Which of the following statements are true?

Using the shell method, the volume integral would be

[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx[/tex]

That is, each shell has a radius of x (the distance from a given x in the interval [0, 2] to the axis of revolution, x = 0) and a height equal to the difference between the boundary curves y = x ⁸ and y = 256. Each shell contributes an infinitesimal volume of 2π (radius) (height) (thickness), so the total volume of the overall solid would be obtained by integrating over [0, 2].

The volume itself would be

[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx = 2\pi \left(128x^2-\frac1{10}x^{10}\right)\bigg|_{x=0}^{x=2} = \boxed{\frac{4096\pi}5}[/tex]

Using the disk method, the integral for volume would be

[tex]\displaystyle \pi \int_0^{256} \left(\sqrt[8]{y}\right)^2\,\mathrm dy = \pi \int_0^{256} \sqrt[4]{y}\,\mathrm dy[/tex]

where each disk would have a radius of x = ⁸√y (which comes from solving y = x ⁸ for x) and an infinitesimal height, such that each disk contributes an infinitesimal volume of π (radius)² (height). You would end up with the same volume, 4096π/5.

The volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

We have a function:

[tex]\rm y = x^8[/tex]   or

[tex]x = \sqrt[8]{y}[/tex]

And  y = 256

By using the vertical axis of rotation method to evaluate the volume of the solid formed by revolving the region bounded by the curves.

[tex]\rm V = \pi \int\limits^a_b {x^2} \, dy[/tex]

Here a = 256, b = 0, and [tex]x = \sqrt[8]{y}[/tex]

[tex]\rm V = \pi \int\limits^{256}_0 {(\sqrt[8]{y}^2) } \, dy[/tex]

After solving definite integration, we will get:

[tex]\rm V = \pi(\frac{4096}{5} )[/tex]  or

[tex]\rm V =\frac{4096}{5}\pi[/tex] cubic unit

Thus, the volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.

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Answer:

Vhjaakkjvvkllmn aar

Step-by-step explanation:

Vbkisavn

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NG Jill quolk

Hill s njknbn

Answer:

396 in ^3

Step-by-step explanation:

The volume of a rectangular prism is

V = l*w*h  where l is the length, w is the width, and h is the height

V = 12 * 3 * 11

V = 396 in ^3

Answer:

x = 150°

Step-by-step explanation:

Interior angle of a hexagon = 120° and interior angle of a square = 90°

so remaining angle, 360-120-90 = 150°

Answer:

the first term is -4

the difference is 3.

*notice how each term increases by 3:

-4 + 3 = -1

-1 + 3 = 2

2 + 3 = 5

Step-by-step explanation:

Step-by-step explanation:

Let

[tex]m_p[/tex] = mass of the painter

[tex]m_s[/tex] = mass of the scaffold

[tex]m_e[/tex] = mass of the equipment

[tex]T[/tex] = tension in the cables

In order for this scaffold to remain in equilibrium, the net force and torque on it must be zero. The net force acting on the scaffold can be written as

[tex]3T = (m_p + m_s + m_e)g\:\:\:\:\:\:\:(1)[/tex]

Set this aside and let's look at the net torque on the scaffold. Assume the counterclockwise direction to be the positive direction for the rotation. The pivot point is chosen so that one of the unknown quantities is eliminated. Let's choose our pivot point to be the location of [tex]m_e[/tex]. The net torque on the scaffold is then

[tex]T(1.4\:\text{m}) + m_sg(1.9\:\text{m}) + m_pg(4.2\:\text{m}) - 2T(5.2\:\text{m}) = 0[/tex]

Solving for T,

[tex]9T = m_sg(1.9\:\text{m}) + m_pg(4.2\:\text{m})[/tex]

or

[tex]T = \frac{1}{9}[m_sg(1.9\:\text{m}) + m_pg(4.2\:\text{m})][/tex]

[tex]\:\:\:\:= 423.3\:\text{N}[/tex]

To solve for the the mass of the equipment [tex]m_e[/tex], use the value for T into Eqn(1):

[tex]m_e = \dfrac{3T - (m_p + m_s)g}{g} = 14.6\:\text{kg}[/tex]

Answer:

Its 2714

Step-by-step explanation:

Khan Academy

The volume of the material that would be needed for each cylindrical cracker is approximately: 2,714 mm³ mm³.

Volume of a cylinder = πr²h

The volume of the material used for each cylindrical cracker = Volume of entire cylindrical cracker - volume of cylindrical hole

Radius of entire cracker (r) = 16/2 = 8 mm

Height (h) = 18 mm

Volume of the entire cracker = π(8²)(18) ≈ 3,619 mm³

Radius of hole (r) = 8/2 = 4 mm

Height (h) = 18 mm

Volume of the entire cracker = π(4²)(18) ≈ 905 mm³

The volume of the material used for each cylindrical cracker = 3,619 - 905 = 2,714 mm³

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Answer:

The Bison is faster by 10 miles per hour.

Step-by-step explanation:

The Bison runs at 3520 ft / min

= 3520/ 5280 miles / minute

= (3520/ 5280) * 60 miles per hour

= 40 miles per hour

Answer:

The degree of this polynomial is 2.

Step-by-step explanation:

The degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer.

The given polynomial is:

[tex]9m^2+11m^2+2m^2[/tex]

The only variable is m.

The power of m in all terms is 2.

So, the degree of this polynomial is 2.

Answer:

D

Step-by-step explanation:

( 40 ( 3.10 ) + 140 ) ( 52 weeks ) = 13,728

Answer:

(7x+4) and (4x)

Step-by-step explanation:

The two expressions are (7x+4) and (4x)

Given:

d = 2

f = 4

To find:

Value of  [tex]\frac{14(7)-d}{2f}[/tex]

Steps:

we need to substitute and then find the value,

[tex]= \frac{14(7)-2}{2(4)}\\ \\=\frac{98-2}{8} \\\\=\frac{96}{8}\\\\=12[/tex]

Therefore, the answer is option C) 12

Happy to help :)

If you need help, feel free to ask

Answer:

Selling price=rs.600.

Profit of rs=100.

Step-by-step explanation:

C.P=500; profit%=20%

S.P.=100+profit%×C.P/100

S.P=120×500/100

=rs.600

S.P>C.P

Profit S.P-C.P

600-500=100

he gained for rs.100.

Step-by-step explanation:

Recognize the relation between the graph and the slope–intercept form of an equation of a line

Identify the slope and y-intercept form of an equation of a line

Graph a line using its slope and intercept

Choose the most convenient method to graph a line

Graph and interpret applications of slope–intercept

Use slopes to identify parallel lines

Use slopes to identify perpendicular lines

Answer:

the correct answer is point b

I cant graph it on here but. if your graph goes by 10 then the slope should increase by 666 every minute on the x line

Answer:

The answer is in the screenshot

Step-by-step explanation:

PLEASE GIVE BRAINLIEST

Answer:

yep it's D

Step-by-step explanation:

Answer

20%

Step-by-step explanation:

9514 1404 393

Answer:

  a.  55%

Step-by-step explanation:

The percentage increase is calculated from ...

  % increase = (amount of increase)/(original amount) × 100%

  = (2219 -1432)/1432 × 100% = 787/1432 × 100% ≈ 54.96%

The number of births increased by about 55% during those 10 years.

Answer:

Step-by-step explanation:

2219-1432/1432 x 100% = 787/1432 x 100 = 54.9581~~ 55%

Answer:

...

Step-by-step explanation:

seeee the above picture

9514 1404 393

Answer:

  43

Step-by-step explanation:

Put the value where t is and do the arithmetic.

  h = 50 -t/5

  h = 50 -35/5 = 50 -7 = 43

The output, h, is 43 when the input is 35.

Answer:

43

Step-by-step explanation:

The answer is 43 on Khan :)

Step-by-step explanation:

A. gof=g(f(x))

= g(f(6))

=6×6

36

9514 1404 393

Answer:

Step-by-step explanation:

The linear speed 12 mi/h translates to inches per minute as follows:

  (12 mi/h) × (5820 ft/mi) × (12 in/ft) ÷ (60 min/h) = 12,672 in/min

The relationship between arc length and angle is ...

  s = rθ

For a constant radius, the relationship between linear speed and angular speed is ...

  s' = rθ'

  θ' = s'/r = (12,672 in/min)/(12 in) = 1056 rad/min

There are 2π radians in one revolution, so this is ...

  (1056 rad/min) ÷ (2π rad/rev) = 168.068 rev/min

Answer:

C

Step-by-step explanation:

Answer:

$275 a month

Step-by-step explanation:

Let x represent how much each friend is paying.

The amount Jane pays can be represented by 2x, since she is paying double than her friends.

Add together these terms and set them equal to 550. Then, solve for x:

x + x + 2x = 550

4x = 550

x = 137.5

So, each friend is paying $137.50. Double this to find how much Jane is paying:

137.5(2)

= 275

So, Jane is paying $275 a month

Answer:

65 feet and 2 inches

Step-by-step explanation:

to find the area of a rectangle you need to multiply length times width in this case 17" times 3'10". But first you must convert everything into the same form(in this case feet) so first you can convert everything to inches by multiplying 3 times 12  which gives you 36 then add the 10, so it is now 46 inches then multiply that by 17 and altogether it is 782 inches, then divide by 12 (to convert it back to feet) and the answer is 65.1666666667. After you can round and get 65 feet and 2 inches.

Answer:

7x is monomial according to question.

Answer:

A - L = O

Step-by-step explanation:

A = L + O

Subtract L from each side

A-L = L + O - L

A - L = O

The way that the given formula A = L + O can be rewritten to solve for O is; O = A - L

We are given the formula to find A as;

A = L + O

Now, to make O the subject of the formula, let us use subtraction property of equality to subtract L from both sides to get;

A - L = L + O - L

O = A - L

Thus, the way the formula can be rewritten to solve for O is;

O = A - L

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Answer: There are 32 dogs and 1 Parrot

Step-by-step explanation: I had a question like this in a math class. What you first do is to recognize that- parrots have 2 legs and dogs have 4. We can do 130/2 = 65 and 130/4= 32.5. Now we know that if there was only one animal, there would be 65 parrots, and 32 dogs- one with half of the legs. Since there is a .5 for the dogs, if we put in one parrot, it would mean that there is exactly 130.

(32 x 4)+(2x1) = 130.  There are 32 dogs and 1 Parrot. I hope this answer is ✅ and helps, i just joined the community and this is the first person I answered. Good Luck!!

Answer:

Step-by-step explanation:

To solve this, we need to list some equations. Letting variable d stand for dogs and p stand for parrots, we have:

d+p=40 (The number of dogs plus the number of parrots equals 40)

4d+2p=130 (Each dog has 4 legs and each parrot has 2 legs and they have 130 legs in total)

With this system of equations, we can quickly solve it for d and p.

Subtract:

 4d+2p=130

- d+p=40

_________

3d+p=90,

p=90-3d

Substitution:

d+(90-3d)=40

90-2d=40

-2d=-50

d=25

Substitution to get p:

p+25=40

p=15

There you have it! There are 25 dogs and 15 parrots. To check our work,

25+15=40

4(25)+2(15)=100+30=130

I hope this helped! :)

Answer:

I I want everything in English

Step-by-step explanation:

it is difficult to read other languages write it in English please