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Kisachek [45]
3 years ago
11

VERY IMPORTANT!! PLEASE HELPPP :(

Mathematics
1 answer:
Marizza181 [45]3 years ago
8 0

Answer:

7

Step-by-step explanation:

Sigma notation means that you will add and continue adding using the function given.  Furthermore,  bottom number i = 1 is your starting point and the top number 3 is where you will stop the summation.  So,

Let i = 1:

4(\frac{1}{2}^{1-1})=4(1)=4

Let i = 2

4(\frac{1}{2}^{2-1})=4(\frac{1}{2})=\frac{4}{2}=2

Let i = 3

4(\frac{1}{2}^{3-1})= 4((\frac{1}{2})^2 )=4\frac{1}{4}=\frac{4}{4}=1

And so let's add up our results:

4+2+1=7

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To understand the algebra, go through the following equations below:

  • First the thing to note is that the top square is the square of the bottom square: Stage 1: 1 & 1^{2} , stage 2 = 2 & 2^{2}, stage 3 = 3 & 3^{2}
  • Second image: Just add the two values above to get the total of tiles needed.  For stage 5: 5 + 5^{2} = 30, Stage 12: 12 + 12^{2} = 156

Part B

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  • second equation: y = n + (n*n)

<h3>Meaning of algebra</h3>

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Find the general solution of the nonhomogeneous differential equation x^2y''-2y=3(x^2) -1, (x&gt;0).
Ira Lisetskai [31]

Answer:

G.S=C_1\frac{1}{x}+C_2x^2+x^2logx+\frac{1}{2}

Step-by-step explanation:

We are given that non-homogeneous differential equation

x^2y''-2y=3(x^2)-1

It is Cauchy Euler equation

Substitute x=e^t  x>0

Auxillary equation

D'(D'-1)-2=0

D'^2-D'-2=0

(D'-2)(D'+1)=0

D'-2=0 \implies D'=2

D'+1=0\implies D'=-1

Complementary solution

y=C_1e^{-t}+C_2e^{2t}

y=C_1\frac{1}{x}+C_2x^2

Particular solution

y_p=\frac{3e^{2t}}{D'^2-D'-2}-\frac{e^{0t}}{D'^2-D'-2}

y_p=te^{2t}+\frac{1}{2}=x^2logx+\frac{1}{2}

G.S=C_1\frac{1}{x}+C_2x^2+x^2logx+\frac{1}{2}

Hence, general solution G.S=C_1\frac{1}{x}+C_2x^2+x^2logx+\frac{1}{2}

6 0
4 years ago
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