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:
according to the question value got less 12% each year
first of all the 12% of 29000$ = 29000÷100×12= 3480 $
in one year truck value deprecates 3480$
in 10 years it will 3480$×10 =34800$
now truck cost will be = 29000-34800$= -5000$
9514 1404 393
Answer:
geometric sequence
Step-by-step explanation:
The terms of the sequence have a common ratio of -12/3 = -4, so the sequence is geometric. The general term is ...
an = 3(-4)^(n-1)
so the sum can be written as ...
(Note the summation starts at n=0, corresponding to a first term of 3.)
Around 6 hours (exact decimal would be 5.99865). I did this by multiplying 14.85*40 (getting 594). After that, I subtracted 594 from 727.65 (getting 133.65), then multiplying 14.85 by 1.5, getting 22.28, and then, I did 133.65/22.28, getting 5.99865, which I rounded to 6.
Answer:
7/12 of a chance
Step-by-step explanation:
If you have 12 batteries and 5 are dead, 12 - 5 is 7, so there's going to be 7/12 of a chance.
