A ramp is propped against the back of a truck. There is a 30 degree
angle between the ramp and the horizontal pavement
If the distance along the ground from the end of the ramp to the point
on the ground below the back of the truck is 9 feet, how long is the
ramp, in feet? Round your answer to the nearest whole number,

Answer:

Step-by-step explanation:

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].

To learn more on solids of revolution, we kindly invite to check this verified question: https://brainly.com/question/338504

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:

2 a 3 d 4 c 5 b

Step-by-step explanation:

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:

29

Step-by-step explanation:

Answer:

Linear expression is linear equations

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I am so sorry if that is incorrect

Answer:

$14.58

13.50+1.08= $14.58

Answer:

give me 1 second to answer with the correct answer

Answer:

ok so in my math class I just learned this so sry if I am wrong but so

Answer:

Options 1, 3, 4, 7

Step-by-step explanation:

I'm guessing you meant the expression 3/5^3.

The base would be 3/5 because that is the number that the exponent is raising.

The exponent is 3 because that's the small number above and to the right of 3/5.

The expanded form is 3/5 × 3/5 × 3/5 because there's an exponent of 3. An exponent means you multiply the number by itself, the number of times it's being raised to. The exponent is 3 and 3/5 is being multiplied 3 times.

The solution would be 27/125 because when you multiply fractions, you just multiply straight across. 3 × 3 × 3 is 27 and 5 × 5 × 5 is 125.

I hope this makes sense, it's kinda hard to make it understandable without being able to actually talk to you.

Answer:

20.25

Step-by-step explanation:

Divide 13.50 by 2 and then multiply by 3.

Answer:

perfect square / rational

4

Step-by-step explanation:

Answer:

root of 16. or 4

Step-by-step explanation:

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

Answer:

The anwser is 1340

Step-by-step explanation:

divide 335 by 5 then multipilyby 20

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 and Step-by-step explanation:

Given

ax + by = c

qx + ry = s

(a) the equation has no solutions if a/q = b/r ≠ c/s, when this happens, we say the system of equations has no solution. For example

x + y = 3

x + y = 5

Subtracting first equation from the second we have:

0 = 2 which is impossible.

(b) the equations have infinite solutions if a/q = b/r = c/s, for example

x + y = 2

x + y = 2

Subtracting the first equation from the second we have

0 = 0, since this is always true, then it has infinite solutions.

(c) the equations have unique solutions if a/q ≠ b/r, for example

x + y = 2

x – y = 1

Adding the first and second equation we have

2x = 3, we can get x from here and definitely y, so we have just one solution.

9514 1404 393

Answer:

  22.5 square feet

Step-by-step explanation:

The area covered by one tile is the product of its dimensions:

  A = lw

  A = (3/2 ft)(3/2 ft) = 9/4 ft²

The area covered by 10 tiles is 10 times the area covered by one tile. The area covered is ...

  covered by tiles = 10 × 9/4 ft² = 90/4 ft²

  covered by tiles = 22.5 ft²

22 1/2 square feet is the area covered by tiles.

Answer:

1

Step-by-step explanation:

When a variable does not have a visible coeffecient then the coefficient is 1. (Double check to make sure I'm correct)

Answer:

SAS

Step-by-step explanation:

Side angle side Test

2 sides are given equal and angle between these two side is equal in both triangle

hence by SAS test

Triangle ABC and EBD are congruent

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

Answer:

is A

Step-by-step explanation:

00000000000000000000000000

Answer:

Its 0 because 12+ (-12) = 0

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

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:

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:

13.3 or 13

Step-by-step explanation:

10x+11=144

10x=144-11

10x=133

x=133/10

x=13.3

Answer:

43.96

Step-by-step explanation:

Circumference formula: 2 x r x pi

2 x 7 x 3.14= 43.96