Answer:
135
Step-by-step explanation:
angle APB is an alternate interior angle to DBC and line DB is supplementary
APD=180-45=135
Answer:
a) 72.25sec
b) 6.25secs
c) after 10.5secs and 2 secs
Step-by-step explanation:
Given the height reached by the rocket expressed as;
s(t)= -4t^2 + 50t - 84
At maximum height, the velocity of the rocket is zero i.e ds/dt = 0
ds/dt = -8t + 50
0 = -8t + 50
8t = 50
t = 50/8
t = 6.25secs
Hence it will reach the maximum height after 6.25secs
To get the maximum height, you will substitute t - 6.25s into the given expression
s(t)= -4t^2 + 50t - 84
s(6.25) = -4(6.25)^2 + 50(6.25) - 84
s(6.25) = -156.25 + 312.5 - 84
s(6.25) = 72.25feet
Hence the maximum height reached by the rocket is 72.25feet
The rocket will reach the ground when s(t) = 0
Substitute into the expression
s(t)= -4t^2 + 50t - 84
0 = -4t^2 + 50t - 84
4t^2 - 50t + 84 = 0
2t^2 - 25t + 42 = 0
2t^2 - 4t - 21t + 42 = 0
2t(t-2)-21(t-2) = 0
(2t - 21) (t - 2) = 0
2t - 21 = 0 and t - 2 = 0
2t = 21 and t = 2
t = 10.5 and 2
Hence the time the rocket will reach the ground are after 10.5secs and 2 secs
9n + 15 < = 10n + 24
9n - 10n < = 24 - 15
-n < = 9
n > = -9
Answer: -3 ≤ x ≤ -1
Step-by-step explanation:
1 ≤ 3 - 4x ≤ 9
1 + 3 ≤ - 4x ≤ 9 + 3; Add 3 on all sides
4 ≤ -4x ≤ 12
1 ≤ -x ≤ 3; Divide 4 on all sides
-1 ≥ x ≥ -3; Multiply -1 on all sides(FYI: When multiplying or dividing negative numbers in inequalities, make sure to reverse the signs as well)
