What number must you add to complete the square for x^2 + 4x = 15 ?
1 answer:
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Answer:
Horizontal distance = 0 m and 6 m
Step-by-step explanation:
Height of a rider in a roller coaster has been defined by the equation,
y =
Here x = rider's horizontal distance from the start of the ride
i).
ii). Since, the parabolic graph for the given equation opens upwards,
Vertex of the parabola will be the lowest point of the rider on the roller coaster.
From the equation,
Vertex → (3, 5)
Therefore, minimum height of the rider will be the y-coordinate of the vertex.
Minimum height of the rider = 5 m
iii). If h = 8 m,
(x - 3)² = 9
x = 3 ± 3
x = 0, 6 m
Therefore, at 8 m height of the roller coaster, horizontal distance of the rider will be x = 0 and 6 m
Answer: a) 79.10 % b) 7% c)19.85 %
Step-by-step explanation:
a) Z = ( × - μ ) ÷ σ Where μ mean of population σ standard deviation Z is the abscissa to give the area or probability we are looking for associated to the value 10 ounces ( × )
So: Z = ( 10 - 9 ) ÷ 1.2 ⇒ Z = 1/1.2 ⇒ Z = 0.83 it has to be below this value
From Z tables we get P [ Z ≤ 0.82 ] = 0.7910 0r 79.10 %
b) Following the same procedure: We look for
P [ Z > ( x - μ ) ÷ σ ] ⇒ Z = ( 12 -10 ) ÷ 1.2 = 2.5
From Z table we get the area under the curve from the left tail up to the point Z < 2.5 ( 2.5 not included) but we were asked for the area out of that previous so 1- 0.9930 = 0.007 is the area we are looking for
So P (b) = 0.007 or 7 %
Finally between the two points above mentioned ( 10 ≤ Z ≤ 12 ) we use the previous values (taking in consideration the limits, according to the problem statement )
Z ≤ 10 Z ⇒( 10-9 ) ÷ 1.2 Z = 0.7967
Z ≥ 12 Z ⇒ ( 12 - 9 ) ÷ 1.2 Z = 0.9952
The interval is between these two points
0.9952 - 0.7967 = 0.1985 ⇒ or 19.85 %
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