Arectangular board is 18 feet by 24 feet. how far from the center of the board should the foci be located in order to cut the largest elliptical tabletop from the board? a. 7.94 ft b. 4.06 ft c. 15 ft d. 15.9 ft

x = 24
y = 18
Length of Major Axis = a
Length of Minor Axis = b

Center (0, 0):

h = 0
k = 0

a = 1/2 x
a = 1/2 *(24)
a = 12
b = 1/2 y
b =1/2 (18)
b = 9
So, Equation of Ellipse:

General : (x - h)² / a² + (y - k)² / b² = 1

(x - 0)² / (12)² + (y - 0)² / (9)² = 1

x² / 144 + y² / 81 = 1

Focus = c:
        
c = √a² - b²
        
c = √(12)² - (9)²
        
c = √144 - 81 = sqrt63 = 7.9372

Focus : ( -7.9372, 0) and ( 7.9372, 0)

15% chance.

step-by-step explanation:

3/10 times, the 5 year old will get a tablet. 5/10 times, the 13 yer old will get a tablet. multiply both fractions to get 15/100 times, both would have a tablet.