3 years ago

Y=2x+3 in ordered pairs

Mathematics

1 answer:

Iteru [2.4K]3 years ago

4 0

Answer:

(0,3) , (1,5) , (2,7)

Step-by-step explanation:

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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 $x(t)$ :

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

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4 years ago

What is the surface area of the solid?

trapecia [35]

Answer:

A. 520 square inches is your surface area of the rectangular prism

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3 years ago

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What is the average rate of change <br>y - 3 = -12 (x + 4)

vagabundo [1.1K]

Answer:

$- 12x$

Step-by-step explanation:

$y - 3 = - 12(x + 4) \\ y - 3 = - 12x - 48 \\ y = - 12x - 45$

Thr answer is the slope.

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Three more than the quotient of a number and 8 is 9

Alborosie

Answer:

Step-by-step explanation:

x/8+3=9

x/8=9-3

x/8=6

x=6*8

x=48

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What adds to make -4 but times to get -12

dimulka [17.4K]

3 because 4×3=12 and if you divide12÷3/4 it helps you check

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