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Fynjy0 [20]
3 years ago
13

What is the volume of the cone with radius 5 m and height 6 m? Express the answer in terms of π.

Mathematics
2 answers:
Arlecino [84]3 years ago
8 0

Answer:

157.80

Step-by-step explanation:

V = r^2 * h * 1/3 * pi

V = 5^2 * 6 * 1/3 * pi

V = 25 * 6 * 1/3 * pi

V = 150 * 1/3 * pi

V = 157.079..

("Gmanyp82iab" forgot to square the radius above)

ra1l [238]3 years ago
5 0

The formula of a volume of a cone:

V=\dfrac{1}{3}\pi r^2H

We have r = 5m and H = 6m. Substitute:

V=\dfrac{1}{3}\pi(5^2)(6)=\pi(25)(2)=50\pi\ m^3

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The acceleration of the particle is given by the formula mentioned below:

a=\frac{d^2s}{dt^2}

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Differentiate both sides of the obtained equation with respect to t.

\begin{gathered} \frac{d^2s(t)}{dx^2}=\frac{3}{2}(\frac{2t}{\sqrt[]{(t^3+1)}}+t^2(-\frac{3}{2})\times\frac{1}{(t^3+1)^{\frac{3}{2}}}) \\ =\frac{3t}{\sqrt[]{(t^3+1)}}-\frac{9}{4}\frac{t^2}{(t^3+1)^{\frac{3}{2}}} \end{gathered}

Substitute t=2 in the above equation to obtain the acceleration of the particle at 2 seconds.

\begin{gathered} a(t=1)=\frac{3}{\sqrt[]{2}}-\frac{9}{4\times2^{\frac{3}{2}}} \\ =1.32ft/sec^2 \end{gathered}

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1 year ago
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Answer:

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Step-by-step explanation:

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3 years ago
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valentina_108 [34]

Step-by-step explanation:

You can find the area of a right triangle the same as you would any other triangle by using the following formula:

A = (1/2)bh, where A is the area of the triangle, b is the length of the base and h is the height of the triangle; However, with a right triangle, it's much more convenient in finding its area if we utilize the lengths of the two legs (the two sides that are shorter than the longest side, the hypotenuse and that are perpendicular to each other and thus form the right angle of the right triangle), that is, since the two legs of a right triangle are perpendicular to each other, when we treat one leg as the base, then, consequently, we can automatically treat the length of the other leg as the height, and if we initially know the lengths of both legs, then we can then just plug this information directly into the area formula for a triangle to find the area A of the right triangle.

For example: Find the area of a right triangle whose legs have lengths of 3 in. and 4 in.

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