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3 years ago

Find the volume of the cone whose base is shown and whose altitude is 8 meters.

Mathematics

1 answer:

Aloiza [94]3 years ago

7 0

$\bf \textit{volume of a cone}\\\\
V=\cfrac{\pi r^2 h}{3}\implies V=\stackrel{base~area}{\pi r^2}\cdot \cfrac{1}{3}\stackrel{height}{h}\\\\
-------------------------------\\\\
\textit{base of this cone}\\\\
B=\stackrel{a~square}{5\cdot 5}+\stackrel{semi-circle}{\frac{\pi r^2}{2}}\implies B=25+\frac{\pi 3^2}{2}\\\\\\ B=\stackrel{square}{25}+\stackrel{semi-circle}{\frac{9\pi }{2}}
\\\\\\
\textit{height of this cone is just 8}\\\\
-------------------------------\\\\$

$\bf \textit{volume of this cone}\\\\
V=B\cdot \cfrac{1}{3}h\implies V=\left( 25+\cfrac{9\pi }{2} \right)\left( \cfrac{8}{3} \right)
\\\\\\
V=\cfrac{200}{3}+\cfrac{3\pi\cdot 4 }{1}\implies V=\cfrac{200}{3}+12\pi$

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John can mow a lawn in 80 minutes. Rocky can mow the same lawn in 120 minutes. How long does it take for both John and Rocky to

mario62 [17]

Answer: it will take them 48 minutes.

Step-by-step explanation:

John can mow a lawn in 80 minutes. This means that the rate at which he moans the lawn per minute is 1/80

Rocky can mow the same lawn in 120 minutes. This means that the rate at which Rocky can mow the same lawn per minute is 1/120

If they work together, they would work simultaneously and their individual rates are additive. This means that their combined working rate would be

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Assuming it takes t hours for both of them to clean the room working together, the working rate per hour would be 1/t. Therefore,

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3 years ago

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NemiM [27]

The recursive formula to find nth term of sequence is:

$a_n = 4n - 1 \text{ where } n \geq 1$ and n = 1, 2, 3, ....

Solution:

Given a sequence is:

3, 7, 11, 15, 19, 23, 27, 31, 35

Let us find the difference between terms

7 - 3 = 4

11 - 7 = 4

15 - 11 = 4

19 - 15 = 4

23 - 19 = 4

27 - 23 = 4

31 - 27 = 4

35 - 31 = 4

Thus the difference between terms is constant

Thus the given sequence is arithmetic sequence

An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant

The nth term of arithmetic sequence is given by:

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

$a_n$ = the nᵗʰ term in the sequence

$a_1$ = the first term in the sequence

d = the common difference between terms

Here in the given sequence

d = 4

$a_1=3$

Substitute in above formula,

$a_n = 3 + (n-1)(4)\\\\a_n = 3 + 4n - 4\\\\a_n = 4n - 1$

Thus the recursive formula to find nth term of sequence is:

$a_n = 4n - 1 \text{ where } n \geq 1$ and n = 1, 2, 3, ......

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3 years ago

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MrMuchimi

Answer:

25/13

Step-by-step explanation:

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drek231 [11]

Recall that, to get the inverse relation of any expression, we start off by doing a quick switcharoo on the variables, then we solve for "y".

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$

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