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

Item 3 Write an equation that describes the function. (0,0) (1,4) (2,8) (3,12)

Answers

Answer:

y = 4x

Hope that helps!

Step-by-step explanation:

I will give brainliest and 5 stars​

Answers

Answer:

I think its C

Step-by-step explanation:

Tom has 50 coins consisting of quarters and dimes. The combined value of coins is $8.30. How many dimes and quarters does Tom have:
dimes
quarters

Answers

Answer:

thirty two quarters and three dimes

Systems of equation:substitution
The 2 problems in here i need done by 11:00pm est
8:00pm pst

Answers

Step-by-step explanation:

8)

describe y in terms of x

y=5+x

so now replace y with terms of x

5+x+3x=37

4x=32

x=8

y=13

9)

do the same here

x=y+1

2y+x=19

2y+y+1=19

3y=18

x=6

y=7

Two similar rectangles are shown. Which statement is true? A) The area of rectangle B is 1 3 the area of rectangle A. B) The area of rectangle B is 1 9 the area of rectangle A. C) The area of rectangle B is nine times the area of rectangle A. Eliminate D) The area of rectangle B is three times the area of rectangle A

Answers

Answer:

I think it is 19 I not really sure

Step-by-step explanation:

o work it out of my paper and I got 19

Answer: The answer to this math question about finding the statement is very true about 2 similar rectangles are being shown here below is B). B) The area of rectangle B is [tex]\frac{1}{9}[/tex] of the area of rectangle A.

Step-by-step explanation: I'm very sorry about that, but I don't have any step-by-step explanation to this math question about finding the statement is very true about 2 similar rectangles are shown here below, so anyways, I hope that my full short given answer without my given step-by-step explanation to your own math question about finding the statement is very true about 2 similar rectangles are being shown here below, please mark me as Brainliest, take care, always be safe, and have a great rest of the day and good night! :D

Sincerely,

Jason Ta,

The Ambitious of The Brainly And The Role of The TDSB And WHCI Student of The High School.

Please help out and make sure to show your work please

Answers

Answer:

80 in

Step-by-step explanation:

To find the whole thing: 12 * 12 = 144

To find one square: 144/9 = 16

To find shaded areas: 16 * 5 = 80

Hope this helps =]

2. Evalute (3a +6b)³​

Answers

Answer:

Here you go Hope it helps!!

Step-by-step explanation:

The price of a toy usually costing £50 is increased to £65
Workout the percentage increase.

Answers

Answer:

30 percent increase

Step-by-step explanation:

Someone help me please

Answers

11, 60, and 62 cuz the internet told me :)

Answer:

{11,60,62} could not represent the sides of a right triangle

what is the value of the digit 253,253,253 in the ten millions' place?

Answers

Answer:

50,000,000

Step-by-step explanation:

10,000,000 has 7 0's I just counted backward from the last three 6x and that gave me the answer of 3,000,000 sorry if it's wrong :c

Sharon made $45 in interest by placing $500 in a savings account with simple interest for 1 year. What was the interest rate?

Answers

Answer: The interest rate was 9%.

Step-by-step explanation:

If principal amount P is invested at the rate of r percent with simple interest(I) for t years, the formula to find rate :

[tex]R=\dfrac{I\times100}{P\times t}[/tex]

As per given,

P = $ 500, I = $45, t = 1 year

Substitute values in formula , we get

[tex]R=\dfrac{45\times100}{500\times1}\\\\\Rightarrow R=9\%[/tex]

Hence,  The interest rate was 9%.

FFFFFRrrRRreeeeeeeee PPPPOOOOOIIIINNNNTTTTTSSSSSS

Answers

Ahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Answer:

OMG! Thank you mate..... :D

Which triangle is a translation of triangle X?
triangle A
triangle B
triangle C
triangle D

Answers

Answer:

triangle b

Step-by-step explanation:

triangle b has the same dimensions and corresponding angles. which means it is a rigid transformation which is what a translation is

Answer:

Triangle b

Step-by-step explanation:

A day at the spa costs $125. You leave a 20% tip. How much tip did you leave?

Answers

Answer: $25

Step-by-step explanation:

20% = 0.20

125 x 0.20 = 25

$125 + $25 = $150 (the entire bill)

Answer:

20%/100 × 125 = 25

$125+25=50

hope it helps

If the sidewall of a cubic structure have length 7m , then find the total surface area.
is this jhit right?​

Answers

Answer:

Surface area of the cube = 294 m²

Step-by-step explanation:

Sidewall of a cube measures in length = 7 m

Formula for the surface area of a cube = Sum of the areas of all six sides of the cube

= 6 × (Side)²

= 6 × (7)²

= 6 × 49

= 294 m²

Therefore, surface area of the cube is 294 m².

The ratio of cakes to cookies in the bakery was 3:5. If there were 90 cakes, how many cookies were in the bakery?
plz help

Answers

Answer:

150 cookies

Step-by-step explanation:

Using the ratio as an equation we can divide 90 by 3 to find the common multiple used to simplify this equation into a more usable ratio.

3 : 5          90 : 5x (x is the common multiple)

90 / 3 = 30, so x is 30

Then we multiply both sides of the original ratio by the common multiple to get our answer.

3 : 5 is equal to 90 : 150

determine an equation and the radius for the circle that has its centre at the origin (0,0) passes through the point A 4-3

Answers

Given:

The center of the circle is at (0,0).

The circle passes through the point A(4,-3).

To find:

The radius and the equation of the circle.

Solution:

Distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The radius of the circle is the distance between the points (0,0) and (4,-3).

[tex]r=\sqrt{(4-0)^2+(-3-0)^2}[/tex]

[tex]r=\sqrt{(4)^2+(-3)^2}[/tex]

[tex]r=\sqrt{16+9}[/tex]

[tex]r=\sqrt{25}[/tex]

[tex]r=5[/tex]

So, the radius of the circle is 5 units.

The standard form of a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where, (h,k) is center of circle and r is the radius.

Putting h=0, k=0, r=5, we get

[tex](x-0)^2+(y-0)^2=5^2[/tex]

[tex]x^2+y^2=25[/tex]

Therefore, the radius of the circle is 5 units and the equation of the circle is [tex]x^2+y^2=25[/tex].

-4(8h-5)= -16 round to the nearnest hundreth

Answers

Answer:

h=9/8 or 1.125 but since yo said round it's 1.13

Step-by-step explanation:

1/4 + 3 = ??
What’s the answer??

Answers

Answer:

3.25

Step-by-step explanation:

divide then add 3

Answer:

3 1/4 or 13/4

Step-by-step explanation:

question is attached​

Answers

okay here you goo

Answer:

are you in a rush or can i do it in like 5 mins

Help I will be marking brainliest!!!

A. 67.1
B. 45.2
C. 93.4
D. 63.0

Show work, if possible. Thanks❤️

Answers

it’s C 93.4 bro and i gotta make this 29 characters long

Help needed immediately

Answers

Answer:

The answer would be B.

Step-by-step explanation:

Because both the triangles have different sides and they don't follow SAS or SSS criterion.

Hope it helped

Stay safe and help others

PLEASEEE HELP ASAP ITS IMPORTANT !!!!

Answers

Answer:

The rate of change in the table is 78 students per year

Step-by-step explanation:

Here, we want to get the rate of change of the function

Mathematically, we can get this by using the formula;

m = (y2-y1)/(x2-x1)

(x1,y1) and (x2,y2) are points we are to select from the table

Let us select the point (4,704) and (17,1718) from the table

The slope is thus;

m = (1718-704)/(17-4) = 78 students per year

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:

A motor cyclist makes a trip of 500km. If he had increased his speed by 10kmh-1, he could have covered 600km in the same time. What was the original speed?

Answers

Answer:

the original speed is 50 km/h

Step-by-step explanation:

Let us assume the original speed be x

and fastest speed be (x+ 10)

Now here apply the time formula

i.e. distance by the speed

Original time = Fastest time

500 ÷ x = 600 ÷ x + 10

Now do cross multiplication

600x = 500(x + 10)

600x = 500x + 5000

100x = 5000

x = 50 km/h

Hence, the original speed is 50 km/h

7
Which fraction, decimal, or percent that is not equivalent to the others

Answers

Answer:

show png of what u talking about

Step-by-step explanation:

not enough info

if p q by the consecutive interior angles theorem which angles must be supplementary​

Answers

Answer:

Angles 3 and 8 are consecutive interior angles

Step-by-step explanation:

Here, we want to use the consecutive interior angles theorem to find the supplementary angles

We start by looking at the transversal line

two angles that are directly above each other on the two lines are consecutive interior angles that are supplementary

We have this two as;

Since it is P and Q that are parallel, it is angles 3 and 8 that are consecutive interior angles

please answer this, I really need help​

Answers

Answer:

????? I am only in first grade

Step-by-step explanation:

???????

Todo numero es divisible por 3, si al sumar el total de sus digitos, se obtiene un numero mutiplo del tres (se puede expresar como tres por un numero entero )

Answers

Answer:

si, eso es correcto

Step-by-step explanation:

Espero que esto ayude a marcar el MÁS CEREBRAL !!!

PLEASE HELP

A circular hot tub has a diameter of 3 feet. What is the approximate
circumference of the hot tub?
9.42
15.70
18.84
25.12

Answers

The answer is 9.42. All you need to do is multiply 3 by pi (3x3.14)
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