What is sin 45°?

Mathematics

1 answer:

Leona [35]3 years ago

6 0

Answer:

Step-by-step explanation:

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A swimming pool is being filled at the rate of 54 pt/min (pints per minute). How many quarts per hour is this?

Rainbow [258]

Answer:

Approximately $1620\; \text{quart} / \text{hour}$ .

Step-by-step explanation:

The given quantity was in the unit $\displaystyle \frac{\text{pint}}{\text{minute}}$ while the required quantity should have the unit $\displaystyle \frac{\text{quart}}{\text{hour}}$ . It would thus be necessary to use conversion factors of the following forms:

$\begin{aligned}\frac{\text{pint}}{\text{minute}} \times \underbrace{\frac{\text{minute}}{\text{hour}} \times \frac{\text{quart}}{\text{pint}}}_{\text{conversion factors}} &= \frac{\text{quart}}{\text{hour}} \end{aligned}$ .

Make use of the fact that:

$1\; \text{pint} = 0.5\; \text{quart}$ , and
$60\; \text{minute} = 1\; \text{hour}$ .

Rearrange the equation $1\; \text{pint} = 0.5\; \text{quart}$ to obtain the conversion factor:

$\begin{aligned} 1 &= \frac{0.5\; \text{quart}}{1\; \text{pint}}\end{aligned}$ .

Similarly, rearrange the equation $60\; \text{minute} = 1\; \text{hour}$ to obtain the conversion factor:

$\begin{aligned} 1 &= \frac{1\; \text{hour}}{60\; \text{minute}}\end{aligned}$ .

Combine both conversion factors and evaluate:

$\begin{aligned} & 54\; \frac{\text{pint}}{\text{minute}} \\ =\; & 54\; \frac{\text{pint}}{\text{minute}} \times \frac{0.5\; \text{quart}}{1\; \text{pint}} \times \frac{60\; \text{minute}}{1\; \text{hour}} \\ =\; & (54 \times 0.5 \times 60) \; \frac{\text{pint} \times \text{quart} \times \text{minute}}{\text{minute} \times \text{pint} \times \text{hour}} \\=\; & 1620\; \frac{\text{quart}}{\text{hour}}\end{aligned}$ .