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vlada-n [284]
3 years ago
13

The function f(x)=x+n is a polynomial? true or false.

Mathematics
1 answer:
Andrew [12]3 years ago
5 0
False I don’t really know why
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B).  $38,821

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By using several of the known mathematical formulas, and what is given to us at the very bottom (and top) of the answer, we can see that the correct answer is  

$38,821

on e2020

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Simplify<br> -3c+5d+3c-d
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Give a counterexample for the statement: All square roots are ration numbers
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Counterexamples:

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the u.s.s harry truman is an aircraft carrier that is 1,092 feet long. find the length in ft and in please help
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Use the variation of parameters method to solve the DR y" + y' - 2y = 1
postnew [5]

Answer:

y(t)\ =\ C_1e^{-2t}+C_2e^t-t\dfrac{e^{-2t}}{3}-\dfrac{1}{3}

Step-by-step explanation:

As given in question, we have to find the solution of differential equation

y"+y'-2y=1

by using the variation in parameter method.

From the above equation, the characteristics equation can be given by

D^2+D-2\ =\ 0

=>D=\ \dfrac{-1+\sqrt{1^2+4\times 2\times 1}}{2\times 1}\ or\ \dfrac{-1-\sqrt{1^2+4\times 2\times 1}}{2\times 1}

=>\ D=\ -2\ or\ 1

Since, the roots of characteristics equation are real and distinct, so the complementary function of the differential equation can be by

y_c(t)\ =\ C_1e^{-2t}+C_2e^t

Let's assume that

     y_1(t)=e^{-2t}          y_2(t)=e^t

=>\ y'_1(t)=-2e^{-2t}        y'_2(t)=e^t

   and g(t)=1

Now, the Wronskian can be given by

W=y_1(t).y'_2(t)-y'_1(t).y_2(t)

   =e^{-2t}.e^t-e^t(-e^{-2t})

   =e^{-t}+2e^{-t}

   =3e^{-t}

Now, the particular solution can be given by

y_p(t)\ =\ -y_1(t)\int{\dfrac{y_2(t).g(t)}{W}dt}+y_2(t)\int{\dfrac{y_1(t).g(t)}{W}dt}

=\ -e^{-2t}\int{\dfrac{e^t.1}{3.e^{-t}}dt}+e^{t}\int{\dfrac{e^{-2t}.1}{3.e^{-t}}dt}

=\ -e^{-2t}\int{\dfrac{1}{3}dt}+\dfrac{e^t}{3}\int{e^{-t}dt}

=\dfrac{-e^{-2t}}{3}.t-\dfrac{1}{3}

=-t\dfrac{e^{-2t}}{3}-\dfrac{1}{3}

Now, the complete solution of the given differential equation can be given by

y(t)\ =\ y_c(t)+y_p(t)

      =C_1e^{-2t}+C_2e^t-t\dfrac{e^{-2t}}{3}-\dfrac{1}{3}

5 0
3 years ago
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