function.

Answer/Conclusion

The range exists from negative value which is -9 to the maximum value which is 5.That means the range is -9<=y<=5
Find the range of the graphed function.

The cost of an adult ticket to a varsity basketball game is $3.00 and the student ticket is $1.50. If the number of adult tickets sold is represented by a and student tickets sold by s, which expression best represents the amount of money collected from the ticket sales? Group of answer choices 4.50as ,4.50(a+s) ,3.00a+1.50s , (3.00a)(1.50s)

Answers

Answer:

3.00a + 1.50s

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Suraj, a tester of software solutions, is conducting a session on coding errors for his project.He wants to present an analysis of issues from the last six months. He is standing beside theprojector screen and is using his laptop to move between the slides of this presentation.What strategy should he use to ensure that his audience is engaged?Ask questions occasionally, orparaphrase questions and provideanswers.Look for opportunities to walk towardsthe audience.B:MAYD:| Request Learning Accommodations | Help | Cookie Preferences and Do Not Sell My InfoMake eye contact with audiencemembers as much as possible.All of these. The velocity function, in feet per second, is given for a particle moving along a straight line. v(t) = t3 9t2 + 23t 15, 1 t 6 (a) find the displacement. (b) find the total distance that the particle travels over the given interval. Explain how the levels of national,proverbial and local government address the interest of civil society Find the average value fave of the function f on the given interval: f(x) = 3x2 + 4x, [-1, 5] fave = _____ please answer all requirements and follow any rounding instructionsor whole number instructionsOriginal Paper Delivery has decided to analyze the profitability of five new customers. It buys recycled paper at $11 per case and sells to retail customers at a list price of $14.80 per case. Data pe what type of tide occurs when the moon is in the positions marked by the straight arrows in this image? please give one word as your answer. The amount a buyer needs to purchase in order to meet next month's stock requirement is called the (1 pt.) Niacinamide (a.k.a. nicotinamide, and often referred to as vitamin B3. See Figure.) is a nitrogen containing organic molecule derived from niacin that makes its way into our metabolic pathways as coenzymes in the forms of NAD and NADP. It is also found in an acne treatment called Nicomide and some people take it as a nutritional supplement to combat high cholesterol. How many atoms of carbon are there in a 1317 mg dose of niacinamide? Enter your answer using scientific notation of the form 1.234e30 or 1.234e-30.atoms of carbon Consider a two year interest rate swap with semi annual payments. Assume a notional principal of $25 million. The swap was entered into 120 days back at a fixed rate of 6.32%. The swap has remaining life of 20 months with pay dates on 2, 8, 14, and 20 months. The term structure of spot LIBOR rates are as follows: 2 months: 6.13%, 8 months : 6.29%, 14 months: 6.53%, 20 months: 6.97%. The 180 days LIBOR at the start of the swap was 5.85%. Calculate the market value of the swap from the point of view of the party paying the floating rate and receiving the fixed rate. 6. Why do many of the Native American teenagers in the text feel conflicted in regards to their identity? Would you be alarmed that Brianna has cyanosis and Christopher does not? Why? For each dozen cookies Rachel used 1 1/2 cups of milk. How many cups of milk did she use for 16 dozen cookies? Show your work. The James Co. plans on saving money to buy some new equipment. The company is opening an account today with a deposit of $15,000. After 3 years, the firm wants to add an additional $50,000 to the account. How much money will the James Co. have in their account five years from now? Assume the James Co. can earn an interest of 4% compounded annually in the first 3 years and an interest of 5% compounded annually in the last 2 years.