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Kitty [74]
3 years ago
8

Find the volume of the solid of revolution formed by rotating about the x--axis the region bounded by the given curves.

Mathematics
1 answer:
Maslowich3 years ago
4 0

Answer:

16 pi cubic units

Step-by-step explanation:

Given that a region is bounded by

f(x)=√x, y=0, x=1, x=4

And the region is rotated about x axis.

We can find that here radius would be y value and height would be dx

So volume would be as follows:

If f(x) is rotated about x axis volume

= \pi \int\limits^b_a {y^2} \, dx \\=\pi \int\limits^4_1 {x} \, dx\\=\pi *x^2  ^4_1\\= \pi*16-1\\=15\pi

cubic units.

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The altitude (i.e., height) of a triangle is increasing at a rate of 2 cm/minute while the area of the triangle is increasing at
s344n2d4d5 [400]

Answer:

A = 1/2 B H       area = 1/2 base X height

B = 2 A / H = 2 * 99 / 12 = 16.5 cm

dA / d t = 1/2 * (B dH / dt + H dB / dt)

dB / dt = (2 dA / dt - B dH / dt) / H

dB / dt = (2 * 1.5 cm^2 / min - 16.5 cm * 2 cm / min) / 12 cm

dB / dt = (3 - 33) / 12 cm/min = -2.5 cm/min

4 0
3 years ago
There are 50 deer in a particular
olchik [2.2K]

answered

There are 50 deer in a particular forest. The population is increasing at a rate of 15% per year. Which exponential growth function represents

the number of deer y in that forest after x months? Round to the nearest thousandth.

1

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dribeiro

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561.4K people helped

Answer:

The expression that represents the number of deer in the forest is

y(x) = 50*(1.013)^x

Step-by-step explanation:

Assuming that the number of deer is "y" and the number of months is "x", then after the first month the number of deer is:

y(1) = 50*(1+ 0.15/12) = 50*(1.0125) = 50.625

y(2) = y(1)*(1.0125) = y(0)*(1.0125)² =51.258

y(3) = y(2)*(1.0125) = y(0)*(1.0125)³ = 51.898

This keeps going as the time goes on, so we can model this growth with the equation:

y(x) = 50*(1 - 0.15/12)^(x)

y(x) = 50*(1.013)^x

8 0
3 years ago
What is pi times 3?<br> Thank you!!!
natta225 [31]
The correct answer is 9.42477796077 because pi 3.14ect you would just multiply it by 3 so the answer would be 9.42477796077
4 0
3 years ago
What is the limit of f (×) as x approaches - infinty
tatyana61 [14]
If the degree of numerator and denominator are equal, then limit will be leading coefficient of numerator divided by the leading coefficient of denominator.

So then the limit would be 3/1 = 3.

Alternatively,

\displaystyle \lim_{x\to\infty}\dfrac{3x^2+6}{x^2-4}=\displaystyle \lim_{x\to\infty}\dfrac{3x^2+6}{x^2-4}\cdot\dfrac{1/x^2}{1/x^2}=\lim_{x\to\infty}\dfrac{3+\frac6{x^2}}{1-\frac4{x^2}} = \dfrac{3+0}{1-0}=\boxed{3}

Hope this helps.
5 0
3 years ago
Write this ratio 1:3.5 in the form p:q where p and q are whole numbers
Orlov [11]

We have to express the ratio 1 : 3.5 in the form p:q where p and q are whole numbers.

Consider the ratio of 1 and 3.5,

1 : 3.5 = \frac{1}{3.5}

= \frac{10}{35}

Reducing the above fraction to its lowest form.

So, we get \frac{10}{35}=\frac{2}{7}

Therefore, the ratio 1 : 3.5 is expressed as \frac{2}{7}

where 2 and 7 are the whole numbers.

4 0
3 years ago
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