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kompoz [17]
3 years ago
15

Are these number sets the same? 1857300 : 1857800

Mathematics
1 answer:
yaroslaw [1]3 years ago
5 0
We are asked to determine if the number sets 1857300 and 1857800 are the same number sets. To answer this, we need to recall and define that number sets are a collection of distinct objects such as elements and numbers. The answer to this question is that these two sets are NOT the same, the first one contains "3" while the second one contains "8".
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Answer:

y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}

Step-by-step explanation:

Given

y=c_1e^x +c_2e^{-x

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Required

The solution

Differentiate y=c_1e^x +c_2e^{-x

y' = c_1e^x - c_2e^{-x}

Next, we solve for c1 and c2

y(1) = 0 implies that; x = 1 and y = 0

So, we have:

y=c_1e^x +c_2e^{-x

0 = c_1 * e^1 + c_2 * e^{-1}

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y'(1) =e implies that: x = 1 and y' = e

So, we have:

y' = c_1e^x - c_2e^{-x}

e = c_1 * e^1 - c_2 * e^{-1}

e = c_1 e - \frac{1}{e}c_2 --- (2)

Add (1) and (2)

0 + e = c_1e + c_1e + \frac{1}{e}c_2 - \frac{1}{e}c_2

e = 2c_1e

Divide both sided by e

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Divide both sides by 2

c_1 = \frac{1}{2}

Substitute c_1 = \frac{1}{2} in 0 = c_1 e + \frac{1}{e}c_2

0 = \frac{1}{2} e+ \frac{1}{e}c_2

Rewrite as:

\frac{1}{e}c_2 = -\frac{1}{2} e

Multiply both sides by e

c_2 = -\frac{1}{2} e^2

So, we have:

y=c_1e^x +c_2e^{-x

y = \frac{1}{2}e^x -\frac{1}{2} e^2 * e^{-x}

y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}

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