Can someone please explain how to find the eccentricity for the ellipse with the following equation?:
1 answer:
Answer:
The answer to your question is e =
Step-by-step explanation:
Data
Ellipse = 36x² + 4y² = 9
e = ?
Formula
e = c/a
Process
1.- Convert the equation of the ellipse to the canonical form
36x² + 4y² = 9
- Divide by 9 both sides
36/9x² + 4/9y² = 9/9
4x² + 4/9y² = 1
x² /(1/4) + y² / (9/4) = 1
b² = 1/4 b = 1/2
a² = 9/4 a = 3/2
2.- Find c
a² = b² + c²
c² = a² - b²
Substitution
c² = 9/4 - 1/4
Simplification
c² = 8/4
c² = 2
c=
3.- Find the eccentricity
e =
e =
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I don't speak Romanian, but the closest translation for this suggests you're trying to compute
Integrate by parts:
where
u = ln(x)² ⇒ du = 2 ln(x)/x dx
dv = x³ dx ⇒ v = 1/4 x⁴
Integrate by parts again:
where
u' = ln(x) ⇒ du' = dx/x
dv' = x³ dx ⇒ v' = 1/4 x⁴
So, we have
<h3>Answer: -2w^2 + 25w = 25 or -2w^2 + 25w - 25 = 0</h3>
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Explanation:
Refer to the diagram below. The width is w. We have two opposite and parallel sides equal to this. The other two parallel congruent sides are L = 25-2w meters long. We start with the total amount of fencing, and then subtract off the two width values, so 25-w-w = 25-2w.
The area of the rectangle is
Area = length*width
Area = L*W
Area = (25-2w)*w
Area = 25w - 2w^2
Area = -2w^2 + 25w
Set this equal to the desired area (25 square meters) to get
-2w^2 + 25w = 25
and we can subtract 25 from both sides to get everything on one side
-2w^2 + 25w - 25 = 0
side note: The two approximate solutions of this equation are w = 1.0961 and w = 11.4039 (use the quadratic formula or a graphing calculator to find this)