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The general equation of a horizontal ellipse is
(x-h)2/a2 + (y-k)2/b2 = 1, at center (h,k) while a = semi-major axis, b = semi-minor axis. These are related through the distance of the focus from the center,c. a2 = b2 + c2.
If you draw the points on a coordinate plane, the center of the ellipse is at (0,0), so h and k equals 0. Then, the minor axis (2b) spans from 8 to -8 of the y-axis. This is equal to 16 units. Hence,
2b = 16
b = 8
b^2 = 64
The distance between the two foci is 2c. Thus,
2c = 12
c = 6
c^2 = 36
Then, a2 = 64 + 36 = 100. Substituting to the general equation:
x^2/100 + y^2/64 = 1
Answer:
It should be 75 inches
Step-by-step explanation:
Total number of marbles=5+3+4=12
Probability of picking a red marble =5/12
Answer:
Intercepts:
x = 0, y = 0
x = 1.77, y = 0
x = 2.51, y = 0
Critical points:
x = 1.25, y = 4
x = 2.17
, y = -4
x = 2.8, y = 4
Inflection points:
x = 0.81, y = 2.44
x = 1.81, y = -0.54
x = 2.52, y = 0.27
Step-by-step explanation:
We can find the intercept by setting f(x) = 0


where n = 0, 1, 2,3, 4, 5,...

Since we are restricting x between 0 and 3 we can stop at n = 2
So the function f(x) intercepts at y = 0 and x:
x = 0
x = 1.77
x = 2.51
The critical points occur at the first derivative = 0


or

where n = 0, 1, 2, 3

Since we are restricting x between 0 and 3 we can stop at n = 2
So our critical points are at
x = 1.25, 
x = 2.17
, 
x = 2.8, 
For the inflection point, we can take the 2nd derivative and set it to 0



We can solve this numerically to get the inflection points are at
x = 0.81, 
x = 1.81, 
x = 2.52, 