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ollegr [7]
3 years ago
14

Find the exact solution for the following system of equations. 2x+3y=48 x+6y=11

Mathematics
1 answer:
TEA [102]3 years ago
4 0
Question <span>2x+3y=48
Answer </span><span>x = 24 + -1.5y

Question </span><span>x+6y=11
</span>Answer x = 11 + -6y
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Answer:

18/35

Step-by-step explanation:

3/5 ÷ 7/6

3/5 × 6/7

18/35

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Find the slope of the line that passes through (3,5) and (-3,-5)
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3 years ago
family of solutions of the second-order DE y y 0. Find a solution of the second-order IVP consisting of this differential equati
Anna35 [415]

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

y(1) = 0

y'(1) =e

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}

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

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

1 = 2c_1

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}

6 0
3 years ago
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