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1 year ago

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For t=2 , 14t−3t is equal to ? and 3t−14t is equal to ?

1 answer:

const2013 [10]1 year ago

8 0

Answer:

14t-3t=22

3t-14t= -22
where there is t multiply by 2

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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

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

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The bird feeder on a pole measures +6 feet and there is a buried treasure chest at -4 feet. 0 is ground level. Determine which i

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the answer is 4

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2 years ago

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Sarah hopes to be 5 feet tall by her next birthday. Right now, she is 148 centimeters tall. how many more centimeter does Sarah

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Sarah needs 4.4 centimeters more to reach 5 feet before her next birthday.

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1 year ago

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Element X is a radioactive isotope such that every 66 years, its mass

LenKa [72]

Answer:

194.5315427 grams

Step-by-step explanation:

The half-life of element x would be 66 years. So, after 20 years you would have:

.5^(20/66) x 240=0.810548 x 240

=194.5315427 grams of the element left ......

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2 years ago

PLS HELP!!! The snowy tree cricket is sometimes called the temperature cricket because the frequency of its chirps varies based

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Answer:

Step-by-step explanation:

62 degrees Fahrenheit

Step-by-step explanation:

The number of snowy tree cricket chirps per minute is 148 less than 4 times the outside temperature in degrees Fahrenheit.

Let x = number of chirps

f = temp in Fahrenheit

x = 4f -148

Now let x = 100

100 = 4f-148

Add 148 to each side

100+148 = 4f-148+148

248 = 4f

Divide each side by 4

248/4 = 4f/4

62=f

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1 year ago