Let V be the volume of the solid obtained by rotating about the y-axis the region bounded y = sqrt(25x) and y = x^2/25. Find V by slicing & find V by cylindrical shells.

Answers

Answer 1

Explanation:

Let [tex]f(x) = \sqrt{25x}[/tex] and [tex]g(x) = \frac{x^2}{25}[/tex]. The differential volume dV of the cylindrical shells is given by

[tex]dV = 2\pi x[f(x) - g(x)]dx[/tex]

Integrating this expression, we get

[tex]\displaystyle V = 2\pi\int{x[f(x) - g(x)]}dx[/tex]

To determine the limits of integration, we equate the two functions to find their solutions and thus the limits:

[tex]\sqrt{25x} = \dfrac{x^2}{25}[/tex]

We can clearly see that x = 0 is one of the solutions. For the other solution/limit, let's solve for x by first taking the square of the equation above:

[tex]25x = \dfrac{x^4}{(25)^2} \Rightarrow \dfrac{x^3}{(25)^3} = 1[/tex]

or

[tex]x^3 =(25)^3 \Rightarrow x = \pm25[/tex]

Since we are rotating the functions around the y-axis, we are going to use the x = 25 solution as one of the limits. So the expression for the volume of revolution around the y-axis is

[tex]\displaystyle V = 2\pi\int_0^{25}{x\left(\sqrt{25x} - \frac{x^2}{25}\right)}dx[/tex]

[tex]\displaystyle\:\:\:\:=10\pi\int_0^{25}{x^{3/2}}dx - \frac{2\pi}{25}\int_0^{25}{x^3}dx[/tex]

[tex]\:\:\:\:=\left(4\pi x^{5/2} - \dfrac{\pi}{50}x^4\right)_0^{25}[/tex]

[tex]\:\:\:\:=4\pi(3125) - \pi(7812.5) = 14726.2[/tex]


Related Questions

A certain brand of coffee comes in two sizes. An 11.5-ounce package costs $.4.24 . A 27.8-ounce package costs $9.98.
Find the unit price for each size. Then state which size is the better buy based on the unit price.

Round your answers to the nearest cent.

Answers

Answer:

Small (11.5) is 37 cents per ounce.

Large (27.8) is 36 cents per ounce.

27.8 ounces is the better buy.

If there is a die that has 12 sides, that are numbered 1 to 12, what is the probability that she will roll either a 3 or a 9

Answers

Answer:

2/12 = 1/6

Step-by-step explanation:

To find the probability of something with an equal chance of each outcome, we can apply the formula (number of favorable outcomes)/(number of total outcomes). Because there is an equal chance for each side of the die to be landed on, we can apply this.

On a 12 sided die, there are 12 sides. Two of those sides are 3 and 9. Therefore, there are two favorable outcomes (3 and 9). There are 12 sides to choose from, so there are 12 total outcomes, making the probability 2/12 = 1/6

The triangles below are similar (being similar means there is a proportional relationship between the measures of each of the sides). What is the length of ED? (HINT: You can solve this question by using the MATH Ratio Table)

Answers

Answer:  B)  18 cm

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

Work Shown:

ED/DF = AB/AC

x/24 = 12/16

16x = 24*12

16x = 288

x = 288/16

x = 18

------------

Explanation:

Because the triangles are similar, we can form the proportion shown above. There are many variations of the proportion that can happen, but they all lead to the same result x = 18.

So for instance, another proportion you could solve is ED/AB = DF/AC.

The key is to keep up the same pattern when forming the ratios.

What I mean by that is when I formed ED/DF I divided the vertical side over the horizontal side for triangle EDF. So to form the second fraction, we must do the same division (vertical over horizontal) for triangle ABC.

Three ounces of cinnamon cost $2.40. If there are 16 ounces in 1 pound, how much does cinnamon cost per pound?

Answers

12.8$, you would divide 2.40 by 3 to get the cost per ounce. Then multiply that by 16 to get the cost for one pound.

write your answer in simplest radical form​

Answers

I believe the correct answer is 8sqrt2.

annual cost of 35,000 expected to save 40,000 during the first year how many months will the take to recover investment

Answers

Answer:

500000

Step-by-step explanation:

Using the Time Series Data for the US Nuclear Electric Power Production, calculate the exponential smoothing forecasts for 2005 through 2010 using alpha equals 0.2. Find the forecast error for each time period. If there is n

Answers

Answer:

????????????

I don't know

A formula for the normal systolic blood pressure for a man age A, measured in mmHg, is given as P = 0.006A*2-0.02A + 120. Find the age of a man whose normal blood pressure measures 129 mmHg. Round your answer to the nearest year. The man would be ? years old.​

Answers

Answer:

The man would be 40 years old.

Step-by-step explanation:

Blood pressure as function of age:

Is given by the following equation:

[tex]P = 0.006A^2 - 0.02A + 120[/tex]

Find the age of a man whose normal blood pressure measures 129 mmHg.

This is A for which P = 129. So

[tex]129 = 0.006A^2 - 0.02A + 120[/tex]

[tex]0.006A^2 - 0.02A - 9 = 0[/tex]

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

[tex]\Delta = b^{2} - 4ac[/tex]

In this question:

Quadratic equation with [tex]a = 0.006, b = -0.02, C = -9[/tex]. So

[tex]\Delta = (-0.02)^2 - 4(0.006)(-9) = 0.2164[/tex]

[tex]A_{1} = \frac{-(-0.02) + \sqrt{0.2164}}{2*(0.006)} = 40.4[/tex]

[tex]A_{2} = \frac{-(-0.02) - \sqrt{0.2164}}{2*(0.006)} = -37.1[/tex]

Age has to be a positive number, so rounding to the nearest year:

The man would be 40 years old.

The director of special events for Sun City believed that the amount of money spent on fireworks displays on the 4th of July was predictive of attendance at the Fall Festival held in October. She gathered the following data to test her suspicion.

4th of July ($000) Fall Festival (000)
10.6  8.8
 8.5  6.4
12.5 10.8
 9.0 10.2
 5.5   6.0
12 11.1
 8.0   7.5
 7.5   8.4
 9.0   9.5
10   9.8
 7.5   6.6
10 10.1
 6.0   6.1
12 11.3
10.5   8.8

Required:
Determine the regression equation. Is the amount spent on fireworks related to attendance at the Fall Festival? Conduct a hypothesis test to determine if there is a problem with autocorrelation.

Answers

Answer:

The complete question and its solution in the attached file please find it.

Step-by-step explanation:

Nadia needs 3/4 cup of orange juice for a punch recipe. She will double the recipe to make
punch for a party. Which statement is true?

Answers

Answer:

she will be using more orange juice

Answer:

she will be using more orange juice

Which graph represents y = |xl?
A
B
C
D

Answers

Answer:

B

Step-by-step explanation:

The equation represented in the question is the parent absolute value question. If you know the different parent functions, then the answer is obvious because absolute value equations always form a V. However, if you do not do this then you can create a table and plugin values. Plugin numbers like 0, -1, and 1 for X and solve for Y. Finally, graph these points and see what graph best fits. If needed you can also plug in more points.

Answer:

B.

Step-by-step explanation:

I got it correct on the warm up

I need help with this ​

Answers

Answer:

D.

Step-by-step explanation:

According to converse of the Pythagorean Theorem, that if the square of the third side (longest side) of a triangle equals the sum of the other two shorter sides, therefore, the triangle formed must be a right triangle.

From the side lengths given, the following satisfies the Pythagorean triple:

5² + 12² = 13².

Therefore, the procedure to use to confirm the converse of the Pythagorean Theorem would be to draw the two shortest side, 5 cm and 12 cm, so that a right angle will be between them. The side measuring 13 cm should therefore fit in to form a right triangle.

Solve this equation for x. Round your answer to the nearest hundredth. 0.77 = log x​

Answers

Answer:

x ≈ 5.89

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Algebra II

Exponential to Logarithmic:                                                                             [tex]\displaystyle b^m=x \rightarrow log_bx=m[/tex]

Step-by-step explanation:

Step 1: Define

Identify

0.77 = log(x)

Step 2: Solve for x

[Equality Property] Raise both sides to the 10th power:                                [tex]\displaysytle 10^{0.77} = 10^{logx}[/tex]Simplify:                                                                                                             [tex]\displaysytle x = 10^{0.77}[/tex]Evaluate:                                                                                                           [tex]\displaysytle x = 5.88844[/tex]

Simplify 7a – 11b + 4ab – 6a + 5b.

Answers

7a-6a-11b+5b+4ab
=a-6b+4ab
Final answer

Do number 7 plz finding QR​

Answers

Answer:

QR = sqrt(147)

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

7^2 + QR^2 = 14^2

49 + QR^2 = 196

QR^2 = 196-49

QR^2 = 147

Taking the square root of each side

QR = sqrt(147)


A train is traveling at a speed of 60 miles per hour. What happens to the number of miles when the number of hours
changes?
Abebe babe

Answers

Answer:

It multiplies

Step-by-step explanation:

if the number of hours changes to example to 2 then you multiply 60 by 2 resulting in 120miles in 2 hours

find m∠H
What does m∠H happened to equal​

Answers

Answer:

[tex]m\angle H = 30^o[/tex]

Step-by-step explanation:

Given

See attachment

Required

Find [tex]m\angle H[/tex]

To calculate [tex]m\angle H[/tex], we make use of:

[tex]\cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]

So, we have:

[tex]\cos(H) = \frac{GH}{HI}[/tex]

This gives:

[tex]\cos(H) = \frac{10\sqrt3}{20}[/tex]

[tex]\cos(H) = \frac{\sqrt3}{2}[/tex]

Take arccos of both sides

[tex]m\angle H = cos^{-1}(\frac{\sqrt3}{2})[/tex]

[tex]m\angle H = 30^o[/tex]

What is the value of the expression i 0 × i 1 × i 2 × i 3 × i 4?
1
–1
i
–i

Answers

Answer:

Answer is -1

Step-by-step explanation:

i1 = i 

i2 = -1 

i3 = -i

i4 = 1

i0 × i1 × i2 × i3 × i4 = 1 × i  × (- 1) × (- i) × 1 = i2 = - 1

Answer:the answer is -1

Step-by-step explanation:

Norman and Suzanne own 35 shares of a fast food restaurant stock and 63 shares of a toy company stock. At the close of the markets on a particular day in​ 2004, their stock portfolio consisting of these two stocks was worth ​$1596.00. The closing price of the fast food restaurant stock was ​$19 more per share than the closing price of the toy company stock on that day. What was the closing price of each stock on that​ day? The price per share of the fast food restaurant stock is ​

Answers

Answer:

closing price of the fast food stock was $997.50

closing price of the toy company stock was $598.50

the price per fast food share was $28.50

Step-by-step explanation:

x = price per share fast food

y = price per share toy company

35x + 63y = 1596

x = y + 19

=>

35(y+19) + 63y = 1596

35y + 665 + 63y = 1596

98y + 665 = 1596

98y = 931

y = $9.50

=>

x = 9.5 + 19 = $28.50

the value of the whole fast food stock was

35x = 35×28.5 = $997.50

the cake if the whole toy company stock was

63y = 63×9.5 = $598.50

construct an angle that bisect 120°​

Answers

Answer:

just make a 120 angle and divide it by 2, 60.

find the constant of variation k for the direct variation. 4x = -y

Answers

Answer:

k = - 4

Step-by-step explanation:

The equation representing direct variation is

y = kx ← k is the constant of variation

Given

4x = - y ( multiply both sides by - 1 )

- 4x = y , that is

y = - 4x ← in standard form

with k = - 4

0.45 0.40 0.11 This question uses the following probability model for the blood type of a randomly chosen person in the United States: Maria has type A blood. She can safely receive blood transfusions from people with blood types O and A. The probability that a randomly chosen American can donate blood to Maria is ______. (Give your answer to 2 decimal places.)

Answers

Answer:

[tex]P(O\ or\ A) = 0.85[/tex]

Step-by-step explanation:

Given

See attachment

Required

[tex]P(O\ or\ A)[/tex]

From the question, we understand that she can only get blood from O or A groups. So, the probability is represented as:

[tex]P(O\ or\ A)[/tex]

This is calculated as:

[tex]P(O\ or\ A) = P(O) + P(A)[/tex]

Using the American row i.e. the blood must come from an American.

We have:

[tex]P(O) = 0.45[/tex]

[tex]P(A) = 0.40[/tex]

So, we have:

[tex]P(O\ or\ A) = 0.45 + 0.40[/tex]

[tex]P(O\ or\ A) = 0.85[/tex]

There are three separate, equal-size boxes, and inside each box there are four separate small boxes, and inside each of the small boxes there are three even smaller boxes. how many boxes are there all together?

Answers

Answer:

There are 51 boxes all together.

Step-by-step explanation:

Since there are three separate, equal-size boxes, and inside each box there are four separate small boxes, and inside each of the small boxes there are three even smaller boxes, to determine how many boxes are there all together, the following calculation must be done:

3 + 3 x 4 + 3 x 4 x 3 = X

3 + 12 + 36 = X

51 = X

Therefore, there are 51 boxes all together.

Jim took a loan of R30 000 for 18 months at simple interest rate of 12,5% per year. determine the amount that Jim will pay in 18 months​

Answers

Answer:

36151,82923

Step-by-step explanation:

30000* ( 1+12,5%/12)^18

Try calculator that works best for me lol

The theoretical mean of a distribution is also known as its ______________.

Answers

Answer:

skewness

Step-by-step explanation:

Average.

The average of a set of observations is the most important and useful measure of statistics and is a position measure, as it shows the positions of the numbers to which it refers. The average value is involved in several types of statistics and is examined in almost all statistical distributions. It is generally defined as the sum of the observations by their number. That is, it is the mathematical operation of finding the "mean distance" between two or more numbers.

Learn more about averages in https://brainly.com/question/22390452

Urgent need answer for this one.

Answers

Answer:

4th option

Step-by-step explanation:

6/sin(65) = 5/sin(x)

or, 6×sin(x) = 5×sin(65)

or, sin(x) = 5×sin(65)/6

or, x = arcsin(5×sin(65)/6)

Perimeter (numerical)

Answers

Answer:

270 m

Step-by-step explanation:

Add up all the sides

P = 19 +18.8+18.8 +18.8+18.8+40.8+19+40.8+18.8+18.8+18.8+18.8

P = 270 m

Identify which of the following is not equivalent to 234.

Question 1 options:

A)




B)

23−−√4

C)

(214)12

D)

214 x 212

Answers

Answer:

A since A is left blank its A

what is the relationship and what does X equal?
help! :)

Answers

Answer:

4x + 3 = 59

x = 14

Step-by-step explanation:

The vertical angles theorem states that when two lines intersect, the angles opposite each other are congruent. One can apply this here by stating the following:

4x + 3 = 59

Solve for (x), use inverse oeprations:

4x + 3= 59

4x = 56

x = 14

Answer:

Relationship : Vertical angle

Step-by-step explanation:

(4x + 3) = 59

4x = 59 - 3

4x = 56

x = 56/4

x = 14

If 1 kilogram (kg) is equal to about 2.2046 pounds (lbs.), what is the value of 1kg/2.2046lbs? What is the value of 2.2046lbs/1kg?

Answers

Step-by-step explanation:

The relation between kg and lbs is :

1 kg = 2.2046 lbs

We need to find the values of 1kg/2.2046lbs and 2.2046lbs/1kg.

So,

[tex]\dfrac{1\ kg}{2.2046\ lbs}=\dfrac{2.2046\ lbs}{2.2046\ lbs}\\\\=1[/tex]

and

[tex]\dfrac{2.2046\ lbs}{1\ kg}=\dfrac{2.2046\ lbs}{2.2046\ lbs}\\\\=1[/tex]

Hence, this is the required solution.

Answer:

Both are same as 1.

Step-by-step explanation:

1 kg = 2.2046 lbs

So,

[tex]\frac{1 kg}{2.2046 lbs }=\frac{1 kg }{1 kg} = 1[/tex]

And

[tex]\frac{2.2046 lbs}{1 kg }=\frac{1 kg }{1 kg} = 1[/tex]

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