F(x) = 18-x^2 is a parabola having vertex at (0, 18) and opening downwards.
g(x) = 2x^2-9 is a parabola having vertex at (0, -9) and opening upwards.
By symmetry, let the x-coordinates of the vertices of rectangle be x and -x => its width is 2x.
Height of the rectangle is y1 + y2, where y1 is the y-coordinate of the vertex on the parabola f and y2 is that of g.
=> Area, A
= 2x (y1 - y2)
= 2x (18 - x^2 - 2x^2 + 9)
= 2x (27 - 3x^2)
= 54x - 6x^3
For area to be maximum, dA/dx = 0 and d²A/dx² < 0
=> 54 - 18x^2 = 0
=> x = √3 (note: x = - √3 gives the x-coordinate of vertex in second and third quadrants)
d²A/dx² = - 36x < 0 for x = √3
=> maximum area
= 54(√3) - 6(√3)^3
= 54√3 - 18√3
= 36√3.
Answer:
slope is undefined
Step-by-step explanation:
Answer:
For a normal distribution 68% of data falls within one standard deviation from mean on both sides of mean
Step-by-step explanation:
A normal distribution's graph is a bell shaped curve that is completely described by its mean and standard deviation. Standard deviation is measured in terms of distance from mean.
34% of data is covered in one standard deviation from mean on one side.
Therefore, for a normal distribution 68% of data falls within one standard deviation from mean on both sides of mean ..
First, find out how much he made in the week total: 24($8.75) = $210
The, find 1.45% of 210: (.0145)(210) = 3.045
*note that 1.45% = .0145*
Round that number to 3.05 and you have your answer
