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Alex73 [517]
3 years ago
12

Find the height of a cone when its diameter is 8 inches and the volume is 100 cubic inches

Mathematics
1 answer:
Aloiza [94]3 years ago
7 0

Answer:

\frac{75}{4\pi } inches or approximately 5.97 inches  

Step-by-step explanation:

Use the cone volume formula: V = \pir²\frac{h}{3}

The diameter is 8 inches, so the radius will be 4 inches.

Plug in the radius and volume, and solve for h

V = \pir²\frac{h}{3}

100 = \pi(4²)(\frac{h}{3})

100 = 16\pi\frac{h}{3}

Divide each side by 16\pi

\frac{25}{4\pi } = \frac{h}{3}

Cross multiply and solve for h:

4\pih = 75

h = \frac{75}{4\pi }

So, the cone's height is \frac{75}{4\pi } or approximately 5.97 inches  

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The expression 4x/5-2x/3 is equivalent to what?
Vinvika [58]

Answer:

(2 x)/15

Step-by-step explanation:

Simplify the following:

(4 x)/5 - (2 x)/3

Put each term in (4 x)/5 - (2 x)/3 over the common denominator 15: (4 x)/5 - (2 x)/3 = (12 x)/15 - (10 x)/15:

(12 x)/15 - (10 x)/15

(12 x)/15 - (10 x)/15 = (12 x - 10 x)/15:

(12 x - 10 x)/15

12 x - 10 x = 2 x:

Answer: (2 x)/15

7 0
3 years ago
An item is regularly priced at 85$. It is on sale for 80% off the regular price. How much is discounted from the regular price?
laila [671]

$68 is discounted from the regular price.

To find this, you first divide 80% by 100 to get 0.8 (the decimal form of the percentage). Then, simply multiply 0.8 by 85 (or vise verse) to get $68. Since the question is asking for how much is discounted from the regular price, the final answer would be $68.

I hope this helps!

4 0
2 years ago
In ΔIJK, k = 57 inches, i = 37 inches and ∠J=141°. Find ∠I, to the nearest degree.
Sonbull [250]

Answer:

<I= 15degrees

Step-by-step explanation:

Using the cosine rule formulae;

j² = i²+k²-2i cos <J

j² = 37²+57² - 2(37)(57)cos <141

j² = 1369+ 3249- 4218cos <141

j² = 4618- 4218cos <141

j² = 4618-(-3,278)

j²= 7,896

j = √7,896

j = 88.86inches

Next is to get <I

i² = j²+k²-2jk cos <I

37² = 88.86²+57² - 2(88.86)(57)cos <I

1369 = 7,896.0996+ 3249- 10,130.04cos <I

1369 = 11,145.0996 - 10,130.04cos <I

1369 - 11,145.0996 = - 10,130.04cos <I

-9,776.0996=- 10,130.04cos <I

cos <I =9,776.0996 /10,130.04

cos<I = 0.96506

<I = 15.19

<I= 15degrees

8 0
2 years ago
6.012<br> as a mixed number in simplest form.
Novosadov [1.4K]
6    3
    ------
    250
ignore this sentence
4 0
3 years ago
Read 2 more answers
If you raise 4 to the 214th power, what is the units digit of the result
Len [333]
\begin{array}{lrlll}&#10;4^1&\boxed{4}\\&#10;4^2&1\boxed{6}\\&#10;4^3&6\boxed{4}\\&#10;4^4&25\boxed{6}\\&#10;4^5&102\boxed{4}\\&#10;4^6&409\boxed{6}&#10;\end{array}\impliedby \textit{see the pattern for 4?}

notice, it goes 4,6 then 4, 6 again, and so on and so on
based on whatever exponent it may have

now, you're being asked, what 214 will give? 4 or 6?
4 0
3 years ago
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