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nikdorinn [45]
3 years ago
9

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

Mathematics
1 answer:
Vadim26 [7]3 years ago
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


Step-by-step explanation:


6 0
4 years ago
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