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Mamont248 [21]
3 years ago
11

If the volume of the planter is 3,072 cubic inches, how tall is the planter?

Mathematics
1 answer:
andrezito [222]3 years ago
4 0

\it \mathcal{V} =\dfrac{\mathcal{A}_b\cdot h}{3} \Rightarrow h = \dfrac{3\mathcal{V}}{\mathcal{A}_b}= \dfrac{3\cdot3072}{\mathcal{A}_b}\ \ \ \ \ (*)
\\\;\\ \\\;\\
\mathcal{A}_b = \dfrac{\ell^2\sqrt3}{4} = \dfrac{16^2\sqrt3}{4} =\dfrac{16\cdot16\sqrt3}{4} =4\cdot16\sqrt3=64\sqrt3\ \ \ \ (**)
\\\;\\ \\\;\\
(*),\ (**) \Rightarrow h=\dfrac{3\cdot3072}{64\sqrt3} = \dfrac{3\cdot48}{\sqrt3} = \dfrac{\sqrt3\cdot\sqrt3\cdot48}{\sqrt3} = 48\sqrt3\  inches


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see explanations

Step-by-step explanation:

Formula for mid-point is;

midpoint=((x_1+x_2)/2,(y_1+y_2)/2)

1.Given S(-3,4), U(-3,0) and T(5,0) then finding the mid-points

SU = [(-3+-3)/2,(4+0)/2] =(-3,2)

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ST=[(-3+5)/2,(4+0)/2]=(1,2)

2.Mid-point formula for this case given W(-5,1) and Z(3,3) will be;

Midpoint = [ (x₁+x₂)/2,(y₁+y₂)/2]

Midpoint= [(-5+3)/2 ,(1+3)/2]

Midpoint=(1,2)

3. Finding the length of segments and the midpoint of the segments

Formula for length of segment, d, is given as;

For C(-1,5) and D(5,1)

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Midpoint of the segment CD will be

[(-1+5)/2,(5+1)/2] = (2,3)

For E (-3,-6) and F(5,0)

d=\sqrt{(0--6)^2+(5--3)^2} =\sqrt{6^2+8^2} =\sqrt{36+64} =\sqrt{100} =10

The midpoint for segment EF will be;

[(-3+5)/2 ,(-6+0)/2] =(1,-3)

For L(-4,4) and M(-1,-5)

d=\sqrt{(-5--4)^2+(-1-4)^2} \\d=\sqrt{-1^2+-5^2} \\\\d=\sqrt{1+25}=\sqrt{26} =5.1

Learn More

Midpoint of a segment :brainly.com/question/10424143

Distance of a segment :brainly.com/question/11591660

Keywords :midpoint, midpoint formula, segment length, line segment

#LearnwithBrainly

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2.7(w-5.2)

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2.7w -2.7*5.2

2.7w -14.04

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