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Answer:

Hence, the Area is [tex]\frac{24}{5} \;\text {and the Volume of the bounded region is } \frac{24\pi}{5}[/tex]

Step-by-step explanation:

Concept :

Area of the region bounded by two curve :

[tex]\int_a^b(R^2-r^2)dx[/tex]

volume of the solid generated by revolving the region about the x-axis is :

 [tex]\int_a^b\pi(R^2-r^2)dx[/tex]   where [tex]R[/tex] is long radius of bounded region from x-axis and [tex]r[/tex] is short radius of bounded region from x-axis.

Given :

[tex]y=6x[/tex] and [tex]y=6x^2[/tex]

To find :

Area of the region bounded by [tex]y=6x[/tex] and [tex]y=6x^2[/tex] and volume of the solid generated by revolving the region about the x-axis.

Explanation :

[tex]\because y=6x\;\text{and}\;y=6x^2[/tex]

[tex]\therefore 6x=6x^2\\\Rightarrow x=1[/tex]

Area of the region bounded by [tex]y=6x[/tex] and [tex]y=6x^2[/tex] is :

     [tex]\int_a^b(R^2-r^2)dx=\int_0^1((6x)^2-(6x^2)^2)dx\\[/tex]

[tex]\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=\int_0^1(36x^2-36x^4)dx\\\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=36\int_0^1(x^2-x^4)dx\\\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=36\left(\frac{x^3}{3}-\frac{x^5}{5}\right)_0^1\\\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=36\left(\frac{1}{3}-\frac{1}{5}\right)\\\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=36\times\frac{2}{15}\\\Rightarrow \int_0^1((6x)^2-(6x^2)^2)dx=\frac{24}{5}[/tex]

Volume of the solid generated by revolving the region about the x-axis.

      [tex]\int_0^1\pi((6x)^2-(6x^2)^2)dx=\int_0^1\pi(36x^2-36x^4)dx[/tex]

[tex]\Rightarrow \int_0^1\pi((6x)^2-(6x^2)^2)dx=36\pi\int_0^1(x^2-x^4)dx\\\Rightarrow \int_0^1\pi((6x)^2-(6x^2)^2)dx=36\pi\left(\frac{x^3}{3}-\frac{x^5}{5}\right)_0^1\\\Rightarrow \int_0^1\pi((6x)^2-(6x^2)^2)dx=36\pi\left(\frac{1}{3}-\frac{1}{5}\right)\\\Rightarrow \int_0^1\pi((6x)^2-(6x^2)^2)dx=36\pi\times\frac{2}{15}\\\Rightarrow \int_0^1\pi((6x)^2-(6x^2)^2)dx=\frac{24\pi}{5}[/tex]  

Answer:

Step-by-step explanation:So for this question, you need to find side KI and you can find it with the pythagorean theorem

[tex]5^2+\sqrt{21}^2 = c^2[/tex]

25+21=c^2

46=c^2

c=sqrt46

c=6.78

sin(opposite/hypotnuse)

sin(sqrt21/ sqrt46) =.0117

Answer:

10

Step-by-step explanation:

1, 1, 4, 6, 6, 12, 12, 13, 15

[tex]LQ=\frac{9+1}{4} =2.5 term= \frac{1+4}{2}=\frac{5}{2}=2.5\\UQ= 3(\frac{9+1}{4}) =7.5 term= \frac{12+13}{2}=\frac{25}{2}=12.5\\IQR=UQ-LQ=12.5-2.5=10[/tex]

C is the point on the ground where the person is standing and which is making the angle of elevation of 60° AB (Height) = ? Example 2 :Height of tree is 8.65m, the angle of elevation of the top of tree is 60° find the distance at which the person is standing away from tree ? Solution : Let AB is the tree. B is the foot and A is the top of tree.

2 ft above

Now

Angle be x

Apply Pythagorean theorem

[tex]\\ \rm\Rrightarrow tanx=\dfrac{10}{400}[/tex]

[tex]\\ \rm\Rrightarrow tanX=\dfrac{1}{40}[/tex]

[tex]\\ \rm\Rrightarrow tanX= 0.025[/tex]

[tex]\\ \rm\Rrightarrow X=tan^{-1}(0.025)[/tex]

[tex]\\ \rm\Rrightarrow X=1.432°[/tex]

AThe chosen topic is not meant for use with this type of problem. Try the examples below.

f (x) = 7x − 2, x = 6

f (x) = 3x − 2, x = 9

f (x) = x^2, x = 12

Answer:

I believe it is 2.2

Step-by-step explanation:

5 goes into 11. 2 times. 2times5= 10 and 11-10=1- 5 goes into 10 2 times- 2 times 5=10; 10-10=0. Therefore it would be 2.2. Hope this helps you. :)

Answer:

The line equation is x=3 because the line covers all of the possible y values within the coordinate x=3.

Answer:

[tex]6x + 6[/tex]

Step-by-step explanation:

Given

[tex]6 (-\frac{1}{2}x + 2) + \frac{1}{2} (18x-12)[/tex]

Required

Express as [tex]ax + b[/tex]

We have:

[tex]6 (-\frac{1}{2}x + 2) + \frac{1}{2} (18x-12)[/tex]

Open brackets

[tex]6 (-\frac{1}{2}x + 2) + \frac{1}{2} (18x-12) = 6 *-\frac{1}{2}x + 6*2 + \frac{1}{2} *18x-\frac{1}{2} *12[/tex]

Evaluate all multiplications

[tex]6 (-\frac{1}{2}x + 2) + \frac{1}{2} (18x-12) = -3x + 12 + 9x-6[/tex]

Collect like terms

[tex]6 (-\frac{1}{2}x + 2) + \frac{1}{2} (18x-12) = 9x-3x + 12-6[/tex]

[tex]6 (-\frac{1}{2}x + 2) + \frac{1}{2} (18x-12) = 6x +6[/tex]

Hence, the expression in form of [tex]ax + b[/tex] is [tex]6x + 6[/tex]

Answer:

-12

Step-by-step explanation:

4y=4*(-3) 4*(-3)=-12

Answer:

It’s -12

Step-by-step explanation:

Answer:

A. 25in.³

Step-by-step explanation:

Volume of a prism = area of base × height

Answer:

Step-by-step explanation:

TAX CALCULATION: 260 x .06 = $15.6

Next, add the tax to the original price.

260 + 15.6 = $275.6

$275.6 is the final price including tax.

Answer:

1

Step-by-step explanation:

Answer:

106°

Step-by-step explanation:

isosceles triangle has two sides equal meaning two sides measure 37 so

37+37=74

180-74=106

(total measurement of a triangle is 180)

Answer:

A. y = 3x + 3

Step-by-step explanation:

y=mx+b

b is the y-intercept (0,y) so lets start with that

We can see that the line touches 3 on the y intercept to get (0,3) meaning b=3

For the slope (m) I like to count rise over run so if we start from (0,3) and go up 3 over 1 we get 3/1 or 3 for m

The whole equation is y=3x+3

Answer:

This length is greater than the 12 cm side of the rectangle, so it confirms our initial guess, the longest line segment is 12.89 cm long.

Answer:

7+2√10

Step-by-step explanation:

Answer:

7+2√10

Step-by-step explanation:

Answer:

24 muffins

240 muffins

2 boxes

Step-by-step explanation:

here is the complete question

Amy is baking muffins. Each baking tray can hold 6 muffins.

a. If Amy bakes 4 trays of muffins, how many muffins will she have in all?

b. The corner bakery produced 10 times as many muffins as Amy baked. How many muffins did the bakery produce?

If the Corner Bakery packages the muffins in the boxes of a 100 how many boxes of a 100 could they make

Number of muffins Amy has = number of trays x capacity of each tray

6 x 4 = 24 muffins

b. Muffins the bakery produces = 10 x 24 = 240 muffins

c. Number of boxes = 240 / 100 = 2. 4

that is 2 boxes of 100

Answer:

A. 846 cm²

Step-by-step explanation:

1539 ÷ 19 = 81

√81 = 9

9 · 9 · 81 = 1539

A = 2(wl + hl + hw)

A = 2(19 · 9 + 9 · 9 + 9 · 19)

846 cm²

Answer:

(46,56)

Step-by-step explanation:

Answer:

7.57363849

Step-by-step explanation: square root of 57.36 = 7.57363849

Answer:

1434/25 is 57.36 the square root of 57.36 is 7.57

Answer:

50

Step-by-step explanation:

10% of 100 is 10 so times it by 5

Answer:

x = 19

Step-by-step explanation:

123°+3x = 180°

3x = 180°-123°

3x = 57

x = 57/3

x = 19

The reason why we use 123° + 3x = 180° because both are adjacent angles. Adjacent angles add up to 180°

Answer:

3 ($0.40) = $1.20

Step-by-step explanation:

[tex]adjacnt {}^{2} = opposite {}^{2} + hypotenuse {}^{2} \\ adjacent {}^{2} = 8 {}^{2} + 12 {}^{2} \\ adj {}^{2} = 64 + 144 \\ adj {}^{2} = 208 \\ adjacent = \sqrt{208} \\ adjacent = 4 \sqrt{13} [/tex]

Answer:

Step-by-step explanation:

From (-5,-4) to (-8, -7) is left 3 and down 3. In arrow notation: <-3 \/3

figure out what the x and y components of the translation are and then write the arrow to show the direction'