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zimovet [89]
3 years ago
10

Pls help me, it’s equations

Mathematics
1 answer:
ANEK [815]3 years ago
3 0

Answer:

  y = (6/5)x

Step-by-step explanation:

A line that does not intersect the given line will have the same slope (6/5) and a different y-intercept (not -4). About the simplest it can be is ...

  y = (6/5)x

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Solve the given initial-value problem. x^2y'' + xy' + y = 0, y(1) = 1, y'(1) = 8
Kitty [74]
Substitute z=\ln x, so that

\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dz}\cdot\dfrac{\mathrm dz}{\mathrm dx}=\dfrac1x\dfrac{\mathrm dy}{\mathrm dz}

\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1x\dfrac{\mathrm dy}{\mathrm dz}\right]=-\dfrac1{x^2}\dfrac{\mathrm dy}{\mathrm dz}+\dfrac1x\left(\dfrac1x\dfrac{\mathrm d^2y}{\mathrm dz^2}\right)=\dfrac1{x^2}\left(\dfrac{\mathrm d^2y}{\mathrm dz^2}-\dfrac{\mathrm dy}{\mathrm dz}\right)

Then the ODE becomes


x^2\dfrac{\mathrm d^2y}{\mathrm dx^2}+x\dfrac{\mathrm dy}{\mathrm dx}+y=0\implies\left(\dfrac{\mathrm d^2y}{\mathrm dz^2}-\dfrac{\mathrm dy}{\mathrm dz}\right)+\dfrac{\mathrm dy}{\mathrm dz}+y=0
\implies\dfrac{\mathrm d^2y}{\mathrm dz^2}+y=0

which has the characteristic equation r^2+1=0 with roots at r=\pm i. This means the characteristic solution for y(z) is

y_C(z)=C_1\cos z+C_2\sin z

and in terms of y(x), this is

y_C(x)=C_1\cos(\ln x)+C_2\sin(\ln x)

From the given initial conditions, we find

y(1)=1\implies 1=C_1\cos0+C_2\sin0\implies C_1=1
y'(1)=8\implies 8=-C_1\dfrac{\sin0}1+C_2\dfrac{\cos0}1\implies C_2=8

so the particular solution to the IVP is

y(x)=\cos(\ln x)+8\sin(\ln x)
4 0
3 years ago
Change five eights into a decimall andpercent​
Stolb23 [73]

Answer:

0.63 as a decimal or 0.625. 63% as a percent.

Step-by-step explanation:

Use a calculator, 5 divided by 8 gives you 0.625 but if you round the 2 up, you get 0.63 or 63%

Brainliest pleaseeeee

5 0
3 years ago
Colleen is selling tubs of popcorn to raise money for the school choir. Her goal is to raise $150. Colleen starts with 40 tubs o
Vanyuwa [196]
Goal: $150
3/4 of 40 : 30
30x3.75= $112.05
She still needs : $37 or $37.05
7 0
3 years ago
Samuel bought a large bag of skittles. 86 of them are red, which is 20% of the bag. How many Skittles are in the bag?
yulyashka [42]

Answer:

430

Step-by-step explanation:

20/100 =5

86 times 5

4 0
2 years ago
Stuart walks 2/3 miles each day. Which is a multiple of 2/3
garik1379 [7]

Answer:



2/3 x 2 = 4/3 or 1 and 1/3

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2/3 x 4 = 8/3 or 2 and 2/3

4 0
3 years ago
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