Show that 6 – 4x - x^2 can never be greater than 10. ( This is an Additional Math Question )
1 answer:
Answer:
see explanation
Step-by-step explanation:
Given
6 - 4x - x²
Since the coefficient of the x² term < 0 then parabola has a maximum vertex.
To find the x- coordinate of the vertex
= -
with a = - 1 and b = - 4 , then
= -
= - 2
The corresponding y- coordinate is found by substituting x = - 2 , that is
6 - 4(- 2) - (- 2)² = 6 + 8 - 4 = 10
vertex = (- 2, 10 )
The maximum value of the function is the y- coordinate of the vertex
Then maximum value is 10
Thus 6 - 4x - x² is never greater than 10
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Answer:
4.72 hours/day
Step-by-step explanation:
Mean time spent watching TV (μ) = 2.8 hours a day
Standard deviation (σ) = 1.5 hours a day
The 90th percentile (upper 10%) of a normal distribution has an equivalent z-score of roughly z = 1.282. The minimum time spent watching TV, X, at the 90th percentile is:
On a typical day, you must watch at least 4.72 hours of TV to be in the upper 10%.