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.
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* 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.
8 a) y=x² stretched vertically by 8
That means (0,0) stays (0,0), and (1,1) becomes (1,8) and (-1,1) becomes (-1,8)
Answer: y = 8x²
8 b) y=x² compressed vertically by 1/5
Answer: y = (1/5) x²
9.
y = ax² + k through (-1,3) and (3,-13)
That means
3 = a (-1)² + k
-13 = a (3²) + k
Subtracting,
16 = a - 9a = -8a
a = -2
3 = -2 + k
k = 5
y = -2x² + 5
Check:
-2(-1)^2 + 5 = 3, good
-2(3)^2+5 = -18 + 5 = -13, good
Answer: a = -2, k = 5
Answer:
2^31.
Step-by-step explanation:
2 * 2^30
= 2^1 * 2^30
= 2^31. (Law of indices)
The triangle in this problem is an equilateral triangle. Equilateral Triangles have 3 equal sides and 3 equal angles. So, the side of x is equal to 16.
Answer: Undefined: Needs more data
Step-by-step explanation: What is the timespan over which they have retired? Is this a direct relationship?
