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2 years ago

A cone has a volume of 314 cubic meters and a height of 12 meters. What is its radius?

Mathematics

1 answer:

Viefleur [7K]2 years ago

4 0

Answer:

About 5 meters

Step-by-step explanation:

v= πr² h/3

r= √3 v/πh= 3•314/ π•12= 4.99873 rounded which then rounds to 5

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Given points A (1, 2/3), B (x, -4/5), and C (-1/2, 4) determine the value of x such that all three points are collinear

AlladinOne [14]

Answer:

$x=\frac{83}{50}$

Step-by-step explanation:

we know that

If the three points are collinear

then

$m_A_B=m_A_C$

we have

A (1, 2/3), B (x, -4/5), and C (-1/2, 4)

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

step 1

Find the slope AB

we have

$A(1,\frac{2}{3}),B(x,-\frac{4}{5})$

substitute in the formula

$m_A_B=\frac{-\frac{4}{5}-\frac{2}{3}}{x-1}$

$m_A_B=\frac{\frac{-12-10}{15}}{x-1}$

$m_A_B=-\frac{22}{15(x-1)}$

step 2

Find the slope AC

we have

$A(1,\frac{2}{3}),C(-\frac{1}{2},4)$

substitute in the formula

$m_A_C=\frac{4-\frac{2}{3}}{-\frac{1}{2}-1}$

$m_A_C=\frac{\frac{10}{3}}{-\frac{3}{2}}$

$m_A_C=-\frac{20}{9}$

step 3

Equate the slopes

$m_A_B=m_A_C$

$-\frac{22}{15(x-1)}=-\frac{20}{9}$

solve for x

$15(x-1)20=22(9)$

$300x-300=198$

$300x=198+300$

$300x=498$

$x=\frac{498}{300}$

simplify

$x=\frac{83}{50}$

8 0

3 years ago

The area of a rectangle is 229.2 m2. If the length is 15 m, what is the perimeter of the rectangle

igor_vitrenko [27]

Answer:

$\large\boxed{P=60.56\ m}$

Step-by-step explanation:

The formula of an area of a rectangle:

$A=lw$

l - length

w - width

We have

$A=229.2\ m^2\\\l=15\ m$

Substitute:

$15w=229.2$ <em>divide both sides by 15</em>

$w=15.28\ m$

The formula of a perimeter of a rectangle:

$P=2(l+w)$

Substitute:

$P=2(15+15.28)=2(30.28)=60.56\ m$

8 0

3 years ago

I need help with geometry

Tju [1.3M]

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hjlf

He would be able to cut 20 sections:)

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3 years ago

Witch is taller 5'3" or 62 inches?

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