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3 years ago

Find a power series representation for the following function.

Mathematics

1 answer:

PSYCHO15rus [73]3 years ago

5 0

a. Recall that

For , we have

By integrating both sides, we get

If , then

so that

We can shift the index to simplify the sum slightly.

b. The power series for can be obtained simply by multiplying both sides of the series above by .

c. We have

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Answer: $(x+10)^2+(y+6)^2=121$

Step-by-step explanation:

The equation of a circle in the general form is:

$ax^{2}+by^2+cx+dy+e=0$

The equaton of a circle in standard form is:

$(x-h)^2+(y-k)^2=r^2$

Where the center is at <em>(h, k)</em> and <em>r</em> is the radius

To write the equation of a circle from general form to standard form, you must complete the squaare, as you can see below:

1- Given the equation in general form:

$x^{2}+y^2+20x+12y+15=0$

2- Complete the square:

-Group the like terms and move the constant to the other side.

- Complete the square on the left side of the equation.

- Add the same value to the other side.

Then you obtain:

$(x^{2}+20x)+(y^2+12y)=-15\\(x^2+20x+(\frac{20}{2})^2)+(y^2+12y+(\frac{12}{2})^2)=-15+(\frac{20}{2})^2+(\frac{12}{2})^2\\\\(x+10)^2+(y+6)^2=-15+100+36\\(x+10)^2+(y+6)^2=121$

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Read 2 more answers

If 60 MG of drug is in b 500 ml of solution, how many ml of solution contain 36 MG of drug

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60/500=36/x
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x=(500*3)/5
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3 years ago