Find the perimeter of the right triangle. If necessary, round to the nearest tenth. a. 13 in. b. 169 in. c. 60 in. d. 30 in.

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: 32 ft.

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

4 feet per minute times 8 minutes equals 32

Answer:

22 + x ≤ 40

x ≤ 18 pounds

Step-by-step explanation:

Maximum weight = 40 pounds

Initial weight = 22 pounds

Let Maximum weight that can be added = x

Mathematically, this means :

Initial weight + additional weight ≤ 40

That is ;

22 + x ≤ 40

Additional weight, x :

x ≤ 40 - 22

x ≤ 18 pounds

Answer:

what do you mean

Step-by-step explanation:

can we see step 43

Answer:

A. contract

Step-by-step explanation:

Answer:

35 is a reasonable amount

Step-by-step explanation:

Since all of the books cost around $7 and there are 5 books

when you multiply 7x5=35

Answer:

Step-by-step explanation:

i think you have to multiply then divide

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:

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

Step-by-step explanation:

2

57

65

566

77788

66777

66788

67899

6789

78899

789999

88889

8888888

788889

888888999999999

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]

Answer:

-12

Step-by-step explanation:

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

Answer:

It’s -12

Step-by-step explanation:

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'

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:

B if its right i better get brainly list or a follow on ig

Step-by-step explanation:

1nspired_jay

Answer:

Correct answer is A

Step-by-step explanation:

When solving the inital problem you get 1405

Solved problems:

A: 1405

B: 1466

C: 3145

D: 3410

Therefore the correct answer is A

Answer:

A. 25in.³

Step-by-step explanation:

Volume of a prism = area of base × height

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:

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:

7+2√10

Step-by-step explanation:

Answer:

7+2√10

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

10% of 100 is 10 so times it by 5

Answer:

0.9412

Step-by-step explanation:

Ultimately, if you know the length of the arc, and you know the length of the radius, the central angle (in radians) is just how many radii long the arc is. angle=arc lengthradius length=16 feet17 feet≈0.9412.

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:

15x

Step-by-step explanation:

5x-20x+30x=15x

Answer:

V=56.5

Step-by-step explanation:

Formula for finding volume of a cylinder is  V=pi r^2h, substitute h for the height and r for radius. V=pi 3^2 2

Answer:

1/2

Step-by-step explanation:

You can change it to multiplication then solve

(2/6)*(3/2)=3/6=1/2

Step-by-step explanation:

You mean

╭☞2/6/2/3?

[tex]╭☞ \sf \: \dfrac{2}{ \dfrac{6}{ \dfrac{2}{3} } } \\ ╭☞ \sf \: \frac{2}{6} \times \frac{3}{2} \\ ╭☞ \sf \: \frac{3}{6} \\ ╭☞ \bf \: \frac{1}{2} [/tex]

Answer:

3 ($0.40) = $1.20

Step-by-step explanation:

Answer:

3750

Step-by-step explanation:

Let the tank contain x gallons of water.

when pumping is done, then tank 1 contain x-2500 gallons

and tank 2 contain x+2500 gallons.

according to question,

5(x - 2500) = x + 2500

or, 5x -12500 =x+ 2500

or, 5x - x =2500+12500

or, 4x =15000

or, x= 3750

hence each tank contains 3750 gallons.