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3 years ago

What are the 2 things we look for when trying to decide if two figures are scaled copies?

1 answer:

5 0

if the angles are the same, and side lengths are equally decreased or increased (depending if you are scaling up or down)

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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

4 years ago

Dawson is covering a large cylinder with brown paper. He'll need to find the volume of the cylinder in order to determine how mu

Arlecino [84]

It is to true!!!!!!!!!!!!!!!!!!!!!!!!

3 0

3 years ago

Mr. Gardner is making 6 treat bags. He has 185 chocolate covered raisins to share evenly among the teat bags. How many chocolate

Hunter-Best [27]

Answer:

30 Chocolate covered raisins will be in each bag and 5 will be left over.

Step-by-step explanation:

In order to solve this, you must divide the number of Chocolate covered raisins by the number of bags you are making. 185 divided by 6 is 30 with 5 left over.

3 0

2 years ago

What is 4(2(329)) LIKE i have no idea how to do that

boyakko [2]

I think it wants you to multiply the numbers.
329×2=658
658×4=2632

Final Answer=2632

5 0

4 years ago

Read 2 more answers

Write an equation in slope intercept form for line with slope 2\5 and y intercept 3.

77julia77 [94]

Answer:

Y= 2/5x +3