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Neko [114]
3 years ago
7

The volume of a cone is 62.8 cubic inches. The height of the cone is 15 inches. What is the radius of the cone, rounded to the n

earest inch? Use π = 3.14.
A 2 inches
B 4 inches
C 8 inches
D 9 inches
Mathematics
2 answers:
Contact [7]3 years ago
5 0

Step-by-step explanation:

\pi {r}^{2}  \frac{h}{3}  = V \\  \\ \pi {r}^{2} \frac{15}{3}  = 62,8 \\  \\ \pi {r}^{2}(5) = 62,8 \\  \\ 5\pi {r}^{2} = 62,8 \\  \\  3,99797217 ≈ \frac{62,8}{5\pi} \\  \\ 3,99797217 ≈  {r}^{2} \\  \\ 1,999492978 ≈ r \\  \\ 2 ≈ r

I am joyous to assist you anytime.

Setler79 [48]3 years ago
3 0
R = sqrt 3 * (V /( pi * h))
V = 62.8
pi = 3.14
h = 15
now we sub
R = sqrt 3 * (62.8 / (3.14 * 15)
R = sqrt 3 * (62.6 / 47.1)
R = sqrt 3 * 1.33
R = sqrt 3.99
R = 1.9 rounds to 2 inches <===

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Part 1) Option B: 0 ≤ x ≤ 4

Part 2) Option C: (5x − 1)(2x − 3)

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Part 6) Option C: (3, 0) and (5, 0)

Step-by-step explanation:

Part 1) we have

h(t)=-5t^{2}+20t

This is a vertical parabola open downward

The vertex is a maximum

The x-intercepts are the points (0,0) and (4,0)

The vertex is the point (2,20) ---> The x-coordinate of the vertex is the midpoint of the x-intercepts

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The range is the interval ----> [0,20]

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Part 2) we have

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x is the time in minutes

V is the volume in gallons

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When the trough is empty, the volume is equal to zero

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The formula to solve a quadratic equation of the form

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10x^{2} -17x+3=0

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x=\frac{-(-17)(+/-)\sqrt{-17^{2}-4(10)(3)}} {2(10)}

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x=\frac{17(+/-)13} {20}

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x=\frac{17(-)13} {20}=\frac{1}{5}

so

10x^{2} -17x+3=10(x-\frac{3}{2})(x-\frac{1}{5})

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