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oee [108]
4 years ago
12

Consider the differential equation 4y'' â 4y' + y = 0; ex/2, xex/2. Verify that the functions ex/2 and xex/2 form a fundamental

set of solutions of the differential equation on the interval (ââ, â). The functions satisfy the differential equation and are linearly independent since W(ex/2, xex/2) = â  0 for ââ < x < â.
Mathematics
1 answer:
Kazeer [188]4 years ago
7 0

Check the Wronskian determinant:

W(e^{x/2},xe^{x/2})=\begin{vmatrix}e^{x/2}&xe^{x/2}\\\frac12e^{x/2}&\left(1+\frac x2\right)e^{x/2}\end{vmatrix}=\left(1+\frac x2\right)e^x-\frac x2e^x=e^x\neq0

The determinant is not zero, so the solutions are indeed linearly independent.

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kondor19780726 [428]

Answer: 18.2

Step-by-step explanation:

14^{2}+b^{2}=23^{2}\\b^{2}=23^{2}-14^{2}\\b=\sqrt{23^{2}-14^{2}} \approx \boxed{18.2}

4 0
2 years ago
-(b - 5) = -4(1-b)-6b solve
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Answer:

-9

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5+4=4b-6b+b

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therefore b=-9

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3 years ago
To the nearest penny, what is the value of x?
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Step-by-step explanation:

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3 years ago
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Find the common difference of the arithmetic sequence 14,7,0 ....
ziro4ka [17]

Answer:

Step-by-step explanation:

the formula for common difference is

d = aₙ - aₙ₋₁

So,

d = a₂-a₁ = a₃-a₂

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d = -7    & d = -7

8 0
3 years ago
An inlet pipe on a swimming pool can be used to fill the pool in 33 hours. The drain pipe can be used to empty the pool in 34 ho
Talja [164]

<u>Answer: </u>

An inlet pipe on a swimming pool can be used to fill the pool in 33 hours. Time it will take to fill the pool = 748 hrs

<u>Solution: </u>

Let x = time it will take to fill the pool

\frac{1}{33} = work rate of inlet pipe

\frac{1}{34} = work rate of drain pipe

Using the formulae

Volume of flow=work rate \times time

Let us assume complete time of pool to fill = 1

Remaining fraction of pool to be filled = 1-\frac{1}{3}=\frac{2}{3}

\begin{array}{l}{\frac{1}{33} x-\frac{1}{34} x=\frac{2}{3}} \\\\ {\frac{x}{33}-\frac{x}{34}=\frac{2}{3}}\end{array}

\frac{34 x-33 x}{33 \times 34}=\frac{2}{3}

34 x-33 x=\frac{2 \times 34 \times 33}{3}

\begin{array}{l}{x=\frac{2244}{3}} \\\\ {x=\frac{3168}{3}} \\\\ {x=748}\end{array}

Time it will take to fill the pool = 748 hrs

5 0
3 years ago
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