Answer:
10
Step-by-step explanation:
Ground level is where h = 0, so solve the equation ...
h(x) = 0
-5(x -4)^2 +180 = 0 . . . . substitute for h(x)
(x -4)^2 = 36 . . . . . . . . . . divide by -5, add 36
x -4 = 6 . . . . . . . . . . . . . . positive square root*
x = 10 . . . . . . add 4
The object will hit the ground 10 seconds after launch.
_____
* The negative square root also gives an answer that satisfies the equation, but is not in the practical domain. That answer would be x = -2. The equation is only useful for time at and after the launch time: x ≥ 0.
The architecture and design of the city was what they were impressed by. They said it may have been better than most European cities.
Answer:
2.275%
Step-by-step explanation:
The first thing to do here is to calculate the z-score
Mathematically;
z-score = (x-mean)/SD
from the question, x = 12,300 hours , mean = 11,500 hours while Standard deviation(SD) = 400 hours
Plugging the values we have;
z-score = (12,300-11,500)/400 = 800/400 = 2
Now, we want to calculate P(z ≤ 2)
This is so because we are calculating within a particular value
To calculate this, we use the z-score table.
Mathematically;
P(z ≤ 2) = 1 - P(z > 2) = 1 - 0.97725 = 0.02275
To percentage = 2.275%
Answer:
a₁ = - 24
Step-by-step explanation:
The n th term of an AP is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₇ = 2a₅ , then
a₁ + 6d = 2(a₁ + 4d) = 2a₁ + 8d ( subtract 2a₁ + 8d from both sides )
- a₁ - 2d = 0 → (1)
The sum to n terms of an AP is
= 
[ 2a₁ + (n - 1)d ]
Given 
= 84 , then
(2a₁ + 6d) = 84
3.5(2a₁ + 6d) = 84 ( divide both sides by 3.5 )
2a₁ + 6d = 24 → (2)
Thus we have 2 equations
- a₁ - 2d = 0 → (1)
2a₁ + 6d = 24 → (2)
Multiplying (1) by 3 and adding to (2) will eliminate d
- 3a₁ - 6d = 0 → (3)
Add (2) and (3) term by term to eliminate d
- a₁ = 24 ( multiply both sides by - 1 )
a₁ = - 24
Answer:
After the 35 gel pens??
Step-by-step explanation:
