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Travka [436]
3 years ago
6

Find the volume of the solid generated by revolving the region bounded by the x-axis, the curve y = 3x^4 , and the lines x = 1 a

nd x = -1 about the x-axis.
Mathematics
1 answer:
Marysya12 [62]3 years ago
8 0

Answer:

Let's define A as the area given by the integral:

\int\limits^1_{-1} {3x^4} \, dx

Which is the area between the curve y = 3*x^4 and the x-axis between x = -1 and x = 1

To find the volume of a revolution around the x-axis, we need to multiply the area by 2*pi (a complete revolution)

where pi = 3.14

First, let's solve the integral:

\int\limits^1_{-1} {3x^4} \, dx = \frac{3}{5}(1^5 - (-1)^5) = \frac{3*2}{5} = \frac{6}{5}

Then the volume of the solid is just:

V = (6/5)*2*3.14 = 7.536

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Adrian's CD player can hold six disks at a time and shuffles all of the albums and their songs. If he has thirteen CD's, how man
EastWind [94]
To answer this problem, the utilization of the provided formula is of utmost importance.

The formula to be used would be for the combination with no repetition since it is what is asked and possibly happens when involving the products mentioned in the problem. The formula would be

      n!                                              where in
-------------                                                   n = number of things to choose from
(n - r)! r!                                                      r = number of things needed to form

the symbol ! is called a factorial function which replaces the sequence of multiplying a number in a descending order.

lets substitute and solve

      13!
--------------
(13 - 6)! 6!

      13!
-------------
   (7!) 6!

6,227,020,800
-------------------
  5,040 x 720

6,227,020,800
-------------------
    3,628,800

1,716

The answer would be 1,716.
6 0
3 years ago
The quotient of a number and four decreased by ten is two. What is the number
MakcuM [25]
X divided by 4 - 10=2 x=48
3 0
3 years ago
Solve:<br>i)x+y=5<br>ii)x-y=3<br>iii)2x+y=7<br>iv)3x-2y=0​
Ulleksa [173]

Answer:

I) X+Y

when X=0

0+y=5

Y=5

When Y=0

X+0=5

X=5

(X,y)=(5,5)

(ii) X-Y=3

When X=0

0-Y=3

Y=-3

When Y=0

X-0=3

X=3

(X,Y)=(3,3(

(III) 2x+Y=7

when X=0

0+Y=7

Y=7

when Y=0

2x+0=7

2x=7

X=7/2 or 3.5

(X,Y)=(3.5,7)

(Iv)

3X-2Y=0

when X=0

0-2Y=0

-2Y=0

Y=0

When Y=0

3x-0=0

3X=0

X=0

(X,Y)=(0,0)

5 0
2 years ago
3. You have decided to wallpaper your rectangular bedroom. The dimensions are 12 feet 6 inches by 10 feet 6 inches by 8 feet 0 i
Shalnov [3]

Answer:

B. 5 rolls

Step-by-step explanation:

The areas of the room, not including the ceiling, are discriminated as follows:

Longer walls: (12.5\times8)\times2=200ft^2 (6 inches equals one foot)

Shorter walls: (10.5\times8)\times2 = 168ft ^ 2 (6 inches equals one foot)

Window area: (4\times3)\times2 = 24ft ^ 2

Door area: (7\times3) = 21ft ^ 2

Area that will be effectively covered:

Total area to wallpaper: 200 + 168 -24 -21 = 323ft ^ 2

Amount of paper needed: 323\times1.1 = 355.3ft ^ 2

30in = 24in + 6in = 2ft + 0.5ft = 2.5ft. That is, the area of ​​a roll of paper is 2.5\times30 = 75ft ^ 2

Number of rolls needed:

\frac{355.3}{75} = 4.73 rolls

5 0
3 years ago
Read 2 more answers
What is 5000x 600000 pls help
lukranit [14]

Answer:

= 3,000,000,000

Step-by-step explanation:

Step 1- Multiply

5×6= 30

Once you've multiplied, you can just add the 0's to 30.

There are a total of eight 0's.

Once you've added all the 0's, you'll get 3,000,000,000.

3 0
3 years ago
Read 2 more answers
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