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3 years ago

A cone with a radius 2 units is shown below. Its volume is 29 cubic units. Find the height of the cone

Mathematics

1 answer:

rusak2 [61]3 years ago

7 0

Answer:

The height of the cone is $6.9\ units$

Step-by-step explanation:

we know that

The volume of the cone is equal to

$V=\frac{1}{3}Bh$

where

B is the area of the circular base of the cone

h is the height of the cone

In this problem we have

$V=29\ units^{3}$

$r=2\ units$

$B=\pi r^{2}$

substitute the value of r

$B=\pi (2)^{2}=4 \pi\ units^{2}$

<em>Find the height of the cone</em>

$29=\frac{1}{3}(4 \pi)h$

$h=29*3/(4 \pi)$

assume $\pi=3.14$

$h=29*3/(4*3.14)=6.9\ units$

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Jimmy ate 3/4 of a pizza. He let his brother eat 1/3 of his leftovers. How much of the entire pizza did Jimmy's brother eat?

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3 years ago

A pilot can fly an airplane 2240 miles with the wind in the same time as she can fly 1920 miles against the wind. If the speed o

Artist 52 [7]

Recall your d = rt, distance = rate * time

so... hmm if the plane has a still air speed of say "r", when it's going with the wind, is not really going "r" fast, is going "r + 40 ", because the wind is adding 40mph to its speed, is really moving.

and when the plane is going against the wind, is not really going "r" fast either, is going " r - 40 ", because the wind is eroding speed from it.

now, it went 2240 miles for say "t" hours, and it did 1920 miles for the same length of time, "t" hours.

$\bf \begin{array}{lccclll}
&distance&rate&time\\
&-----&-----&-----\\
\textit{with the wind}&2240&r+40&t\\
\textit{against the wind}&1920&r-40&t
\end{array}
\\\\\\
\begin{cases}
2240=(r+40)t\implies \frac{2240}{r+40}=\boxed{t}\\
1920=(r-40)t\\
----------\\
1920=(r-40)\left( \boxed{\frac{2240}{r+40}} \right)
\end{cases}
\\\\\\
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3 years ago

Write the equation in standard form for the circle that has a diameter with endpoints (6, -9)

nevsk [136]

Answer:

Step-by-step explanation:

By definition a diameter goes through the center of the circle. So if we find the midpoint of the diameter, we will have the h and k of the center. Then we will use one of the points ON the circle as x and y and solve for r. Here goes:

$M=(\frac{6+(-6)}{2},\frac{-9+(-9)}{2})$ to get a midpoint/center of (0, -9).

The standard form of a circle is

$(x-h)^2+(y-k)^2=r^2$

Filling in with h, k, x, and y:

$(6-0)^2+(-9-(-9))^2=r^2$ which simplifies to

$6^2+0^2=r^2$ so

$r^2=36$

Now we can write the equation of the circle:

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3 years ago

Read 2 more answers

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arsen [322]

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