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melomori [17]
2 years ago
15

Write 9x² - 36x = 4y² + 24y + 36 in standard form

Mathematics
1 answer:
Kisachek [45]2 years ago
5 0

Answer:

9·x² - 36·x = 4·y² + 24·y + 36 in standard form is;

(x - 2)²/2² - (y + 3)²/3² = 1

Step-by-step explanation:

The standard form of a hyperbola is given as follows;

(x - h)²/a² - (y - k)²/b² = 1 or (y - k)²/b² - (x - h)²/a² = 1

The given equation is presented as follows;

9·x² - 36·x = 4·y² + 24·y + 36

By completing the square, we get;

(3·x - 6)·(3·x - 6) - 36 = (2·y + 6)·(2·y + 6)

(3·x - 6)² - 36 = (2·y + 6)²

(3·x - 6)² - (2·y + 6)² = 36

(3·x - 6)²/36 - (2·y + 6)²/36 = 36/36 = 1

(3·x - 6)²/6² - (2·y + 6)²/6² = 1

3²·(x - 2)²/6² - 2²·(y + 3)²/6² = 1

(x - 2)²/2² - (y + 3)²/3² = 1

The equation of the hyperbola  is (x - 2)²/2² - (y + 3)²/3² = 1.

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The sum of a number and its square is 182. Find the number.
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Answer:

13 and -14 satisfy this condition

Step-by-step explanation:

Let's represent that number as x

and the square of x is x^2

So,

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rearrange the quadratic equation

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let's use the quadratic formula

\frac{-b+\sqrt{b^2-4ac} }{2a}       or      \frac{-b-\sqrt{b^2-4ac} }{2a}

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\frac{-1+\sqrt{1+728} }{2}      or         \frac{-1-\sqrt{1+728} }{2}

\frac{-1+\sqrt{729} }{2}            or    \frac{-1-\sqrt{729} }{2}

\frac{-1+{27} }{2}     or    \frac{-1-{27} }{2}

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13 or    - 14

Lets check

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