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:
The objective of the problem is obtained below:
From the information, an urn consists of, 4 black, 2 orange balls and 8 white.
The person loses $1 for each white ball selected, no money is lost or gained for any orange balls picked and win $2 for each black ball selected. Let the random variable X denotes the winnings.
No winnings probability= 0.011
Probability of winning $1=0.3516
Probability of winning $2= 0.0879
Probability of winning $4= 0.0659
The answer would be because
Answer:
Length of NM is 36 cm
Step-by-step explanation:
Length of MN + Length of NO = Length of MNO (Or only MO)
cm
Thus, length of MN is equal to length of NO i.e 36 cm
The line MNO has point N, that bisect it into two equal half.
Thus, the line MNO has two parts
Total length of line MNO = MN + NO = 
cm
Answer:
15
Step-by-step explanation:
lets begin to set up this question. i personally find questions like these easiest when i begin to set up ideas to help my brain process it better, for example:
person a
person b
person c
person d
we know that each (person) must receive at least 1 candy. we also know that we have 7 candies. therefore if we want do draw this out :
person a- 1
person b- 1
person c- 1
person d -1
notice that we now have given away 4 of the 7 candies. now we have 3 candies left. we can simply:
person a- 2
person b-2
person c-2
person d- 1
but, keep in mind that there are still many more ways that we can distribute the candies to other kids. the question we are asked is how may ways can we do this. since i have already illustrated the question, you can either learn how to put this into an equation, or experiment how many variations there are. the answer, either way is 15.
