Answer:
7/9
Step-by-step explanation:
the line above the 7 just means that it is repeating. so instead of writing 0.777777777, you just pu t the line on top
Your answer is C because 12•10= 12
Answer:
Use the formula,
Volume of cylinder =πr²h
<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>=</em><em>3</em><em>.</em><em>1</em><em>4</em><em>×</em><em>1</em><em>6</em><em>×</em><em>1</em><em>1</em>
<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>=</em><em>5</em><em>5</em><em>2</em><em>.</em><em>6</em><em>4</em><em> </em><em>cm³</em>
The required time is mathematically given as
t-150 minutes.
This is further explained below.
<h3>What is the time?</h3>
We know that the volume of the prism is given by.
Volume ![$=$ (Base Area $) \times$ Height](https://tex.z-dn.net/?f=%24%3D%24%20%28Base%20Area%20%24%29%20%5Ctimes%24%20Height)
Base Area ![$=\frac{1}{2} \times(1.4+0.6) \times 2$](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%281.4%2B0.6%29%20%5Ctimes%202%24)
Base Area ![$=2 \mathrm{~m}^2$](https://tex.z-dn.net/?f=%24%3D2%20%5Cmathrm%7B~m%7D%5E2%24)
Now,
![Volume $=2 \times 1=2 \mathrm{~m}^3$](https://tex.z-dn.net/?f=Volume%20%24%3D2%20%5Ctimes%201%3D2%20%5Cmathrm%7B~m%7D%5E3%24)
Given that there is a twenty percent drop in the level of the pond during the first thirty minutes.
Because of this, the volume increases.
![Volume $=2 \times 0.8=1.6 \mathrm{~m}^3](https://tex.z-dn.net/?f=Volume%20%24%3D2%20%5Ctimes%200.8%3D1.6%20%5Cmathrm%7B~m%7D%5E3)
Now, the rate of emptying the tank is,
![=\frac{2-1.6}{30}=\frac{1}{75} \mathrm{~m}^3 / \mathrm{min}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B2-1.6%7D%7B30%7D%3D%5Cfrac%7B1%7D%7B75%7D%20%5Cmathrm%7B~m%7D%5E3%20%2F%20%5Cmathrm%7Bmin%7D)
In conclusion, We also know that,
$$
![\begin{aligned}&\text { time }=\frac{\text { volume }}{\text { rate }} \\&\text { time }=\frac{2}{\frac{1}{75}}-150 \mathrm{~min}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%26%5Ctext%20%7B%20time%20%7D%3D%5Cfrac%7B%5Ctext%20%7B%20volume%20%7D%7D%7B%5Ctext%20%7B%20rate%20%7D%7D%20%5C%5C%26%5Ctext%20%7B%20time%20%7D%3D%5Cfrac%7B2%7D%7B%5Cfrac%7B1%7D%7B75%7D%7D-150%20%5Cmathrm%7B~min%7D%5Cend%7Baligned%7D)
Therefore, Colin must wait for the pond to drain for a total of 150 minutes.
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