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s344n2d4d5 [400]

3 years ago

10

What is 2/4^2 x 2/6^2

2 answers:

KIM [24]3 years ago

7 0

Answer:

1/72

Step-by-step explanation:

NikAS [45]3 years ago

5 0

Answer:

1/36

Step-by-step explanation:

(2/4)^2 X (2/6)^2

(2/4) X (2/4) = 4/16 -> 1/4

(2/6) X (2/6) = 4/36 -> 1/9

1/4 X 1/9 = 1/36

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Find the general solution of the given higher-order differential equation. d3u dt3 + d2u dt2 − 2u = 0

STALIN [3.7K]

$\dfrac{\mathrm d^3u}{\mathrm dt^3}+\dfrac{\mathrm d^2u}{\mathrm dt^2}-2u=0$

This ODE has characteristic equation

$r^3+r^2-2=(r^3-r)+(r^2+r-2)=r(r^2-1)+(r+2)(r-1)$

$=(r(r+1)+(r+2))(r-1)=(r^2+2r+2)(r-1)=0$

which has roots at $r=1,-1\pm i$ . Then the characteristic solution to the ODE is

$u(t)=C_1e^t+C_2e^{(-1+i)t}+C_3e^{(-1-i)t}$

$\implies\boxed{u(t)=C_1e^t+C_2e^{-t}\cos t+C_3e^{-t}\sin t}$

6 0

4 years ago

Which situation matches the inequality below?

mars1129 [50]

Answer:

C is the correct answer

8 0

3 years ago

What are the two binomials for the expression x(x + 3) + 3(x + 3)?

Alja [10]

Answer:

5

Step-by-step explanation:

6 0

3 years ago

Ya'll fr get 50 points if you answer this. <br> What is the rate of change of <img src="https://tex.z-dn.net/?f=f%28x%29%3D2%5Ex

Evgesh-ka [11]

Answer:

$\dfrac{dy}{dx}=2^x\ln 2$

Step-by-step explanation:

**This is a non-linear function and therefore <u>does not have a constant rate of change</u>. It will have a different slope depending on what points you use in the average rate of change formula: $\mathsf{average \ rate \ of \ change = \dfrac{change \ in \ y}{change \ in \ x}}$

To calculate rate of change, differentiate.

substitute y for $f(x)$ :

$\implies y=2^x$

Take natural logs of both sides:

$\implies \ln y=\ln 2^x$

Apply the log rule $\ln a^b=b \ln a$ :

$\implies \ln y=x\ln 2$

Differentiate with respect to $x$ :

$\implies \dfrac{1}{y} \frac{dy}{dx}=\ln 2$

Mulitply both sides by $y$ :

$\implies \dfrac{dy}{dx}=y\ln 2$

Replace $y$ with $y=2^x$

$\implies \dfrac{dy}{dx}=2^x\ln 2$

Therefore, rate of change of the function is :

$\dfrac{dy}{dx}=2^x\ln 2$

8 0

3 years ago

What is 7 and one fifth divided by 8? Plz help

USPshnik [31]

$7 \frac{1}{5} \div 8$ = 4/5

8 0

3 years ago