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2 years ago

Solve the following system of equations by graphing. - 4x + 3y -12 - 2x + 3y -18

Mathematics

1 answer:

My name is Ann [436]2 years ago

6 0

Answer:

The solution of the graph is at (-3,-8).

Step-by-step explanation:

The given equations are :

-4x+3y=-12

and

-2x+3y=-18

These are the system of equations in two variables.

The graphs for the equations are :

The solution of the graph is at (-3,-8).

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nalin [4]

Answer:

$\frac{1}{3}$

Step-by-step explanation:

2 = 2 × 1

6 = 2 × 3

GCF = 2

$\frac{2 /2 }{6/2} =\frac{1}{3}$

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2 years ago

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Find the solution of the initial value problem<br><br> dy/dx=(-2x+y)^2-7 ,y(0)=0

Leokris [45]

Substitute $v(x)=-2x+y(x)$ , so that $\dfrac{\mathrm dv}{\mathrm dx}=-2+\dfrac{\mathrm dy}{\mathrm dx}$ . Then the ODE is equivalent to

$\dfrac{\mathrm dv}{\mathrm dx}+2=v^2-7$

which is separable as

$\dfrac{\mathrm dv}{v^2-9}=\mathrm dx$

Split the left side into partial fractions,

$\dfrac1{v^2-9}=\dfrac16\left(\dfrac1{v-3}-\dfrac1{v+3}\right)$

so that integrating both sides is trivial and we get

$\dfrac{\ln|v-3|-\ln|v+3|}6=x+C$

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$\dfrac{v-3}{v+3}=Ce^{6x}$

$\dfrac{v+3-6}{v+3}=1-\dfrac6{v+3}=Ce^{6x}$

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Given the initial condition $y(0)=0$ , we find

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so that the ODE has the particular solution,

$\boxed{y=2x+\dfrac6{1+e^{6x}}-3}$

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3 years ago

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Gnom [1K]

Answer:

The perpendicular slope is -4/3

Step-by-step explanation:

Perpendicular slopes multiply to -1

m * 3/4 = -1

Multiply each side by 4/3

m * 3/4 *4/3 = -1 * 4/3

m = -4/3

The perpendicular slope is -4/3

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Allushta [10]

180-48= 132 ( I think)

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lyudmila [28]

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