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4 years ago

(2x^3 - 2x^2) Divide or subtract exponents ?

Mathematics

1 answer:

Agata [3.3K]4 years ago

6 0

Answer:

Neither.

Step-by-step explanation:

You can only add exponents when multiple, or subtract when dividing.

Also, 2x^3 and 2x^2 are two different terms, not like terms, so cannot subtract the two.

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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

What is the equation of the line?

ki77a [65]

Answer:

y=1/2+2

Step-by-step explanation:

go up 1 and right 2 thats how you get 1/2 also its 2 point above the orgin so its +2

remember y=x+b 1/2 is the x(slope) and 2 is b

7 0

2 years ago

Read 2 more answers

Which equation represents the table of values

zzz [600]

Answer:

y=1/3x-2

Step-by-step explanation:

Now first we have to find a pattern in this.

for x_1 we notice that there is a difference of 3. For x_2 we notice that there is a difference of 1.

For graphs I suggest you use desmos . com/calculator ;)

Thanks for the points

4 0

3 years ago

Number 7 help ASAP ASAP

MariettaO [177]

Answer:

Step-by-step explanation:

7 0

3 years ago

A fish was swimming 3 in a half feet below the water surface at 7:00 a.M. Four hours later, the fish as at a depth that is 5 one

Mekhanik [1.2K]

Answer:

8 3/4 below sea level

Step-by-step explanation:

Given that:

Depth of fish at 7:00 A. M = 3 1/2 feets below sea level

Depth at 11:00a.m (4 hours later) = 5 1/4 feets below it's position at 7:00 a. M

Rational number to represent position of fish with respect to the water surface at 11:00 a. M

Position at 11:00 a. M :

Addition of the two depth distances given :

(3 1/2 + 5 1/4)

7/2 + 21/4 = (14 + 21) / 4 = 35 / 4

35/4 = 8 3/4 feets below sea level

5 0

4 years ago

Read 2 more answers