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 answer in simple solution is 6x^3-x^2+2x+8
Answer:
1.107 = r
Step-by-step explanation:
To solve this for r, do the following:
Add 10 to both sides, to isolate the r term on the left: 18r^(-8) = 8
Divide both sides by 18, to isolate r^(-8): r^(-8) = 8/18
Invert both sides: r^8 = 9/4
Take the natural log or both sides:
8 ln r = ln 9 - ln 4, or
8 ln r = 0.8109, so that ln r = 0.1014
to find r, raise e to the power ln r on the left and e to the power 0.1014 on the right:
ln r 0.1014
e = e = 1.107 = r
