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2 years ago

–2x + y = 3 2x – y = 4 Using elimination to solve this system results in the equation .

Mathematics

1 answer:

tankabanditka [31]2 years ago

6 0

Answer:

1 = x and -2 = y

I am fairly happy with this answer

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Consider the system of differential equations dxdt=−4ydydt=−4x. Convert this system to a second order differential equation in y

koban [17]

$\dfrac{\mathrm dy}{\mathrm dt}=-4x\implies x=-\dfrac14\dfrac{\mathrm dy}{\mathrm dt}\implies\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}$

Substituting this into the other ODE gives

$-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}=-4y\implies y''-16y=0$

Since $x(t)=-\dfrac14y'(t)$ , it follows that $x(0)=-\dfrac14y'(0)=4\implies y'(0)=-16$ . The ODE in $y$ has characteristic equation

$r^2-16=0$

with roots $r=\pm4$ , admitting the characteristic solution

$y_c=C_1e^{4t}+C_2e^{-4t}$

From the initial conditions we get

$y(0)=5\implies 5=C_1+C_2$

$y'(0)=16\implies-16=4C_1-4C_2$

$\implies C_1=\dfrac12,C_2=\dfrac92$

So we have

$\boxed{y(t)=\dfrac12e^{4t}+\dfrac92e^{-4t}}$

Take the derivative and multiply it by -1/4 to get the solution for $x(t)$ :

$-\dfrac14y'(t)=\boxed{x(t)=-\dfrac12e^{4t}+\dfrac92e^{-4t}}$

7 0

3 years ago

PLEASE HELP!! Find the coordinates.

Mazyrski [523]

Answer:

Option (D)

Step-by-step explanation:

Coordinates of the points J, E and V are,

J → (-4, -5)

E → (-4, -3)

V → (-1, -1)

This triangle is translated by the rule $T_{}$ given in the question.

Coordinates of the image will follow the rule,

(x, y) → [(x + 2), (y + 4)]

following this rule coordinates of the image triangle will be,

J(-4, 5) → J'(-2, -1)

E(-4, -3) → E'(-2, 1)

V(-1, -1) → V'(1, 3)

Therefore, points given in the option (D) will be the answer.

7 0

3 years ago

MATH-IXL , Look at the picture below to answer CORRECTLY. Only give me one right answer So i can mark yall as Brainliest!

Rom4ik [11]

The correct answer is 20 plz give me a like

8 0

2 years ago

How much money is required to buy 2 cakes of soap at $.18 a cake an 1 dozen eggs at $.65 a dozen

mestny [16]

Answer: 1.01$

Step-by-step explanation:

.18 + .18=.36

.36 + .65=1.01$

8 0

3 years ago

PLEASE HURRY!!!

RoseWind [281]

terms is x first then terms in y and constant after the equals

Its C

4 0

3 years ago