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3 years ago

Two fuel tanks with the dimensions shown have the same volume. What is the value of h?

Mathematics

1 answer:

Luda [366]3 years ago

7 0

(See attached picture for the diagram of both fuel tanks)

Answer:

2ft

Step-by-step Explanation:

==> Given:

Two cylindrical fuel tanks, one has a radius of 3ft, and height of 8ft, the second tank has a radius of 6ft and unknown height.

Also, volume of 1st tank = volume of 2nd tank

==> Required:

Find h = unknown height of the the 2nd tank.

=>Solution:

To find the height of the 2nd tank = h, we need to know the volume. Thus, volume of first tank = volume of 2nd tank.

Since the dimensions of the 1st tank are all given, let's find its volume.

Thus, volume of 1st tank using the formula V = πr²h (where π = 3.14, r = 3ft, h = 8ft)

V = 3.14*3²*8

= 3.14*9*8 = 226.08 ft³

Volume of first tank = volume of 2nd tank = 226.08 ft³

=> Let's find the height of the 2nd tank with same volume of 226.08ft³

Therefore, V = πr²h (V = 226.08, r = 6ft, h = ?)

226.08 = 3.14*6²*h

226.08 = 3.14*36*h

226.08 = 113.04*h

226.08/113.04 = h

2 = h

Height of the second fuel tank (h) = 2ft

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15, 11, 7, 3, -1, ... explicit formula and recursive formula

monitta

Recursive formula is: $a_n = a_{n-1} -4$

Explicit formula is: $a_n = 19-4n$

Step-by-step explanation:

Given sequence is:

15,11,7,3,-1

Here

$a_1 = 15\\a_2 = 11\\a_3 = 7$

First of all, we have to find the common difference

Common difference is the difference between consecutive terms of an arithmetic sequence

So,

$d = a_2-a_1 = 11-15 = -4\\d = a_3-a_2 = 7-11 = -4$

Recursive Formula:

A recursive formula is used to find the next term of an arithmetic sequence using previous term and common difference

General form of recursive formula for a given common difference d is:

$a_n = a_{n-1} + d$

Putting the value of d

$a_n = a_{n-1} -4$

Explicit Formula:

The explicit formula is given by:

$a_n = a_1 + (n-1)d$

Putting the first term and common difference

$a_n = 15 + (n-1)(-4)\\a_n = 15 -4n+4\\a_n = 19-4n$

Hence,

Recursive formula is: $a_n = a_{n-1} -4$

Explicit formula is: $a_n = 19-4n$

Keywords: Arithmetic sequence, common difference

Learn more about arithmetic sequence at:

#LearnwithBrainly

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4 years ago

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tatyana61 [14]

Answer:

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Step-by-step explanation:

(5x − 2y)³

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Step-by-step explanation:

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Thus, the situation correctly states the ratio.

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Thus, the situation does not state the ratio correctly.

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Thus, the ratio does not state the situation correctly.

* * * The number of horses in a kingdom is 100, and the number of knights is 50. The ratio of knights to horses is = 50 : 100 = 1 :2. That is, There is one knight for every two horses.

Thus, the ratio states the situation correctly.

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Thus, the ratio does not state the situation correctly.

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