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kenny6666 [7]
3 years ago
7

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the curves x=4y2

−y3 and x=0 about the x-axis.
Mathematics
1 answer:
xenn [34]3 years ago
7 0

Answer = 321.7

Explanation:

radius = y

height = 4y^{2} - y^{3}

area of cylinder = 2π*r*h

Integrate the area to calculate the volume:

= \int\limits^0_4 {2\pi(4y^{3} -y^{4})  } \, dy

= 2\pi (\int\limits^0_4 {4y^{3}dy -\int\limits^0_4  y^{4} dy )} \,

= 2\pi (256-\frac{1024}{5} )

=\frac{512\pi }{5}

= 321.7

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Answer:

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2 years ago
7-5=2 so what is 7-2=? , free
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2 years ago
There are 20 parrots at the animal sanctuary. Their population is increasing at a rate of 15% per year. There are also 24 snakes
worty [1.4K]
For the answer to the questions above,
A) Parrots are following a Geometric Progression of 15% increase.

20(1.15),  20(1.15)², 20(1.15)³,

Function  = 20(1.15)^n      Where n is at the end of year, n =1, 2, 3, ..

Snakes are increasing by 4.

28, 32, 36,....

Function =  24 + 4n          n = number of end year,      n =1, 2, 3,...

<span>B) After 10 years:              </span>
Parrot =  20(1.15)¹⁰    = 80.91115471

Snakes =  24 + 4(10) = 64

<span>C) After what time they are the same: </span>
We use trial and error:


Test:  n                             20(1.15^n)                        (24 + 4n)
          1                                    23                                   28
          2                                    26.45                              32
<span>          3                                    30.41                             36    </span>
          4                                    34.98                              40
          5                                    40.23                              44
          6                                    46.26                              48
          7                                    53.20                              52
          8                                    61.18                              56
          9                                    70.36                              60

After year 7, the Parrots increases far more.
<span>At year 7 they are roughly the same.</span>
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The answer is 4.25 km
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