2 years ago

Add. (3x2 - 2x) + (4x-3)

Mathematics

2 answers:

polet [3.4K]2 years ago

7 0

I think it would be 3x2 +2x -3

ra1l [238]2 years ago

6 0

Answer:

3x^2 +2x−3

Step-by-step explanation:

3x^2 −2x+4x−3

Combine −2x and 4x to get 2x.

3x^2 +2x−3

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given y>0 and dy/dx=(3x^2+4x)/yif the point (1,√10) is on the graph relating x and y, then what is y when x=0

jonny [76]

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{3x^2+4x}y\iff y\,\mathrm dy=(3x^2+4x)\,\mathrm dx$
$\implies\displaystyle\int y\,\mathrm dy=\int(3x^2+4x)\,\mathrm dx$
$\implies \dfrac12y^2=x^3+2x^2+C$

When $x=1$ you have $y=\sqrt{10}$ , so

$\dfrac12(\sqrt{10})^2=1^3+2(1)^2+C\implies 5=1+2+C\implies C=2$

and so the particular solution to the ODE is

$\dfrac12y^2=x^3+2x^2+2$

Then when $x=0$ , you get

$\dfrac12y^2=0^3+2(0)^2+2=2$
$\implies y^2=4$
$\implies y=2$

where we omitted the negative root because it's given that $y>0$ .