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3 years ago

A cone has a diameter of 30 in. and a slant height of 17 in.

Mathematics

1 answer:

prisoha [69]3 years ago

3 0

Use the given formula :

$V=\frac{1}3\pi r^2h=\frac{1}3\pi (\frac{D}2)^2h$ where $D$ is the diameter.

By Pythagoras, $h=\sqrt{17^2-(30/2)^2}=8\text{ in}$

Hence $V\approx\frac{3.14}3*15^2*8=\boxed{1884.0\text{ in}^3}$

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In triangle XYZ, angle Y = 45º and angle Z = 60º. If XZ = 4, then what is XY?

Katena32 [7]

Answer:

$XY = 4.9$

Step-by-step explanation:

Given

$XZ= 4$

$\angle Y = 45$

$\angle Z = 60$

Required

Determine the measure of side XY

To do this, we make use of sine law. This is as follows:

$\frac{a}{\sin\ A} = \frac{b}{\sin\ B} = \frac{c}{\sin\ C}$

In this case:

$\frac{4}{\sin(45)} = \frac{XY}{\sin(60)}$

Cross Multiply

$XY * \sin(45) = 4 * \sin(60)$

$XY * 0.7071 = 4 * 0.8660$

Make XY the subject

$XY = \frac{4 * 0.8660}{0.7071}$

$XY = \frac{3.4640}{0.7071}$

$XY = 4.89888276057$

$XY = 4.9$ -- <em>approximated</em>

3 0

3 years ago

An open box with a square base is to have a volume of 18 ft^3.

kotegsom [21]

Answer:

2.29 ft of side length and 1.14 height

Step-by-step explanation:

a) Volume V = x2h, where x is side of square base and h is hite.

Then surface area S = x2 + 4xh because box is open.

b) From V = x2h = 6 we have h = 6/x2.

Substitude in formula for surface area: S = x2 + 4x·6/x2, S = x2 + 24/x.

We get S as function of one variable x. To get minimum we have to find derivative S' = 2x - 24/x2 = 0, from here 2x3 - 24 = 0, x3 = 12, x = (12)1/3 ≅ 2.29 ft.

Then h = 6/(12)2/3 = (12)1/3/2 ≅ 1.14 ft.

To prove that we have minimum let get second derivative: S'' = 2 + 48/x3, S''(121/3) = 2 + 48/12 = 6 > 0.

And because by second derivative test we have minimum: Smin = (12)2/3 + 4(12)1/3(12)1/3/2 = 3(12)2/3 ≅ 15.72 ft2

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2 years ago

What is the solution to q/-7=6?

marta [7]

Answer:

q in (-oo:+oo)

q/(-7) = 6 // - 6

q/(-7)-6 = 0

-1/7*q-6 = 0 // + 6

-1/7*q = 6 // : -1/7

q = 6/(-1/7)

q = -42

Hope I was helpful! :)

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3 years ago

Hey people can u please go follow my always. cammmm

Stels [109]

Answer: oh kayy

Step-by-step explanation:

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2 years ago

Need quick help with this math best answer gets brainliest

frosja888 [35]

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3 years ago