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3 years ago

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Mathematics

1 answer:

Nostrana [21]3 years ago

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Seniors have the higher hourly pay rate and seniors make more money

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(15 pts) 4. Find the solution of the following initial value problem: y"-10y'+25y = 0 with y(0) = 3 and y'(0) = 13

jolli1 [7]

Answer:

$y(x)=3e^{5x}-2xe^{5x}$

Step-by-step explanation:

The given differential equation is $y''-10y'+25y=0$

The characteristics equation is given by

$r^2-10r+25=0$

Finding the values of r

$r^2-5r-5r+25=0\\\\r(r-5)-5(r-5)=0\\\\(r-5)(r-5)=0\\\\r_{1,2}=5$

We got a repeated roots. Hence, the solution of the differential equation is given by

$y(x)=c_1e^{5x}+c_2xe^{5x}...(i)$

On differentiating, we get

$y'(x)=5c_1e^{5x}+5c_2xe^{5x}+c_2e^{5x}...(ii)$

Apply the initial condition y (0)= 3 in equation (i)

$3=c_1e^{0}+0\\\\c_1=3$

Now, apply the initial condition y' (0)= 13 in equation (ii)

$13=5(3)e^{0}+0+c_2e^{0}\\\\13=15+c_2\\\\c_2=-2$

Therefore, the solution of the differential equation is

$y(x)=3e^{5x}-2xe^{5x}$

5 0

3 years ago

Which inequality is equivalent to 7x-2y>8?

Crazy boy [7]

$7x-2y\ \textgreater \ 8 \\ 7x-8 \ \textgreater \ 2y /:2 \\ \frac{7}{2} x -4\ \textgreater \ y \\ y\ \textless \ \frac{7}{2} x-4$

4 0

3 years ago

Which expression is equivalent to 16x +42y?

V125BC [204]

Find the Greatest Common Factor (GCF)

GCF = 2

Factor out the GCF (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

2(16x/2 + 42y/2)

Simplify each term in parenthesis

4 0

3 years ago

Given the endpoint (4, −2)and midpoint (9, 4), find the other endpoint.

marissa [1.9K]

Answer:

Step-by-step explanation:

(x + 4)/2 = 9

x + 4 = 18

x = 14

(y-2)/2 = 4

y - 2 = 8

y = 10

(14, 10)

4 0

3 years ago

What is 55 percent of 80 proportion

stiks02 [169]

The answer is 44.

All u have to do is multiply 80 * 55% and u get 44, hope this helps.

5 0

3 years ago

Help pleaseeeeeeeeeee​

Help pleaseeeeeeeeeee