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4 years ago

What is 4x-8=9y-5 in standard form

Mathematics

1 answer:

givi [52]4 years ago

4 0

4x-8=9y-5 in standard form is 4x-9y=3

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Find the general solution to 1/x dy/dx - 2y/x^2 = x cos x, y(pi) = pi^2

Finger [1]

Answer:

$\frac{y}{x^2}=\sin x+\pi$

Step-by-step explanation:

Consider linear differential equation $\frac{\mathrm{d} y}{\mathrm{d} x}+yp(x)=q(x)$

It's solution is of form $y\,I.F=\int I.F\,q(x)\,dx$ where I.F is integrating factor given by $I.F=e^{\int p(x)\,dx}$ .

Given: $\frac{1}{x}\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{2y}{x^2}=x\cos x$

We can write this equation as $\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{2y}{x}=x^2\cos x$

On comparing this equation with $\frac{\mathrm{d} y}{\mathrm{d} x}+yp(x)=q(x)$ , we get $p(x)=\frac{-2}{x}\,\,,\,\,q(x)=x^2\cos x$

I.F = $e^{\int p(x)\,dx}=e^{\int \frac{-2}{x}\,dx}=e^{-2\ln x}=e^{\ln x^{-2}}=\frac{1}{x^2}$ { formula used: $\ln a^b=b\ln a$ }

we get solution as follows:

$\frac{y}{x^2}=\int \frac{1}{x^2}x^2\cos x\,dx\\\frac{y}{x^2}=\int \cos x\,dx\\\\\frac{y}{x^2}=\sin x+C$

{ formula used: $\int \cos x\,dx=\sin x$ }

Applying condition: $y(\pi)=\pi^2$

$\frac{y}{x^2}=\sin x+C\\\frac{\pi^2}{\pi}=\sin\pi+C\\\pi=C$

So, we get solution as :

$\frac{y}{x^2}=\sin x+\pi$

4 0

4 years ago

What is the distance between point (7,9) and point (-2,7)

skad [1K]

Answer:

9.21954445729

Step-by-step explanation:

use distance formula

3 0

3 years ago

Write and solve a real-world problem that can be modeled by the equation 0.75x-18.50=0.65x

Scilla [17]

Diana had chocolate, and ate some, leaving 0.75 of it for Sarah.

Sarah ate 18.5 grams of it and return the rest to Diana, which was 65% of the original chococate.

how much chocolate did Diana have at the beginning?

and the solution is:

0.75x-18.50=0.65x

0.75x-0.65x=18.50
0.1x=18.50
x=185

so Diana had 185 grams of chocolate.

6 0

3 years ago

BRAINLIEST IF CORRECT

Kisachek [45]

Answer:

The two values are 100 x 100 x 100 and 1 x 10 to the power of 3

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

If f(x)=5x+7 and g(x)=-2x-4 find f(g(x))=___x+___

USPshnik [31]

Answer:

Step-by-step explanation:

g(x) = -2x - 4

f(-2x -4)

5(-2x - 4) + 7

-10x - 20 + 7

-10x - 13

5 0

4 years ago