Mathematics, 05.10.2019 09:00 peggycab4201

The time, t, required to empty a tank varies inversely as the rate, r, of pumping. if a pump can empty a tank in 2.5 hours at a rate of 400 gallons per minute, how long will it take to empty a tank at 500 gallons per minute?

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Answer from: pilarmonsivais

Variation can be direct, inverse and joint.

It will take 2 hours to empty the tank at a rate of 500 gallons per minutes

Let time be represented with t, and r represent rate.

The inverse variation is represented as:

$\mathbf{t \alpha \frac{1}{r}}$

Represent as an equation

$\mathbf{t = \frac{k}{r}}$

Make k the subject

$\mathbf{k = rt}$

When t = 2.5 and r = 400, we have:

$\mathbf{k =400 \times 2.5}$

$\mathbf{k =1000}$

When r = 500, we have:

$\mathbf{k = rt}$

$\mathbf{1000 = 500t}$

Divide both sides by 500

$\mathbf{2 = t}$

Rewrite as:

$\mathbf{t = 2}$

Hence, it will take 2 hours to empty the tank at a rate of 500 gallons per minutes

Read more about variations at:

link

Answer from: Silvanade

$\bf \qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf \stackrel{\textit{\underline{t} varies inversely with \underline{r}}}{t = \cfrac{k}{r}} \qquad \qquad \qquad \textit{we also know that } \begin{cases} t=2.5\\ r=400 \end{cases} \\\\\\ 2.5=\cfrac{k}{400}\implies 1000=k~\hfill \boxed{t = \cfrac{1000}{r}} \\\\\\ \textit{when r = 500, what is \underline{t}?}\qquad \qquad t = \cfrac{1000}{500}\implies t=2$

Answer from: Quest

The third question is correct.
Can someone me with this i am confused and need

Answer from: Quest

"it's not the heat, it's the humidity". that's a partly valid phrase you may have heard in the summer, but it's actually both. the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature. this has important considerations for the human body's comfort. when the body gets too hot, it begins to perspire or sweat to cool itself off. if the perspiration is not able to evaporate, the body cannot regulate its temperature. evaporation is a cooling process. when perspiration is evaporated off the body, it effectively reduces the body's temperature. when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases. in other words, the human body feels warmer in humid conditions. the opposite is true when the relative humidity decreases because the rate of perspiration increases. the body actually feels cooler in arid conditions. there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

75% of the temperatures are below what value? how do you know? 75% of the temperatures are above w

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