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motikmotik
3 years ago
8

An artist creates a​ cone-shaped sculpture for an art exhibit. If the sculpture is 6 feet tall and has a base with a circumferen

ce of 21.352 ​feet, what is the volume of the​ sculpture? Use 3.14 for pi.
Mathematics
1 answer:
Scorpion4ik [409]3 years ago
6 0

Answer:

Step-by-step explanation:

Cone Volume = (π • r² • h) ÷ 3

109.9 = PI * 5 * radius^2 / 3

3* 109.9 / (3.14 * 5) = radius^2

329.7 / 15.7

radius^2 = 21

radius = 4.582575695

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2 years ago
3.1 Find the equation of the line passing through (4, 5) and parallel to the line 3x – 2y = 4.
valentinak56 [21]

                   \rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}

            <em>Find the equation of the line passing through (4, 5) and parallel to </em>

<em>                 3x-2y=4.</em>

<em />

<em>  </em>\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}

First of all, We need to convert this equation from standard form (ax+by=c) into slope-intercept form (y=mx+b).

\rightarrow First, add 2y on both sides:-

                            \Large\textsf{3x+2y=4}

\rightarrow Now, subtract 3x on both sides:-

                  \Large\textsf{2y=-3x+4}

\rightarrow Divide by 2 on both sides

    \Large\text{$y=-\displaystyle\frac{3}{2}x +2$}

\rule{300}{3}

Now, let's find the equation of the line that's parallel to the given line.

Remember, if lines are parallel to each other, then their slope's the same.

So the slope of the line that's parallel to the line whose equation we just found, is

\Large\text{$-\displaystyle\frac{3}{2}$}

Now let's write the equation in point-slope form:-

\hookrightarrow\sf{y-y_1=m(x-x_1)}

Replace numbers with letters, as follows:-

\sf{y-5=-\displaystyle\frac{3}{2} (x-4)}

The equation above is the equation in point-slope form.

Incase you need it converted to slope intercept form, refer to the steps below ~

Multiply -3/2 times x and -4:-

\hookrightarrow\sf{y-5=-\displaystyle\frac{3}{2} x-6}

Now, Add 5 on both sides:-

\hookrightarrow\sf{y=\displaystyle\frac{3}{2} x+1}

\Uparrow\sf{Our\:equation\:in\:slope\;intercept\;form}

<h3>Good luck with your studies.</h3>

#TogetherWeGoFar

\rule{300}{1}

4 0
2 years ago
Select the two expressions that equivalent to 4 + w + 12w
Korvikt [17]

Answer:

A and C :)

Have an amazing day!!

Please rate and mark brainliest!!

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2 years ago
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