One polynomial identity that crops up often in various areas is the difference of squares identity:
A2-b2=(a-b) (a+b)
We meet this in the context of rationalising denominators.
The interior angles of a parallelogram will always equal 360. The interior angles of a triangle are 180 if it is a equilateral triangle then the angles are 60 degrees each. You know 2 sides of parallelogram. The 100 degree and 90 degree. You can find the one opposing the x because it’s on a straight line and a straight line is 180 degrees if a triangle is 60 degree angle then the opposing angle to complete the straight line must be 180-60 so you get 120. You now know 3 sides. 120, 90 and 100
They should add up to be 360 so you can set up an equation like so
120+90+100+x=360
And x = 50
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.
Transmission must be in third gear as both are running at the same speed ! so third gear !!!
Answer:
Step-by-step explanation:
It was given that, florida manatee population is 3,000 and is decreasing by 11% each year.
We want to write a function for this situation.
Since the population is decreasing annually, it is modelled by:
We substitute the give initial population and rate of decrease to get:
This simplifies to:
