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2 years ago

The equation v=1/3 represents the volume of a cone where r is the radius of the cone

Mathematics

1 answer:

Goryan [66]2 years ago

4 0

The cone has a height value of 7.01 cm

<h3>How to determine the height of the cone using the volume formula?</h3>

From the question, we have the following parameters that can be used in our computation:

Formula: Volume, v = 1/3πr²h

The above formula represents the volume of a cone

Such that

V = Volume; R = Radius and H = Height

Also, we have

Volume, v = 66

Radius, r = 3

Recall that

v = 1/3πr²h

Multiply both sides by 3

So, we have the following equation

3v = πr²h

Divide both sides by πr²

So, we have the following equation

h = 3v/πr²

Substitute 66 for v and 3 for r

So, we have the following representation

h = 3 * 66/(3.14 * 3²)

Evaluate

So, we have the following equation

h = 7.01 cm

Hence, the height of the cone is 7.01 cm

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If 80 is divided by the sum of 4 and a certain number , the result is 16 .find the number

nata0808 [166]

Answer:

x = 60

Step-by-step explanation:

80/ 4+x = 16

(4 + x) * 80/ 4+x = 16 = 16 (4 + x)

80 = 16 + 4 + x

80 = 20 + x

60 = x or x = 60

3 0

4 years ago

A population of flies grows according to the function p(x) = 3(2)x, where x is measured in weeks. A local spider has set up shop

kifflom [539]

The answer is 14 flies

1. Calculate the population of flies after 3 weeks without the spider: p(3)
2. Calculate the number of eaten flies by the spider after 3 weeks: s(3)
3. Subtract p(3) and s(3) to get the population of flies after three weeks with the introduced spider.

1. Calculate the population of flies after 3 weeks without the spider:
p(x) = 3(2)ˣ
x = 3 (because it is the period of three weeks)
⇒ p(3) = 3 · 2³ = 3 · 8
p(3) = 24

2. Calculate the number of eaten flies by the spider after 3 weeks:
s(x) = 2x + 4
x = 3 (because it is the period of three weeks)
⇒ s(3) = 2 · 3 + 4 = 6 + 4
s(3) = 10

3. Subtract p(3) and s(3) to get the population of flies after three weeks with the introduced spider:
p(3) - s(3) = 24 - 10 = 14
Therefore, there are 14 flies after three weeks with the introduced spider.

6 0

4 years ago

A device contains two circuits. The second circuit is a backup for the first, so the second is used only when the first has fail

Wittaler [7]

Answer:

Step-by-step explanation:

The pdf of X is given by 3e^x(1-e^-2y). Please check the screenshot for the workings.

The pdf of Y is given by 6e^-2y. Please check the screenshot for the workings.

The expected time the device fails is the expected time Y fails, so we are going to find the expected time of Y which equals to 0.83.

Please check the screenshop for the workings. Thanks