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The point slope form of the asymptote of the hyperbola is; y - 4 = ±(6/7)(x - 6)
- We are given the equation of the hyperbola as;
[(y + 4)²/36] - [(x - 6)²/49] = 1
- We can rewrite this equation as;
[(y + 1)²/6²] - [(x - 6)²/7²] = 1
- The general equation form of hyperbola is;
[(y - k)²/a²] - [(x - h)²/b²] = 1
- Comparing this general form to our given equation we can see that;
k = -4
h = 6
a = 6
b = 7
- Now the equation of the asymptote of a hyperbola follows the general formula;
y = ±[a(x - h)/b] + k
- Plugging in the relevant values gives us;
y = ±(6/7)(x - 6) - 4
>> y - 4 = ±(6/7)(x - 6)
Read more about hyperbola asymptotes at; brainly.com/question/12919612
Answer:
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Explanation:
The width of the rectangle using synthetic division is; 5x² + 4x - 6
<h3>Synthetic division of Polynomials</h3>
We are given;
Area of rectangle = 5x³ + 19x² + 6x - 18
Length of rectangle = x + 3
We know that;
Width of rectangle = Area/length.
Using synthetic division, we have;
<u>5x² + 4x - 6 </u>
(x + 3) | 5x³ + 19x² + 6x - 18
- <u>5x³ + 15x²</u>
4x² + 6x
- <u>4x² + 12x</u>
-6x - 18
<u> -6x - 18</u>
0
Thus, the width of the rectangle is 5x² + 4x - 6
Read more about polynomial synthetic division at; brainly.com/question/24323423