The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method. y = −x2 + 17x − 72, y = 0; about the y−axis

Answers

Answer 1

Answer:

The volume is 17π/6

Step-by-step explanation:

We are going to apply first the shell method where the slice is parallel to the axis of revolution, then we need to determine the medium radius ahd the height of the shell, in this case as the region is rotated about the y-axis $R=x$ and the height is $h=-x^{2} +17x-72$

Then the integral is $V=2\pi \int\limits^a_b {radius*height} \, dx$

$V=2\pi \int\limits^8_9 {x*(-x^{2}+17x-72)} \, dx$

$V=2\pi [-\frac{x^{4} }{4} +\frac{17}{3}x^{3}-36x^{2} ]_8^9$

$V=2\pi [-\frac{2465}{4}+\frac{3689}{3}-612 ]$

$V=\frac{17\pi }{6}u^{3}$

To show the answer we can apply the ring method where the the inner radius is $r=\frac{17}{2}-17\sqrt{\frac{1}{4}-y }$ and the outter radius $R=\frac{17}{2}+\sqrt{\frac{1}{4}-y }$

The formula is $V=\pi \int\limits34 \sqrt{\frac{1}{4}-y }dy$ evaluated between $y=0$ and $y=\frac{1}{4}$

Solving the integral we can get the same solution of $\frac{17\pi }{6} u^{3}$

Finally, the volumen is $\frac{17\pi }{6} u^{3}$

Related Questions

I need help with this

Answers

The statement that is equivalent to |6x-3|=3 is: 6x-3=3 or 6x-3=-3

For the equation to be true, two scenarios need to be considered:

When the expression 6x-3 is positive and equals 3:

6x-3 = 3

When the expression 6x-3 is negative and equals -3:

6x-3 = -3

By solving these two equations, we can find the equivalent statement:

Solving 6x-3 = 3:

Adding 3 to both sides gives us:

6x = 6

Dividing both sides by 6:

x = 1

Solving 6x-3 = -3:

Adding 3 to both sides gives us:

6x = 0

Dividing both sides by 6:

x = 0

Therefore, the equivalent statement to |6x-3|=3 is:

6x-3=3 or 6x-3=-3, which can be further simplified to:

6x-3=3 or 6x-3=-3

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Let p be "You build it," and let q be "They will come." What statement is equivalent to the symbolic form p⟹q?Select the correct answer below:If you build it, then they will come.If they will come, then you build it.Your not building it implies that they will come.They will not come if you build it.

Answers

We have the following facts:

p = You build it

q = They will come

From a list of options, we must select the one equivalent to the symbolic statement:

$p\Rightarrow q$

Now, we see that in the symbolic statement appears the symbol: ⟹, we must interpret this symbol as "then".

So, reading the list of options, we see that the correct one is:

"If you built it, then they will come".

The pie chart below shows how we, as a nation, commute to work. Change each percent to a fraction in lowest
terms.
How We Commute
Car pool
11%
Drive alone
80%
Public transit
5%
Other
4%

$The pie chart below shows how we, as a nation, commute to work. Change each percent to a fraction in$

Answers

Answers:

Public transit = 1/20Other = 1/25

======================================================

Explanation:

We divide the percentage values over 100 as you have done so for the first two boxes.

Drive alone = 80/100 = 4/5

Car pool = 11/100

----------

For the remaining two boxes, we do the same thing.

Public transit = 5/100 = 1/20

Other = 4/100 = 1/25

-----------

To reduce the fraction 5/100, we divide both parts by the GCF 5

5/5 = 1100/5 = 20

So that's how 5/100 turns into 1/20

The same idea applies to 4/100 turning into 1/25 (except the GCF is 4 this time).

Mrs Johnson is planning a bbq. There will be 18 people there. Each person will get 1/4 pound burger. How many pounds of burger meat will mrs Johnson need to buy?

Answers

18 x 1/4

=18/4

=9/2

Burger meat needed= 4 1/2 or 4.5lbs

10 points :)

Square OABC is drawn on a centimetre grid.

O is (0,0) Ais (3,0) Bis (3, 3) C is (0, 3)

Write down how many invariant points there are on the perimeter of the square when

OABC is reflected in y = x

Answers

Answer:

No invariant point

Step-by-step explanation:

Yo!

When we translate a form, in this case a polygon We must observe the direction of the vector. Since our vector is:

1) Let's apply that translation to this polygon, a square. Check it below:

2) The invariant points are the points that didn't change after the transformation, simply put the points that haven't changed.

Examining the graph, we can see that no, there is not an invariant point, after the translation. There is no common point that belongs to OABC and O'A'B'C' simultaneously. All points moved.

I hope you understood !

Which expressions are equal to z+(z+6)

Answers

Answer:

2(z+3)

Step-by-step explanation:

2z+6

take out the 2: 2(z+3)

which property of exponents must you apply to the express p 1/2 to derive p as the result

Answers

The expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2) Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

The property of exponents that must be applied to the expression p^(1/2) to derive p as the result is the Power of a Power Property.

The Power of a Power Property states that when a power is raised to another power, the exponents are multiplied.

For instance, consider the expression p^(1/2). We can apply the Power of a Power Property to this expression as follows: p^(1/2) = (p^(1/2))^1 By applying the Power of a Power Property, the exponent (1/2) is multiplied by the exponent 1, giving a result of 1/2.

Therefore, the expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2)Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

So we have derived p as the result using the Power of a Power Property.

In summary, we must apply the Power of a Power Property to the expression p^(1/2) to derive p as the result.

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Which of the scenarios below are considered seller-based discounts? options are in the picture

Answers

The scenarios that can be considered a seller-based discount are:

A. The offer by Wire and Cable

B. Carfna's Fine Foods

C. Mouser Electronics offer

E. Carchex Car Maintenance

What is a seller-based discount?

A seller-based discount is a discount that is offered by a seller for the early purchase of a product. The goal of the seller in this case is to get cash as he or she is in an immediate need for cash.

The most outstanding example is that of Carchex Car Maintenance where an offer is made by the seller for the early purchase of products.

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could someone help me with this and show work?

Answers

The volume of the shape is 490cm³

What is volume of prisms?

A prism is a solid shape that is bound on all its sides by plane faces. prism is named after the shape of these bases.

The base of this prism is rectangular. The volume of a prism is expressed as;

V = base area × height

base area = 7 × 10 = 70cm²

height = 7cm

the volume of the shape = 70× 7 = 490cm²

therefore the volume of the shape is 490cm³.

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A certain insecticide kills 80% of all insects in laboratory experiments. A sample of 12 insects is exposed to the insecticide in a particular experiment. What is the probability that every insect will die? Round your answer to four decimal places.

Answers

As per the binomial distribution, the probability that every insect will die is 0.22%.

Binomial distribution:

Binomial distribution refers a discrete probability distribution that gives only two possible results in an experiment, either success or failure.

The formula for calculating binomial distribution is

P = ⁿCₓ pˣ qⁿ⁻ˣ

P = binomial probability

x = number of times for a specific outcome within n trials

p = probability of success on a single trial

q = probability of failure on a single trial

n = number of trials

Given,

A certain insecticide kills 80% of all insects in laboratory experiments. A sample of 12 insects is exposed to the insecticide in a particular experiment.

Here we need to find the probability that every insect will die and round off it into four decimal places.

While we looking into the given question we have identified that it is the binomial type probability distribution.

And we have identified the following values,

The number of trials n= 12

Probability of the success trial = 0.8,

Number of success trials k = 12

Now, we have apply the values on the binomial distribution formula, then we get,

=> P = ¹²C₁₂ x (0.6)¹² x (1 - 0.6)¹²⁻¹²

When we simplify it then we get,

=> P = 1 x 0.0022 x (0.4)⁰

=> P = 0.0022

When we convert this into percentage then we get, 0.22%

Therefore, the resulting probability is 0.22%.

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Find the value of x and the measure of the missing angle labeled A:

Answers

Answer:

x = -2

∠A = 35

Step-by-step explanation:

x + 37 + x + 57 = 90

reduce:

2x = -4

x = -2

∠A = 37-2 = 35

Two rectangles of the same shape have areas of 676 and 3,457 square centimetres. If the shorter side of the larger rectangle is 41 centimetres, what are the dimensions of the smaller one?

Answers

The dimensions of the smaller rectangle are 13 centimeters by 52 centimeters.

Let's assume the dimensions of the smaller rectangle are length L and width W (in centimeters).

We know that the area of the smaller rectangle is 676 square centimeters:

L * W = 676 ----(1)

We also know that the larger rectangle has a shorter side of 41 centimeters. Let's say the corresponding longer side of the larger rectangle is H centimeters.

The area of the larger rectangle is 3457 square centimeters:

41 * H = 3457 ----(2)

Our current set of equations contains two unknowns. In order to get the smaller rectangle's dimensions, we can simultaneously solve these equations.

In order to find H, we can use equation (2):

H = 3457 / 41

H ≈ 84.22

Now we can substitute this value of H into equation (1):

L * W = 676

We need to find the dimensions (L and W) that multiply to give 676. We can start by looking for factors of 676.

Factors of 676: 1, 2, 4, 13, 26, 52, 169, 338, 676

By trial and error, we can see that the factors that give a close match to the dimensions of the larger rectangle (41 and 84.22) are 13 and 52:

L = 13

W = 52

Therefore, the smaller rectangle has measurements of 13 by 52 centimetres.

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Simplify the expression. Write the answer without using negative exponents. Assume that the variable is restricted to those numbers for which the expression is defined.
−m−8m9

Answers

The simplified expression is m^1 or simply m.

To simplify the expression −m^(-8) * m^9 without using negative exponents, we can utilize the properties of exponents.

First, let's deal with the negative exponent. A negative exponent indicates that the term should be moved to the denominator. So, we can rewrite −m^(-8) as 1/m^8.

Now, we can simplify the expression further: 1/m^8 * m^9.

When multiplying terms with the same base, we add the exponents. In this case, we have m^(-8) * m^9, which becomes m^(-8 + 9) = m^1 = m.

Finally, multiplying 1/m^8 by m gives us (1/m^8) * m = 1/m^(8-1) = 1/m^7.

Therefore, the simplified expression is 1/m^7, where m is the variable restricted to those numbers for which the expression is defined. By eliminating the negative exponent and combining like terms, we've simplified the expression without using negative exponents.

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Proportionality with tables (yes) or (no)

x y

___ -------

-4 -5

-3 -6

-2 -7

-1 -8

Answers

Based on the given table of value for x and y, there is no proportional relationship between x and y.

The correct answer is no

How to determine proportionality?

x y

___ -------

-4 -5

-3 -6

-2 -7

-1 -8

Based on the given task content;

x is increasing by 1, that is,

-4 + 1 = -3

-3 + 1 = -2

-2 + 1 = -1

y is decreasing by -1, that is,

-5 - 1 = -6

-6 - 1 = -7

-7 - 1 = -8

In conclusion, there is no proportional relationship between x and y.

Answers

Answer:

{(1, 0), (1, 1), (2,0), (2,1), (2, 2), (3,0), (3,1), (3,2), (3,3), (4, 0), (4,1), (4,2), (4,3), (4,4), (5,0), (5,1),(5,2), (5,3), (5,4), (5,5), (6,0), (6,1),(6,2), (6,3), (6,4), (6,5), (6,6)}

B.)

{(2,2), (3,2), (4,2), (4,4), (5,2), (5,4), (6,2), (6,4), (6,6)}

Step-by-step explanation:

Sample space :

Die roll, then number of coin tosses based on the outcome of the die roll, then number of heada from the toss(es) is recorded along with the outcome of the die roll.

{(1, 0), (1, 1), (2,0), (2,1), (2, 2), (3,0), (3,1), (3,2), (3,3), (4, 0), (4,1), (4,2), (4,3), (4,4), (5,0), (5,1),(5,2), (5,3), (5,4), (5,5), (6,0), (6,1),(6,2), (6,3), (6,4), (6,5), (6,6)}

Event that the total number of head is even:

{(2,2), (3,2), (4,2), (4,4), (5,2), (5,4), (6,2), (6,4), (6,6)}

Can somebody help me I’m crying????

Answers

Go to your happy place! Think happy thoughts! Whatever the reason it is, never hold it in, no matter where you are let it out! After you're done, relax and calm down. Rest! I hope this helps!

IM CRYING TOO but honestly don’t cause that just makes everything worse obviously, first let it all out then you want to breathe and think of things that make you happy and make you feel excited for like upcoming things and stuff . I know you will feel better soon !!

A new cylindrical can with a diameter of 4cm is being designed by a local company. The surface area of the can is 140 square centimeters. What is the height of the can? Estimate using 3.14 for pi and round to the nearest hundredth. Apply the formula for the surface area of a cylinder SA=2B+Ph

Answers

The height of the can of cylinder shape is 9.14 cm.

What is a cylinder?

In mathematics, a cylinder is a three-dimensional solid that maintains two parallel bases separated by a curved surface at a specific distance. These bases frequently have a circular shape (like a circle), and an axis connects their respective centres.

We are given the diameter as 4 cm.

So, the radius is 2cm.

Also, it is given that the surface area of the can is 140 square centimeters.

So, using the surface area of cylinder, we get

⇒Area = 2πr (h + r)

⇒140 = 2π * 2 (h + 2)

⇒140 = 4π (h + 2)

⇒140 = 4 * 3.14 * (h + 2)

⇒140 = 12.56 * (h + 2)

⇒11.14 = h + 2

⇒h = 9.14

Hence, the height of the can of cylinder shape is 9.14 cm.

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You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 5 years of the actual mean with a confidence level of 94%, how many citizens should be included in your sample? Assume that the standard deviation of the ages of all the citizens in this community is 22 years.

Answers

Answer:

The sample size is $n = 68 $

Step-by-step explanation:

From the question we are told that

The margin of error is $E = 5 \ years$

The standard deviation is $\sigma = 22$

From the question we are told the confidence level is 94% , hence the level of significance is

$\alpha = (100 - 94 ) \%$

=> $\alpha = 0.06$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.881$

Generally the sample size is mathematically represented as

$n = [\frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ] ^2$

=> $n = [\frac{1.881 } * 22 }{5} ] ^2$

=> $n = 68 $

Now you try on your own.

Kelly wants to build a new wardrobe for herself with only clothing pieces she loves, fit her well, and coordinate together. She already has most of the pieces she will use, but needs to save up to go shopping for the remaining items. She has already saved some money from her job, and she decides to set aside money weekly from her tips. The expression $25w+$65
represents the amount of money Kelly will have saved after some amount of weeks. What does each part of this expression represent?

$25=
Answer

w=
Answer

$65=
Answer

For this specific expression, would it make sense to plug in a negative number for w
? Answer

For this specific expression, would you ever expect to get a number less than 65
for your total amount saved?

Answers

The Interpretatiom of the equation is that;

w represents number of weeks she will have saved for the remaining items

$25 represents the amount she saves per week

$65 represents the amount she has already saved

How to solve algebra word problems?

The algebra word problem can be solved by using variables to denote certain parameters I'm the question.

The general form of equation of a line in slope intercept form is;

y = mx + c

Where;

m is slope

c is y-intercept

We are given the equation:

$25w + $65

This equation represents the amount of money Kelly will have saved after some amount of weeks.

Thus;

w represents number of weeks she will have saved for the remaining items

$25 represents the amount she saves per week

$65 represents the amount she has already saved

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What is the solution set for −4x−38<2

Answers

The solution set for the inequality is x < -10

What are inequalities?

The different signs for representing inequalities are;

< represents the sign for less than> represents the sign for greater than≥ represents greater than or equal to≤ represents less than or equal to

From the information given, we have that;

−4x−38<2

To solve for the value of x, take the steps;

collect the like terms

-4x> 2 + 38

Add the values

-4x> 40

Divide both sides by the coefficient of x, we have;

x > -10

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5. Jane sold her genset for $ 20000 at a profit of $ 1737. Find the CP of genset

Send me the answer pls

Answers

Answer:

18263

Step-by-step explanation:

sp= 20000

profit= 1737

CP= sp- profit

20000-1737

18263

Determine the polynomial y(x) that has roots at x=-0.7, x=0.5, x=3.4 and x=5.8
Make a plot of the polynomial in the domain -1<=x<=6

Answers

The polynomial with given roots is,

y(x) = x^4 - 9x^3 + 17.53x^2 + 7.164x - 6.902.

What is factor of polynomial?

In mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain.

Given:

The polynomial y(x) that has roots at x = -0.7, x = 0.5, x = 3.4 and x = 5.8.

Since if 'a' is a root of the polynomial then (x - a) is the factor of the polynomial.

So, the factors of the polynomial are, (x + 0.7), (x - 0.5), (x - 3.4), (x - 5.8).

⇒ y(x) = (x + 0.7)(x - 0.5)(x - 3.4)(x - 5.8)

= (x^2 - 0.5x + 0.7x - 0.35)(x^2 - 5.8x - 3.4x + 19.72)

= (x^2 + 0.2x - 0.35)(x^2 - 9.2x + 19.72)

y(x) = x^4 - 9x^3 + 17.53x^2 + 7.164x - 6.902

The graph of the polynomial on the domain -1 ≤ x ≤ 6 is attached below.

Hence, the polynomial with given roots is,

y(x) = x^4 - 9x^3 + 17.53x^2 + 7.164x - 6.902.

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Determine the polynomial y(x) that has roots at x=-0.7, x=0.5, x=3.4 and x=5.8Make a plot of the polynomial

20. Rafael has a business selling computers. He buys computers from the manufacturer for $450
each and sells them for $800. Each month, he must also pay fixed costs of $3000 for rent and
utilities at his store. If he sells n computers in a month, which of the following equations can be used
to calculate his profit?
A. P = n(800 - 450)
B. P = n(800 - 450 - 3000)
C. P = 3000n(800 - 450)
D. P = n(800 - 450) - 3000
E. P = n(800 - 450) + 3000
Yeah

Answers

Answer: D , p = n (800 - 450) - 3000

Step-by-step explanation: Firstly, you have to account for how much money Rafael is making off of each computer (800 - 450). That factor is then multiplied by the variable "n" which represents the amount of computers sold. Lastly, since this is an equation to calculate his monthly profits, you have to subtract the rent that he is paying ($3000) from the total profit that he made off of selling the computers. Therefore, giving you the equation

P (profit) = n (amount of computers sold) (800-450) - 3000 (rent).

The equation that represents Rafael's monthly profit selling 'n' numbers of computers is D. P = n(800 - 450) - 3000.

What is an equation?

An equation represents equality for the terms that are on the both side of the equal sign.

Given Rafael buys computers for 450 dollars and sells them for 800 dollars each.

He also had to pay 3000 dollars for rent and utilities for the store and the number of computers sold in each month is given by 'n'.

∴ The equation that represents his profit(P) in a month is,

P = n(800 - 450) - 3000.

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Find the class boundaries mid point and width for the class 37-46

Answers

The mid point is 4.5 or 4 and 5 depending on how they wnat u to answer

1.7% of 35 is what number?

Answers

Answer:

0.595

Step-by-step explanation:

I multiplied 1.7 by 35 and moved the decimal.

A population has a mean of 300 and a standard deviation of 70. Suppose a sample of size 100 is selected and is used to estimate . Use z-table.

What is the probability that the sample mean will be within +/- 6 of the population mean (to 4 decimals)? (Round z value in intermediate calculations to 2 decimal places.)

Answers

Step-by-step explanation:

Sol

Given that ,

mean =300

standard deviation =a =70

n=100

ux=128

a ) within 6 =300 +/-6 : 294, 306

P(294' ' 306)

: P(-0.86 : Z ' 0.86)

: P(Z ' 0.86) - P(Z ' -0.86)

Using z table,

: 0.8051-0.1949

: 0.6102

Probability : 0.6102

a ) within 18 =300 18 : 294, 318

P(294' ' 306)

: P(Z ' 2.57) - P(Z ' -2.57)

Using z table,

:0.9949-0.0051

:0.9898

Probability =0.9898

A population has a mean of 300 and a standard deviation of 70. Suppose a sample of size 100 is selected

In a pre algebra class containing 43 students, there are 4 freshman, 35 sophomores, and 4 juniors. what fraction of the class are sophomores

Answers

The fraction of the class that is sophomores is $35/43$.

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores $= 35 / 43$

Therefore, the fraction of the class that are sophomores is = $35/43$.

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The function h(t) = -16t2 + 48t + 28 models the height (in feet) of a ball where t is the time (in seconds).
What is the maximum height that the ball reaches? Just write the numerical answer - do not include h = or any units in your
answer.

Answers

Answer:

Step-by-step explanation:

[using calculus] When the function h(t) reaches its maximum value, its first derivative will be equal to zero (the first derivative represents velocity of the ball, which is instantaneously zero). We have $h'(t) = -32t + 48$, which equals zero when $t = 3/2 = 1.5$. The ball therefore reaches its maximum height when t = 1.5. To find the maximum height, we need to find h(1.5), which is 64 feet.

[without calculus] This is a quadratic function, so its maximum value will occur at its vertex. The formula for the x-coordinate of the vertex is -b/2a, so the maximum value occurs when t = -48/(2*16), which is 1.5. The maximum height is h(1.5), which is 64 feet.

The function h(t) = -16t2 + 48t + 28 models the height (in feet) of a ball where t is the time (in seconds).What

The manager of the video department at a department store plans to purchase a large number of DVDs of a recent movie. One supplier is selling boxes of 20 DVD movies for $240, and a second supplier is selling boxes of 14 DVD movies for $170. Only complete boxes of DVD movies can be purchased. Complete part a) and b) below. a)

a) If the manager can purchase boxes of DVD movies from either or both suppliers, determine the maximum number of DVD movies that can be purchased for $415. Indicate how many boxes of 20 and how many boxes of 14 will be purchased.
— box(es) of 20 and — box(es) of 14

b) How much will the DVD movies cost?
They will cost $—

Answers

Answer:

1 box of 20 and 1 box of 14

They will cost $410

Step-by-step explanation:

1. Find how many boxes of 20 DVD movies can be bought

415 - 240 = 175

1 box of 20 DVD movies can be sold

2. Find how many boxes of 14 DVD movies can be bought from $175

175 - 170 = 5

1 box of 14 DVD movies can be bought

3. Find the cost

240 + 170 = 410

Shown below is a blueprint for a rectangular kennel at a pet hotel.
The blueprint of the rectangular kennel shows one side is 22 feet and another side is 14 feet.
What is the total length of fencing needed to enclose the kennel?
The total length needed is blank feet.
The solution is

Answers

Answer:

72 ft.

Step-by-step explanation:

In this problem, we are looking for the perimeter of the kennel. The perimeter of a rectangle has the formula, $P=2l+2w$, where l represents the length of the rectangle and w represents the width of the rectangle. We are given both the length and the width (or simply the two sides) of the rectangle, and all we need to do is plug it into the formula!

$P=2*22+2*14\\P=44+28\\P=72$

Therefore, it would require 72 ft. of fencing to enclose the kennel.

I hope this helps! Let me know if you have any questions :)

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