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3 years ago

Please help me with this???

Mathematics

1 answer:

Fiesta28 [93]3 years ago

7 0

Answer:

X=3

Step-by-step explanation:

Since all the sides of a square are equal, hence;

5x-2 = x+10

Collect like terms

5x-x = 10+2

4x =12

X = 12/4

X =3

Hence the value of x is 3

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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

Which point lies on the line with point-slope equation y - 3 = 4(x + 7)?

Sav [38]

Answer:

y=4x+31

your answer will have a line that

3 is your y-intercept located at your y-axis

and 4x your slope.

we start from our point on the y-axis 31

and rise/run

rise over run = 4/1

rise 4

run 1

so move up 4

and to the right 1

Step-by-step explanation:

Since there is no image for me to tell you which line it is you can easily find out by chancing this expression to y=mx+b form. also known as slope intercept form.

y-3=4(x+7)

we want to do order of operations. pemdas

so first we do Parenthesis to do so we need to distribute the 4.

after we do so we get...

y-3=4x+28

now we need to move -3 to isolate y

to do so we need add 3

y=4x+31

5 0

4 years ago

Which of the following is the equation for the line perpendicular to the line y=−x+20 that passes through the point (−4, 2)?

coldgirl [10]

I have a feeling it’s a but I’m not that sure good luck might want to wait on other peoples opinions

7 0

3 years ago

I saved $360 for one year.the bank paid me 20% interest.how much do i now have

Ann [662]

You have 360+360*20%=360+360*20/100=360+72
So you have 432

4 0

3 years ago

Read 2 more answers

If ◻SLED ~ ◻PARK which of the following statements are incorrect?

san4es73 [151]

Answer:

◻DELS ~ ◻KARP is incorrect

Step-by-step explanation:

All of the similarity statements have corresponding letters in the same order except ...

◻DELS ~ ◻KARP . . . . (incorrect)

_____

The correct version would be ...

◻DELS ~ ◻KRAP

3 0

3 years ago