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3 years ago

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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:

olasank [31]3 years ago

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
           <u>25x²</u> + <u>9(y + 4)²</u> = <u>225</u>
   225    225    225
      <u> x²</u> + <u>9(y + 4)²</u> = 1
   25 25

The conic section is an ellipse.

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3 years ago

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4 years ago

Read 2 more answers

Given that y varies directly with x and that y = 60 when x = 20, find y when x = 12.

wolverine [178]

1.y varies directly with x

2.substitute the value of x and y in the equation below

y=kx

where k is the constant term

60=20k

k=60\20

k=30

:y=30x.....is the law

To find y when x is 12

You reinstate the law which is y=30x

Then substitutes the value of x to determine y

y=30*12

y=36.

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3 years ago

I am so lost. can someone help?? the question is in the picture.

Juliette [100K]

We are given the following function:

$f(x)=x^2$

We are asked to do the following tranformations:

1. Shift down 5 units and left 77 units.

First, to shift a function down a number "n" of units we follow the next rule:

$h(x)=f(x)-n$

And, to shift a function "m" units to the left we use the following rule:

$h(x)=f(x+m)$

Applying both rules simultaneously we get:

$h(x)=(x+77)^2-5$

2. Reflect about the y-axis.

The rule to reflect a function about the y-axis is the following:

$r(x)=h(-x)$

The means that we will change "x" for "-x" in the function we are going to reflect. Applying the rule we get:

$r(x)=(-x+77)^2-5$

3. Compress vertically by a factor of 2.

To compress a function vertically by a factor "m" we multiply the entire function by 1/m, like this:

$g(x)=\frac{1}{m}r(x)$

Applying the rule we get:

$g(x)=\frac{1}{2}((-x+77)^2-5)$

And thus we get to the final function.

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1 year ago