An equation of an ellipse is given. x2 16 + y2 25 = 1 (a) Find the vertices, foci, and eccentricity of the ellipse. vertex (x, y) = 0,−5 (smaller y-value) vertex (x, y) = 0,5 (larger y-value) focus (x, y) = 0,−3 (smaller y-value) focus (x, y) = 0,3 (larger y-value) eccentricity 3 5 (b) Determine the length of the major axis.

(a)

(b)Length of the major axis=10

Step-by-step explanation:

When the major axis of an ellipse is parallel to the y-axis.The standard form of the equation of an ellipse is given as:

Given the equation:

(I)The coordinates of the vertices are

Therefore, the vertices are at (0,-5) and (0,5).

(II)The coordinates of the foci are

The coordinates of the foci are (0,-3) and (0,3).

(III)Eccentricity

This is the ratio of the distance c between the center of the ellipse and each focus to the length of the semi major axis.

Simply put, Eccentricity =c/a

Eccentricity=3/5

(b)Length of the major axis

The length of the major axis=2a

=2(5)=10.

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.

n=9

step-by-step explanation:

7 times a number = 7n

decreased by 13 = 7n-13

same as is =

5 times the number = 5n

increased by 5 = 5n+5

7n-13 = 5n+5

2n=18

n=9