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Bingel [31]
3 years ago
14

Simplify the expression: 4(x + 3) + 3(5 – x) A X + 27 B X + 8 C 2x + 15 D. 19x + 11​

Mathematics
2 answers:
Jobisdone [24]3 years ago
4 0

Answer:

A

Step-by-step explanation:

4(x+3)+3(5-x)

=4x+12+15-3x

=x+27

cestrela7 [59]3 years ago
4 0

Answer:

A. x+27

Step-by-step explanation:

  1. you have to open the brackets
  2. it will be 4x+12+15-3x
  3. for more easier you can organise it
  4. 4x-3x+12+15=x+27
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Answer:

\frac{y}{x}-2ln(\frac{y}{x}+1)=lnx+C

Step-by-step explanation:

Given differential equation,

(x^2 + y^2) dx + (x^2 - xy) dy = 0

\implies \frac{dy}{dx}=-\frac{x^2 + y^2}{x^2 - xy}----(1)

Let y = vx

Differentiating with respect to x,

\frac{dy}{dx}=v+x\frac{dv}{dx}

From equation (1),

v+x\frac{dv}{dx}=-\frac{x^2 + (vx)^2}{x^2 - x(vx)}

v+x\frac{dv}{dx}=-\frac{x^2 + v^2x^2}{x^2 - vx^2}

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v+x\frac{dv}{dx}=\frac{1 + v^2}{v-1}

x\frac{dv}{dx}=\frac{1 + v^2}{v-1}-v

x\frac{dv}{dx}=\frac{1 + v^2-v^2+v}{v-1}

x\frac{dv}{dx}=\frac{v+1}{v-1}

\frac{v-1}{v+1}dv=\frac{1}{x}dx

Integrating both sides,

\int{\frac{v-1}{v+1}}dv=\int{\frac{1}{x}}dx

\int{\frac{v-1+1-1}{v+1}}dv=lnx + C

\int{1-\frac{2}{v+1}}dv=lnx + C

v-2ln(v+1)=lnx+C

Now, y = vx ⇒ v = y/x

\implies \frac{y}{x}-2ln(\frac{y}{x}+1)=lnx+C

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