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3 years ago

25x^2+9y^2+72y-81=0. Find the standard form of the equation by completing the square. Then identify and graph each conic.

1 answer:

8 0

25x² + 9y² + 72y - 81 = 0
 25x² + 9y² + 72y - 81 + 81 = 0 + 81
 25x² + 9y² + 72y = 81
 25x² + 9(y² + 8y + 16) = 81 + 9(16)
 25x² + 9(y² + 4y + 4y + 16) = 81 + 144
 25x² + 9(y(y) + 4(y) + 4(y) + 4(4)) = 225
 25x² + 9(y(y + 4) + 4(y + 4)) = 225
 25x² + 9(y + 4)(y + 4) = 225
 25x² + 9(y + 4)² = 225
 225 225 225
 x² + 9(y + 4)² = 1
 25 25

The conic section is an ellipse.

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The length of a log of wood is 90 in. How many cuts do you need to make to obtain

Ilia_Sergeevich [38]

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<h3>What is a sequence?</h3>

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

The total length of the wood = 90 in

We have to cut it into the greatest number of pieces, where each piece will have a different length and the length of each piece is a whole number, in inches.

We can cut it like:

1 in, 2 in, 3 in, 4 in, and so on

The above shows the arithmetic sequence,

The sum of the n natural number is given by:

$\rm S_n = \dfrac{n(n+1)}{2}$

$\rm 90 = \dfrac{n(n+1)}{2}$

After solving, we will get a quadratic equation:

n² + n -180 = 0

After solving, we will get:

n = 12.92 and n = -13.92(term can not be negative)

n = 12 (taking whole number)

Thus, the greatest number of pieces will be 12 where each piece will have a different length and the length of each piece is a whole number, in inches and the remaining piece length will be 12 in(90 - 78).

Learn more about the sequence here:

brainly.com/question/21961097

#SPJ1

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2 years ago