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s2008m [1.1K]
2 years ago
8

The volume of this cone is 3,183.96 cubic meters. What is the height of this cone?

Mathematics
1 answer:
Rom4ik [11]2 years ago
5 0

Answer:

height = 18m

Step-by-step explanation:

cone volume = 3183.96 m³

1/3 πr²h = 3183.96

1/3×3.14×13×13×h = 3183.96

h = 3183.96×3/13×13×3.14

h = 9551.88/530.66

h = 18

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8 x² + 14 x + 5 = 0
2 ( 4 x² + 7 x ) = - 5
2 ( 4 x² + 7 x + 49/16 - 49/16 ) = -5
2 ( 4 x² + 7 x + 49/16 ) - 98/16 = - 5
2 ( 2 x + 7/4 )² = - 5 + 98/16
2 ( 2 x + 7/4 )² = -80/16 + 98/16
2 ( 2 x + 7/4 )² = 18/16 = 9/8       / : 2
( 2 x + 7/4 )² = 9/16     / √
2 x + 7/4 = 3/4
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x = - 1
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8 0
3 years ago
Using the numbers 8, 6, 4, and 2 write an expression that equals 32.
Dennis_Churaev [7]
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4 0
3 years ago
a. Find symmetric equations for the line that passes through the point (4, −4, 8) and is parallel to the vector −1, 4, −3b. Find
daser333 [38]

The line has equation

\vec r(t)=(4,-4,8)+(-1,4,-3)t

where t is any real number. (-1,4,-3)t is the line containing all scalar multiples of the vector (-1, 4, -3); we add (4, -4, 8) to shift the line so that it passes through this point while remaining parallel to the the line.

To get the symmetric form, we have

\begin{cases}x(t)=4-t\\y(t)=-4+4t\\z(t)=8-3t\end{cases}

Solving for t in each equation gives the symmetric form,

t=\boxed{4-x=\dfrac{y+4}4=\dfrac{8-z}3}

The line has intercepts in the coordinate planes wherever either the x, y, or z coordinate is 0.

xy-plane:

z=0\implies\begin{cases}4-x=\frac83\\\frac{y+4}4=\frac83\end{cases}\implies\left(\dfrac43,\dfrac{20}3,0\right)

yz-plane:

x=0\implies\begin{cases}\frac{y+4}4=4\\\frac{8-z}3=4\end{cases}\implies\left(0,12,-4\right)

xz-plane:

y=0\implies\begin{cases}4-x=1\\\frac{8-z}3=1\end{cases}\implies\left(3,0,5\right)

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Let p= x^2-7.
Advocard [28]

Since p = x² - 7, you can substitute/plug in p for x² - 7

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3 years ago
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