Question to Find Maximum Distance in the Elliptical Orbit

Topic : Ellipse

Question : Halley's comet has an elliptical orbit with the sun at one focus and a major axis of 1,636,484,848 miles. The closest the comet comes to the sun is 54,004,000miles. What is the maximum distance from the comet to the sun?

Solution :

2a = 1,636,484,848miles
so SC = 54,004,000miles
maximum distance from comet to the sun will be DS.
That is when comet comes at D
there is a maximum distance from sun
So SD = CD - SC ; CD = major axis = 1,636,484,848 miles
= 1,636,484,848 - 54004000
= 1582480848miles
So maximum distance is 1582480848miles.

Word Problem to Find Combinations of Tickets

Topic : Word problem

Question : The owner of a movie theater was counting money from1 days sales. he knew that the total of 150 tickets were sold. adult tickets cost 7.50 annd children tickets coast 4.7.5 each if the total recipt for the day were 891.25 how many of each kind of ticket was sold?

Solution :
Number of adult's ticket sold be 'x'
number of children ticket sold be 'y'

the total tickets are 150
So the first equation becomes x+y = 150 ------ (1)

cost of one adult's ticket be 7.50
cost of a child ticket be 4.75

total amount after selling all the tickets makes another equation
7.50x + 4.75y = 891.25 -------- (2)
________________
(x+y = 150) X 7.50
7.50x + 7.50y = 1125
7.50x + 4.75y = 891.25
- _____ -______-______
2.75y = 233.75
divide by 2.75
y = 233.75/2.75
y = 85
x + y = 150
x = 150 - y = 150 - 85 = 65

Problem to Find Unknown Angle of a Triangle

Topic : Angle of a Triangle