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maw [93]
2 years ago
5

CALCULUS: Determine which function is a solution to the differential equation y ' − y = 0.

Mathematics
1 answer:
Montano1993 [528]2 years ago
8 0

C: none of these are solutions to the given equation.

• If<em> y(x)</em> = <em>e</em>², then <em>y</em> is constant and <em>y'</em> = 0. Then <em>y'</em> - <em>y</em> = -<em>e</em>² ≠ 0.

• If <em>y(x)</em> = <em>x</em>, then <em>y'</em> = 1, but <em>y'</em> - <em>y</em> = 1 - <em>x</em> ≠ 0.

The actual solution is easy to find, since this equation is separable.

<em>y'</em> - <em>y</em> = 0

d<em>y</em>/d<em>x</em> = <em>y</em>

d<em>y</em>/<em>y</em> = d<em>x</em>

∫ d<em>y</em>/<em>y</em> = ∫ d<em>x</em>

ln|<em>y</em>| = <em>x</em> + <em>C</em>

<em>y</em> = exp(<em>x</em> + <em>C </em>)

<em>y</em> = <em>C</em> exp(<em>x</em>) = <em>C</em> <em>eˣ</em>

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Caroline has some dimes and some quarters. She has a maximum of 15 coins worth at least $2.85 combined. If Caroline has 3 dimes,
gayaneshka [121]

Answer:

11, 12.

Step-by-step explanation:

Let q represent number of quarters.

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We can represent this information in an inequality as:

q+3\leq 15...(1)

We are also told that the coins worth at least $2.85 combined. This means that the worth of all coins is greater than or equal to 2.85.

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0.25q+0.30\geq 2.85

0.25q+0.30-0.30\geq 2.85-0.30

0.25q\geq 2.55

\frac{0.25q}{0.25}\geq \frac{2.55}{0.25}

q\geq 10.2

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10.2\leq q\leq 12

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Since we cannot have 0.2 of a coin, therefore, Caroline could have 11 or 12 quarters.

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2 years ago
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