1) The region enclosed by the x-axis, the line x=3 and the curve y = sq. Rt x is rotated about the x-axis. What is the volume of the solid generated? *

Answers

Answer 1

Using the disk method, the volume would be

[tex]\displaystyle \pi \int_0^3 (\sqrt x)^2 \,\mathrm dx=\pi \int_0^3 x\,\mathrm dx=\frac\pi2 x^2\bigg|_0^3=\boxed{\frac{9\pi}2}[/tex]

That is, you split up the solid into disks of some small height ∆x, and each disk has radius at point x equal to the distance (√(x)) from the axis of revolution (the x-axis, y = 0) to the curve y = √(x). The volume of such a disk is then π (√(x))² ∆x. Take the sum of these volumes to get the total volume, then as the heights get smaller and smaller, replace ∆x with dx and the sum with the integral.

Answer 2

In this exercise we have to use the knowledge of the integral to calculate the volume of the disk that will correspond to:

[tex]V= \frac{9\pi }{2}[/tex]

That is, you split up the solid into disks of some small height ∆x, and each disk has radius at point x equal to the distance (√(x)) from the axis of revolution (the x-axis, y = 0) to the curve y = √(x). The volume of such a disk is then π (√(x))² ∆x. Take the sum of these volumes to get the total volume, then as the heights get smaller and smaller, replace ∆x with dx and the sum with the integral. Using the disk method, the volume would be:

[tex]\pi \int\limits^3_0 {(\sqrt{x})^2} \, dx = \pi \int\limits^3_0 {x} \, dx = \frac{\pi x^2}{2} = \frac{9 \pi }{2}[/tex]

See more about volume at brainly.com/question/1578538


Related Questions

PLEASE HELP IMMIDEATIALY BFHBGDWAHDW

Answers

Answer:

zeros and AoS

Step-by-step explanation:

zeros, x = (1 , -7)

AoS:x =-1

heyy could you help me out with this question I have been stuck in this question??​

Answers

i think the first box is perpendicular good luck

One of my homework problems say: Solve the proportion. X/4=2/5. I am stuck on this one. It will be appreciated if you explain the steps to complete this problem. Thanks for your help!

Answers

Answer:

1.6

Step-by-step explanation:

Given :

X/4 = 2/5

To solve for X ;

We can use cross multiplication ; multiply opposite values :

X * 5 = 2 * 4

5X = 8

To isolate X ;

Divide both sides by 5

5X/5 = 8/5

X = 8/5

X = 1.6

A soup kitchen cooks up a total of 200 cups of soup. If their standard serving size is 2 1/2 cups, how many servings can they hand out, at most?

Answers

Answer: They can hand out exactly 80
Explanation: 200 divided by 2 1/2 = 80

x = (y/2) - 1
Please help me find the answer.

Answers

Answer:

Step-by-step explanation:

Well you didn't give directions on what to solve for,

I'm gonna assume you want to solve for y

x = (y/2) - 1 (add 1 to both sides)

x + 1 = y/2 (multiply both sides by 2)

2(x + 1) = y (distribute the 2)

y = 2x + 2

what is a slope of a line between the x-axis and y-axis​

Answers

Answer:

Mercedes, look at the graph i'm attaching... do you see ? what's the slope?

Step-by-step explanation:

In ΔTUV, the measure of ∠V=90°, the measure of ∠U=70°, and UV = 9.6 feet. Find the length of TU to the nearest tenth of a foot.

Answers

28.1 feet

explaination

\cos U = \frac{\text{adjacent}}{\text{hypotenuse}}=\frac{9.6}{x}

cosU=

hypotenuse

adjacent

=

x

9.6

\cos 70=\frac{9.6}{x}

cos70=

x

9.6

x\cos 70=9.6

xcos70=9.6

Cross multiply.

\frac{x\cos 70}{\cos 70}=\frac{9.6}{\cos 70}

cos70

xcos70

=

cos70

9.6

Divide each side by cos 70.

x=\frac{9.6}{\cos 70}=28.0685\approx 28.1\text{ feet}

x=

cos70

9.6

=28.0685≈28.1 feet

Type into calculator and roundto the nearest tenth of a foot.

What is the straight-line distance between (-2, -7) and (-4, -9) on a coordinate graph?

Answers

Answer:

yeah, the selected is correct

Step-by-step explanation:

distance is...

2 and 2 square root

What is the solution to the system graphed below? How do you know?

Answers

Answer:

(1,7)

Step-by-step explanation:

It is where the line intersects. coordinates x axis 1, coordinates y axis 7.

President Jackson favored state banks over the Second Bank of the United States because he
believed
A.
the Constitution called for a series of state banks.
B.
state banks should issue a uniform national currency.
C.
the Bank could not control the nation's loans.
D.
the Bank had too much power over the nation's economy.

Answers

I believe it’s D! Good luck!

Simplify each expression. Show all work from credit.
Plz help me

Answers

Answer:

1. = 1 because any numbers to the power 0 is one

2. = 1/64

3.= b^15 base same power added up

Quick prints makes custom t-shirts. They charge $10 for each t-shirt ordered plus a $5 design fee. Which situation best represents y, the total cost to order x t-shirts?

Answers

Answer:

y = 10x+5

Step-by-step explanation:

The price of each T-shirt = $10

Design fee on each T-shirt = $5

We need to find the expression for the total cost. Let the total cost be y. So,

Let he has ordered x T-shirts. So,

y = 10x+5

Hence, this is the required solution.

Fifteen pencils are sold for $750. what is the cost for 1 pencil ?

a. 20
b.50
c.30
d.100​

Answers

Answer:

b) 50

Step-by-step explanation:

750/15 = 50

250 is 1.5cm. How thick is 400 pages

Answers

Answer: 2.4 cm

Step-by-step explanation:

1.5 divided by 250 gives that each page is .006cm. 400 times .006 is 2.4cm

2. In Ella's math class, there are 12 girls and 15 boys. Which of the following is the ratio of boys to girls in Ella's math class?
A 12/27
B 12/15
C15/12
D27/12​

Answers

Answer:

C. 15/12

Step-by-step explanation:

15 boys and 12 girls

Answer:

b

Step-by-step explanation:

12/15

In a survey, some children were asked to choose whether they like to stay up late or get up early.
35% of the students said they prefer to get up early. 28 students prefer getting up early. How many students in total were surveyed?
students

Answers

Answer:

80 Students

Step-by-step explanation:

So I set up my problem like this(This is a way to figure a certain amount of a percent or vice versa):

35            28

____ = _____

100         x

First, you do 100 x 28= 2800

Second, do 2800 divided by 35= 80

The number in students surveyed is 80.

I agree with him 80 students

for part of a recipe jada adds 0.35 milliliters of vanilla extract to 16.4 milliliters of milk. How many milliliters does the mixture contain??

Answers

Answer: 16.75 milliliters
Step-by-step explanation:
I believe it is 16.75 because 0.35 + 16.4 is 16.75 why is it addition decimals? Because it says How many milliliters does the mixture contain. It is talking about both combined.

33°
114"
33
A) right scalene
B) acute scalene
C) obtuse isosceles
D) equilateral

Answers

Answer:

b acute I think so ok but that was a weird quistoin

what is the ratios to 25:90

Answers

Answer:

5/18

Step-by-step explanation:

25 / 90 =5*5 / 5*18 =5/18

To prepare for a party, Jada poured 0.45 liter of juice into each of several cups. Altogether she poured 9 liters of juice into the cups.

Answers

Answer: 20 cups

Step-by-step explanation:

Question would like to know the number of cups that Jada poured juice into.

If each cup got 0.45 litres, the number of cups that Jada poured drinks into would be the total amount of juice poured divided by the quantity per cup:

= Total juice poured / Quantity per cup

= 9 litres/ 0.45 litres per cup

= 20 cups

Okay, I and my mom do not know how to do this- please help-
Distribution Skill
3 (-5y²- 3)

Help p-p

Answers

3(-5y^2-3)
=-15y^2-9

Answer:

Step-by-step explanation:

this is the start of your mad algebra skilz.. it does take constant practice, like anything you want to get better at :)  keep trying

this is called  "Distribution" and is used often

3(-5[tex]y^{2}[/tex] -3)

-15[tex]y^{2}[/tex] +9

if you need more explanation just put your questions at the comments of this problem ... i'll see them   :)

Which of the following shows the extraneous solution to the logarithmic equation log7(3x^3+x)-log7(x)=2?

Answers

Answer:

x=4

Step-by-step explanation:

on edge

The extraneous solution to the logarithmic equation log₇(3x²+x)-log₇x=2 is x=16

What is logarithm?

When you raise a number with an exponent, there comes a result.

Lets say you get[tex]a^b = c[/tex]

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

[tex]b = \log_a(c)[/tex]

'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

We are given the function as;

log₇(3x²+x)-log₇x=2

Domian: 3x²+x>0

x(3x+1)>0

x∈(-∞,-1/3)U(0,∞)

Hence, x∈(0,∞), Thus x∈(0,∞)

In this problem we use the following formula:

 [tex]\boxed {log_ax-log_ay=log_a\frac{x}{y}}\displaystyle\\log_7(3x^2+x)-log_7x=2\\\\log_7(x(3x+1))-log_7x=2(1)\\\\log\frac{x(3x+1)}{x} =2(log_77)\\\\log(3x+1)=log_77^2\\\\log_7(3x+1)=log_749\\\\\\\\3x+1=49\\\\3x+1-1=49-1\\\\3x=48\\\\x=16[/tex]

Learn more about logarithm here:

https://brainly.com/question/20835449

#SPJ7

PLZ HELPPPP ILL GIVE BRAINLIEST

Answers

Answer:

(A).

Step-by-step explanation:

yo my boy look at the problem first because that was so easy

Tonya drives for 5 hours at 55 mph. How far does she go?

Answers

I believe it’s 275 because you would multiply 5 by 55

HELP WILL MARK BARINLIEST IF RIGHT!!!

Answers

Step-by-step explanation:

Hence the value of x is 70.14cm.

Which equation is the inverse of y =2x^2 - 8?
A. y = + √x+8/2
B. y = +√x+8/2
C. y = + √ x/2 + 8
D. y = +√x/2 +4​

Answers

Answer:

a

Step-by-step explanation:

Find the volume. Round your answer to the nearest tenth and show your work

helllllllllllllllllllppppppppp!!!!!!!!!!!!!!!!!!!!!!!!
pleeeeeeeeeeeease

Answers

Answer:

1:5 is the ratio so 1 cow for every 5 sheep, 2 cows for 10 sheep and 3 cows for 15 sheep.

Step-by-step explanation:

please help first image pleaseeeeee............................................

Answers

I think the answer is 2 for the math , not sure mark brainliest pls

Answer:

1:2

Step-by-step explanation:

Cecilia is saving money to buy a bicycle. She started with $75 and saves $10 each week from her allowance. Which equation represents how much money, y, Cecilia has at the end of x weeks? O A. y = 75x + 10 o B. y = 10x + 75 O C. x = 75y + 10 O D. X = 10y + 75​

Answers

Answer:

y = 10x + 75 If not then

X = 10y + 75

Tywaun wants to know how much candy his container can hold. The
container is 20 centimetres tall, 10 centimetres long and 10 centimetres
wide. What is the container's volume?

Answers

Answer:

100 pieces maybe?

Step-by-step explanation:

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