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3 years ago

3 serving of a fruit punch recipe serves 36 people. How many people can be

Mathematics

1 answer:

zalisa [80]3 years ago

5 0

Answer:

Step-by-step explanation:

If 3 servings of fruit punch serves 36 people, we can divide to find out that 1 serving of fruit punch serves 12 people.

Next, you can multiply to figure out that 8 servings servers 96 people (8x12 = 96)

~theLocoCoco

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Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were millio

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Answer:

The amount of oil was decreasing at 69300 barrels, yearly

Step-by-step explanation:

Given

$Initial =1\ million$

$6\ years\ later = 500,000$

Required

At what rate did oil decrease when 600000 barrels remain

To do this, we make use of the following notations

t = Time

A = Amount left in the well

So:

$\frac{dA}{dt} = kA$

Where k represents the constant of proportionality

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$\frac{dA}{dt} * \frac{dt}{A} = kA * \frac{dt}{A}$

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Integrate both sides

$\int\ {\frac{dA}{A} = \int\ {k\ dt}$

$ln\ A = kt + lnC$

Make A, the subject

$A = Ce^{kt}$

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So, we have:

$A = Ce^{kt}$

$1000000 = Ce^{k*0}$

$1000000 = Ce^{0}$

$1000000 = C*1$

$1000000 = C$

$C =1000000$

Substitute $C =1000000$ in $A = Ce^{kt}$

$A = 1000000e^{kt}$

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$t = 6\ A = 500000$

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Take natural logarithm (ln) of both sides

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$\frac{dA}{dt} = kA$

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$\frac{dA}{dt}$ = Rate

So, when

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The rate is:

$\frac{dA}{dt} = -0.1155 * 600000$

$\frac{dA}{dt} = -69300$

Hence, the amount of oil was decreasing at 69300 barrels, yearly

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