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3 years ago

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While cruising at a steady speed of 400km/h, you identify a storm cloud straight ahead 45km away.

1 answer:

Artist 52 [7]3 years ago

7 0

It would take 6 minutes and 45 seconds

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I don’t know how to do this question

noname [10]

Can you post link cause there’s no question

5 0

2 years ago

Apply the method of undetermined coefficients to find a particular solution to the following system.wing system.

jarptica [38.1K]

$y''-y'+y=\sin x$

The corresponding homogeneous ODE has characteristic equation $r^2-r+1=0$ with roots at $r=\dfrac{1\pm\sqrt3}2$ , thus admitting the characteristic solution

$y_c=C_1e^x\cos\dfrac{\sqrt3}2x+C_2e^x\sin\dfrac{\sqrt3}2x$

For the particular solution, assume one of the form

$y_p=a\sin x+b\cos x$

${y_p}'=a\cos x-b\sin x$

${y_p}''=-a\sin x-b\cos x$

Substituting into the ODE gives

$(-a\sin x-b\cos x)-(a\cos x-b\sin x)+(a\sin x+b\cos x)=\sin x$

$-b\cos x+a\sin x=\sin x$

$\implies a=1,b=0$

Then the general solution to this ODE is

$\boxed{y(x)=C_1e^x\cos\dfrac{\sqrt3}2x+C_2e^x\sin\dfrac{\sqrt3}2x+\sin x}$

$y''-3y'+2y=e^x\sin x$

$\implies r^2-3r+2=(r-1)(r-2)=0\implies r=1,r=2$

$\implies y_c=C_1e^x+C_2e^{2x}$

Assume a solution of the form

$y_p=e^x(a\sin x+b\cos x)$

${y_p}'=e^x((a+b)\cos x+(a-b)\sin x)$

${y_p}''=2e^x(a\cos x-b\sin x)$

Substituting into the ODE gives

$2e^x(a\cos x-b\sin x)-3e^x((a+b)\cos x+(a-b)\sin x)+2e^x(a\sin x+b\cos x)=e^x\sin x$

$-e^x((a+b)\cos x+(a-b)\sin x)=e^x\sin x$

$\implies\begin{cases}-a-b=0\\-a+b=1\end{cases}\implies a=-\dfrac12,b=\dfrac12$

so the solution is

$\boxed{y(x)=C_1e^x+C_2e^{2x}-\dfrac{e^x}2(\sin x-\cos x)}$

$y''+y=x\cos(2x)$

$r^2+1=0\implies r=\pm i$

$\implies y_c=C_1\cos x+C_2\sin x$

Assume a solution of the form

$y_p=(ax+b)\cos(2x)+(cx+d)\sin(2x)$

${y_p}''=-4(ax+b-c)\cos(2x)-4(cx+a+d)\sin(2x)$

Substituting into the ODE gives

$(-4(ax+b-c)\cos(2x)-4(cx+a+d)\sin(2x))+((ax+b)\cos(2x)+(cx+d)\sin(2x))=x\cos(2x)$

$-(3ax+3b-4c)\cos(2x)-(3cx+3d+4a)\sin(2x)=x\cos(2x)$

$\implies\begin{cases}-3a=1\\-3b+4c=0\\-3c=0\\-4a-3d=0\end{cases}\implies a=-\dfrac13,b=c=0,d=\dfrac49$

so the solution is

$\boxed{y(x)=C_1\cos x+C_2\sin x-\dfrac13x\cos(2x)+\dfrac49\sin(2x)}$

7 0

3 years ago

If every student is independently late with probability 10%, find the probability that in a class of 30 students: a) nobody is l

gladu [14]

Answer:

a) 4.2%

b) 14.1%

Step-by-step explanation:

a) 0.9³⁰ = 0.0423911583

b) 30C1 × 0.1 × 0.9²⁹ = 0.1413038609

5 0

3 years ago

Read 2 more answers

Alice works 42 hours, is paid $2.65 per hour, and receives $540.50 in tips. How much did Alice earn?

Talja [164]

Answer:

$651.8

Step-by-step explanation:

Alice earns $2.65 per hour

In 42 hours she will earn = 42 * 2.65 = $111.3

Her total tip after 42hours is 540.5

Total money earned is 540.5+111.3 = 651.8

3 0

2 years ago

How do you combine like terms and solve for the variable?<br> 8 - 3x - 5x = -8

Nitella [24]

<span>8 - 3x - 5x = -8
8 - 8x = -8
-8x = -8 - 8
-8x = -16
8x = 16
x = 16/8
x = 2</span>

7 0

3 years ago

Read 2 more answers