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vitfil [10]
3 years ago
14

Help with finding the volume of the cone pictured

Mathematics
1 answer:
jasenka [17]3 years ago
4 0

Volume of the cone = 56.52 in³

Solution:

Diameter of the cone = 6 in

Radius of the cone = 6 ÷ 2 = 3 in

Height of the cone = 6 in

The value of π = 3.14

<u>To find the volume of the cone:</u>

Volume of the cone = \frac{1}{3} \pi r^{2} h

                                 $=\frac{1}{3} \times 3.14 \times 3^{2} \times 6

                                 $=3.14 \times 18

                                 = 56.52

Volume of the cone = 56.52 in³

Hence the volume of the given cone is 56.52 \text{in}^3.

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The mass of the particles that a river can transport is proportional to the sixth power of the speed of the river. A certain riv
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The river flows at 2 miles per hour. This is the speed of the current, or the speed at which the water itself is moving.

The mass of the particles moving in river is proportional to the sixth power of 2, or 2^6 = 64 miles per hour. So, if x is the mass of the particle, then the speed is modeled by an inverse relationship x * 2^6 = k, for some constant k. 

For particles that are 15 times the usual mass, the speed of the river itself must increase for the particles to travel at the same speed as before. The mass of the particles is still proportional to the sixth power of the speed of the river, but the speed of the river can no longer be 2 miles per hour. It is some speed y, which we are solving for.

So, the key here is proportional. We can set up two proportions and cross multiply.

\dfrac{x}{2^6} =  \dfrac{15x}{y^6}  \\ (x)(y^6)=(2^6)(15x)

Cancelling our x's (because we don't need to solve for them), we have

y^6 = 15(2^6) = 15(64)=960

To solve for y, we must take the sixth root of both sides, or raise both sides to the one-sixth power.

\sqrt[6]{y^6} =  \sqrt[6]{960}

Using a calculator, we see that \sqrt[6]{960} = 3.14 \ miles \ per \ hour.
6 0
3 years ago
What is the inerquartile of the data set [40,48,62,40,25,50,20 30
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You just find the quartiles which are 62 and 50 the mines them which equals 12.

5 0
3 years ago
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Make an equivalent fraction with the denominator 10,100, or 1000 ​
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10000/10,000. :) :) dh
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3 years ago
In December of 2003, the average price for a gallon of regular gas in the United States was $1.50.
12345 [234]

Answer:

yes

Step-by-step explanation:

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8 0
2 years ago
Find the product of √3 and 5√3 in simplest form. Also, determine whether the
pshichka [43]

The product of √3 and 5√3  in its simplest form is 15.

<h3>What is a rational number?</h3>

A rational number is defined as a numerical representation of a part of a whole that represents a fraction number.

It can be a/b of two integers, a numerator a, and a non-zero denominator b.

To determine the product of √3 and 5√3

So, (√3 )(5√3)

⇒ 5 (√3 )(√3 )

⇒ 5(3)

⇒ 15

The result is rational because 15, can be expressed as a ratio of two integers can be 15/1 of two integers, a numerator 15, and denominator 1 ( which is a non-zero).

Thus, the result is rational.

Learn more about rational numbers here:

brainly.com/question/10354322

#SPJ1

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