Equation of an ellipse
→having center (0,0) , vertex ( and covertex
and focus
is given by:
As definition of an ellipse is that locus of all the points in a plane such that it's distance from two fixed points called focii remains constant.
Consider two points (a,0) and (-a,0) on Horizontal axis of an ellipse:
Distance from (a,0) to (c,0) is = a-c =
Distance from (-a,0) to (c,0) is = a + c =
a -c + a +c
= a + a
= 2 a →(Option A )
Answer:
750 < p < 1500
Step-by-step explanation:
The total cost of the affair for p attendees is ...
750 +2.25p
The average cost is that number divided by p. The answer choices suggest that "between" means that the cost per person cannot be 2.75 or 3.25. Applying the limits to the average cost, we get ...
2.75 < (750 +2.25p)/p < 3.25
2.75 < 750/p + 2.25 < 3.25 . . . . . . . . separating the fraction parts
0.50 < 750/p < 1.00 . . . . . . . . . . . . . . subtract 2.25
2 > p/750 > 1 . . . . . . . . . . . . . . . . . . . . . take the reciprocal*
1500 > p > 750 . . . . . . . . matches choice 4
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* Taking the reciprocals of numbers with the same sign reverses their order:
2 < 3 but 1/2 > 1/3
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An alternate approach to the solution would be to multiply by p:
0.50p < 750 < 1.00p
To solve this requires it be made into two inequalities:
0.50p < 750 ⇒ p < 1500
and
750 < 1.00p ⇒ 750 < p
Then these would need to be recombined to form the answer:
750 < p < 1500
