Refer to the figure and find the volume V generated by rotating the given region about the specified line.

Mathematics

1 answer:

ANEK [815]3 years ago

7 0

Volume generated by the areas R2 + R3 around the line OC
= (1/3) pi 1^2 * 3 = pi sq units

Volume generated by area R2 around OC is found as follows

the equation of the curve can be written as x = y^4 / 81

Integral between limits y = 0 and 3 of the curve is

pi INT x^2 dy = INT pi y^8 / 81^2 dx

= pi [3^9 / 9*81^2]

= pi/3

So the volume generated by R3 about OC = pi - pi/3 = 2pi/3

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5) You randomly choose a marble from a jar. The jar contains 4 red

Dmitry [639]

the probability of the event choosing a yellow marble is 2/9 .

<u>Step-by-step explanation:</u>

Here we have , to choose a marble from a jar. The jar contains 4 red

marbles, 10 blue marbles, 7 green marbles, and 6 yellow marbles. We need to Find the probability of the event choosing a yellow marble . Let's find out:

According to question question we have following parameters as :

Red marbles = 4

Blue marbles =10

Green marbles = 7

Yellow marbles = 6

Now , Probability to chose a yellow marble is :

Favorable outcomes = 6(Number of yellow marbles )

Total outcomes = 4+10+7+6 = 27( Total marbles )

Hence ,

⇒ $Probability = \frac{6}{27}$