Answer:
a) t = 4 secs
b) t = 3 secs
Step-by-step explanation:
h = 64 ft
Initial velocity = 48 ft/s
S = 64 + 48t - 16t^2
a) Set S = 0 and solve for t
0 = 64 + 48t - 16t^2
Divide through by 16
0 = 4 + 3t - t^2
t^2 - 3t - 4 = 0
t^2 - 4t + t - 4 = 0
t(t - 4) + 1(t - 4) = 0
(t + 1) (t - 4) = 0
t + 1 = 0 or t - 4 = 0
t = -1 or t = 4
t = {-1,4}
t = 4 seconds
b) Set S = 64 and solve for t
64 = 64 + 48t - 16t^2
64 - 64 = 48t - 16t^2
0 = 48t - 16t^2
Divide through by 16
0 = 3t - t^2
t^2 - 3t = 0
t(t - 3) = 0
t = 0 or t-3 = 0
t = 0 or t = 3
t = {0,3}
t = 3 secs
You have to multiply the total number of possibilities for each character on the tag by each other. The first two are letters so there are 26 different possibilities (A-Z) for those characters. The next four are digits, so there are 10 different possibilities for them (0-9). That would give 26 x 26 x 10 x 10 x 10 x 10 = 6,760,000
Greatest common factor of 42, 98, and 14 is 14
The factors of 14 are: 1, 2, 7, 14
The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
The factors of 98 are: 1, 2, 7, 14, 49, 98
Then the greatest common factor is 14.