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3 years ago

Find the volume of a cylinder either enter an exact number in the terms of pi areU3.14 for pie 5 and 2

Mathematics

1 answer:

gizmo_the_mogwai [7]3 years ago

3 0

Answer:

$V=384\pi \ \text{unit}^3$

Step-by-step explanation:

The attached figure shows a cylinder of radius 8 units and height 6 units. We need to find the volume of the cylinder. The formula is as follows :

$V=\pi r^2h\\\\V=\pi (8)^2\times 6\\\\V=384\pi$

So, the required volume of the cylinder is $384\pi \ \text{unit}^3$ .

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2 years ago

Standard form of a line passing through points (1, 3) and (-2, 5)

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Answer:

Step-by-step explanation:

As we move from (-2, 5) to (1, 3), x increases by 3 and y decreases by 2.

Hence, the slope of this line is m = rise / run = -2/3.

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Substitute 3 for y and 1 for x and -2/3 for m:

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3 years ago

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3 years ago

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2 years ago

Biologists stocked a lake with 80 fish and estimated the carrying capacity (the maximal population for the fish of that species

kotegsom [21]

Answer:

$P(t) = \frac{160000e^{1.36t}}{2000 + 80(e^{1.36t} - 1)}$

Step-by-step explanation:

The logistic equation is the following one:

$P(t) = \frac{KP(0)e^{rt}}{K + P(0)(e^{rt} - 1)}$

In which P(t) is the size of the population after t years, K is the carrying capacity of the population, r is the decimal growth rate of the population and P(0) is the initial population of the lake.

In this problem, we have that:

Biologists stocked a lake with 80 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 2,000. This means that $P(0) = 80, K = 2000$ .