solve this equation pleaseee

Answer:

[tex]Volume = \frac{384}{7}\pi[/tex]

Step-by-step explanation:

Given (Missing Information):

[tex]y = x^\frac{3}{2}[/tex]; [tex]y = 8[/tex]; [tex]x=0[/tex]

Required

Determine the volume

Using Shell Method:

[tex]V = 2\pi \int\limits^a_b {p(y)h(y)} \, dy[/tex]

First solve for a and b.

[tex]y = x^\frac{3}{2}[/tex] and [tex]y = 8[/tex]

Substitute 8 for y

[tex]8 = x^\frac{3}{2}[/tex]

Take 2/3 root of both sides

[tex]8^\frac{2}{3} = x^{\frac{3}{2}*\frac{2}{3}}[/tex]

[tex]8^\frac{2}{3} = x[/tex]

[tex]2^{3*\frac{2}{3}} = x[/tex]

[tex]2^2 = x[/tex]

[tex]4 =x[/tex]

[tex]x = 4[/tex]

This implies that:

[tex]a = 4[/tex]

For [tex]x=0[/tex]

This implies that:

[tex]b=0[/tex]

So, we have:

[tex]V = 2\pi \int\limits^a_b {p(y)h(y)} \, dy[/tex]

[tex]V = 2\pi \int\limits^4_0 {p(y)h(y)} \, dy[/tex]

The volume of the solid becomes:

[tex]V = 2\pi \int\limits^4_0 {x(8 - x^{\frac{3}{2}}}) \, dx[/tex]

Open bracket

[tex]V = 2\pi \int\limits^4_0 {8x - x.x^{\frac{3}{2}}} \, dx[/tex]

[tex]V = 2\pi \int\limits^4_0 {8x - x^{\frac{2+3}{2}}} \, dx[/tex]

[tex]V = 2\pi \int\limits^4_0 {8x - x^{\frac{5}{2}}} \, dx[/tex]

Integrate

[tex]V = 2\pi * [{\frac{8x^2}{2} - \frac{x^{1+\frac{5}{2}}}{1+\frac{5}{2}}]\vert^4_0[/tex]

[tex]V = 2\pi * [{4x^2 - \frac{x^{\frac{2+5}{2}}}{\frac{2+5}{2}}]\vert^4_0[/tex]

[tex]V = 2\pi * [{4x^2 - \frac{x^{\frac{7}{2}}}{\frac{7}{2}}]\vert^4_0[/tex]

[tex]V = 2\pi * [{4x^2 - \frac{2}{7}x^{\frac{7}{2}}]\vert^4_0[/tex]

Substitute 4 and 0 for x

[tex]V = 2\pi * ([{4*4^2 - \frac{2}{7}*4^{\frac{7}{2}}] - [{4*0^2 - \frac{2}{7}*0^{\frac{7}{2}}])[/tex]

[tex]V = 2\pi * ([{4*4^2 - \frac{2}{7}*4^{\frac{7}{2}}] - [0])[/tex]

[tex]V = 2\pi * [{4*4^2 - \frac{2}{7}*4^{\frac{7}{2}}][/tex]

[tex]V = 2\pi * [{64 - \frac{2}{7}*2^2^{*\frac{7}{2}}][/tex]

[tex]V = 2\pi * [{64 - \frac{2}{7}*2^7][/tex]

[tex]V = 2\pi * [{64 - \frac{2}{7}*128][/tex]

[tex]V = 2\pi * [{64 - \frac{2*128}{7}][/tex]

[tex]V = 2\pi * [{64 - \frac{256}{7}][/tex]

Take LCM

[tex]V = 2\pi * [\frac{64*7-256}{7}][/tex]

[tex]V = 2\pi * [\frac{448-256}{7}][/tex]

[tex]V = 2\pi * [\frac{192}{7}][/tex]

[tex]V = [\frac{2\pi * 192}{7}][/tex]

[tex]V = \frac{\pi * 384}{7}[/tex]

[tex]V = \frac{384}{7}\pi[/tex]

Hence, the required volume is:

[tex]Volume = \frac{384}{7}\pi[/tex]

The volume of the solid of revolution generated by revolving the plane region about the y-axis is [tex]\frac{10240\pi}{3}[/tex] cubic units.

Let be [tex]f(x) = x^{5/2}[/tex] and [tex]g(x) = 32[/tex], whose point of intersection is [tex](x,y) = (4, 32)[/tex]. Solid of revolution generated by revolving the plane region about the y-axis is defined by the following formula:

[tex]V = 2\pi\int\limits^{32}_0 {y\cdot g(y)} \, dy[/tex] (1)

If we know that [tex]g(y) = y^{2/5}[/tex], then the volume of the solid of revolution is:

[tex]V = 2\pi\int\limits^{32}_{0} {y^{7/5}} \, dy[/tex]

[tex]V = 2\pi\cdot \left(\frac{5}{12}\cdot y^{12/5}\right)\left|_{0}^{32}[/tex]

[tex]V = \frac{5\pi}{6} \cdot y^{12/5}|\limit_{0}^{32}[/tex]

[tex]V = \frac{5\pi}{6}\cdot 32^{12/5}[/tex]

[tex]V = \frac{10240\pi}{3}[/tex]

The volume of the solid of revolution generated by revolving the plane region about the y-axis is [tex]\frac{10240\pi}{3}[/tex] cubic units. [tex]\blacksquare[/tex]

The statement is incomplete. Complete form is shown below:

Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the y-axis. [tex]y = x^{5/2}[/tex], [tex]y = 32[/tex], [tex]x = 0[/tex].

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Answer:

Its B.

Step-by-step explanation:

Because [tex]11^{2}[/tex] + [tex]12^{2}[/tex] does not equal [tex]15^{2}[/tex]

121 + 144 [tex]\neq[/tex] 225

265 [tex]\neq[/tex] 225

9514 1404 393

Answer:

  x = 19

Step-by-step explanation:

Corresponding sides are proportional.

  full length/right segment = 36/20 = (x+5+30)/30

Multiplying by 30 gives ...

  54 = x +35

  19 = x . . . . . . . subtract 35

Answer:

$14.58

13.50+1.08= $14.58

Now im not 100% sure, but this is what i got (for number one).

y=2x−1

Swap sides so that all variable terms are on the left hand side.

2x−1=y

Add 1 to both sides.

2x=y+1

Divide both sides by 2.

2x/2 = y+1/2

​Dividing by 2 undoes the multiplication by 2.

So therefore, X = Y+1/2.

(i couldnt explain that very well im sorry, i dont know the 2nd answer im very bad at these)

​  

Answer:

I need 1 Brainliest before I can become Virtuoso

Step-by-step explanation:

The point which is a reflection of (-3,-3) across the y-axis is, (3, - 3)

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

We have to given that;

The point is,

⇒ (- 3, - 3)

Now, We know that;

The rule of reflection after across the y - axis is,

⇒ (x, y) = (- x, y)

Thus, The point which is a reflection of (-3,-3) across the y-axis is,

⇒ (x, y) = (- x, y)

⇒ (-3, -3) = (- (-3), -3)

              = (3, - 3)

Learn more about the coordinate visit:

https://brainly.com/question/24394007

#SPJ2

Answer:

A(1.15)

Step-by-step explanation:

Answer:

Linear expression is linear equations

Step-by-step explanation:

Answer:

y = -x + 1

Step-by-step explanation:

y=mx+b

m:slope= rise/run, the line goes down 1 and over 1 so it would be -1/1 which is -1

b:y-intercept: the line crosses the y-axis at 1

plug in m=-1 and b=1 into y=mx+b

y=-1x+1

y=-x+1

9514 1404 393

Answer:

  (x, y) = (8, 2)

Step-by-step explanation:

The relevant equations are ...

  3x -y = 22

  x +2y = 12

__

We can eliminate y by adding twice the first equation to the second.

  2(3x -y) +(x +2y) = 2(22) +(12)

  7x = 56

  x = 8

Substituting into the first equation gives ...

  3(8) -y = 22

  y = 24 -22 = 2

The first number is 8; the second number is 2.

Answer:

perfect square / rational

4

Step-by-step explanation:

Answer:

root of 16. or 4

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

Answer:

(12x8) + 5

Step-by-step explanation:

The product of 12 and 8 would be multiplication, so you can represent that as

(12x8) or 12x8

"5 more" simply means addition

So if you were to put all that together as a numerical expression it would be

(12x8) + 5

Hope  this helps!

Answer:

56.757 and if u divide it : 676.75

Step-by-step explanation:

uwu

Answer:

13.3 or 13

Step-by-step explanation:

10x+11=144

10x=144-11

10x=133

x=133/10

x=13.3

Answer:

2 a 3 d 4 c 5 b

Step-by-step explanation:

Answer:

20.25

Step-by-step explanation:

Divide 13.50 by 2 and then multiply by 3.

Answer:

Can’t trust anyone these days fake is becoming the new trend.

Answer:

$7.25.

Step-by-step explanation:

Given that, when Brandon went bowling, it cost $ 4.95 per game, plus a one-time fee to rent the shoes, and knowing that Brandon played 5 games and paid $ 32, to find the cost to rent the shoes the following equation must be performed :

4.95 x 5 + X = 32

24.75 + X = 32

X = 32 - 24.75

X = 7.25

Thus, the cost of renting the shoes was $ 7.25.

Answer:

In the question, it says that this is a proportional relationship.

A proportional relationship is something like:

y = k*x

So when we have x = 0, we also need to have y = 0.

For the case in the question, this does not happen, so i guess that the actual question is:

"At a gourmet coffee shop. 3.5 pounds of dark-roast coffee beans cost $56 and 7 pounds of the same coffee cost $112."

We can define:

x = amount of coffee

y = price of that coffee

Now we have two pairs:

$56 to get 3.5lb

$112 to get 7lb

Then we have two points:

(3.5lb, $56)

(7lb, $112)

We can draw these two points and then connect them with a line, this line will represent the proportional relationship.

Now we need to look at the value 1 in the x-axis, then draw a vertical line

At the point where this vertical line intersects the graph, we draw a horizontal line, and the value of y is the value at which this horizontal line intersects the y-axis.

(you can see a rough sketch of this in the image below)

The solution is 1lb of coffee costs $16.

Answer:

is A

Step-by-step explanation:

00000000000000000000000000

Answer:

Its 0 because 12+ (-12) = 0

Answer:

give me 1 second to answer with the correct answer

Answer:

[tex]x^2+2x-3[/tex]

Step-by-step explanation:

Note that [tex]x^2-x-20=(x-5)(x+4)[/tex], so, if the denominator is [tex](x-5)(x+4)(x+3)[/tex], we need to multiply the numerator by [tex](x+3)[/tex]. And [tex](x-1)(x+3)=x^2+2x-3[/tex].

Answer:

Step-by-step explanation:

Let the transmitter be located at (0,0)

The equation for its effective coverage area will be a circle centered at  (0,0)  with a radius of 49.

So....the equation is  

[tex]x^2 + y^2 = 49^2[/tex]

[tex]x^2 + y^2 = 2401[/tex]

Let the point 67 miles north of the transmitter be (0, 67)

Let the point 63  miles east of the transmitter be (63, 0)

The line connecting these (the line of travel)  will have a slope of

[67 - 0] / [ 0 - 63]  =  -67/63

The equation of this line will be: y  = (-67/63)x  + 67

The signal will be received between the points:

(21.681, 43.942)  and (45.192, 18.938)

The distance between these points  is

[tex]\sqrt{[ ( 45.192 - 21.681)^2 + ( 43.942 - 18.938)^2 ] } = 34.322 miles[/tex]    (1)

The distance  between (0, 63) and (67, 0)

[tex]\sqrt{[ ( 63)^2 + ( 67)^2 ] }=91.97miles[/tex] (2)

So....you will receive the signal using  (1)/ (2)    

(34.322 / 91.97) x 100  ≈  37%  of the drive

Answer:

B

Step-by-step explanation:

I am so sorry if that is incorrect

Answer:

The answer is 61.

Step-by-step explanation:

7(9)-2

63-2

61

Answer:61

7*(9)-2

63-2

61

Hope it's useful