Hello from MrBillDoesMath!
Answer: 500
Discussion:
The idea is to represent p(x) with a squared component...
3 + 4x - 4x^2 =
3 - ( 4x^2 - 4x) =
Add and subtract 1:
(3+1) - (4x^2-4x +1) =
4 - (2x-1)^2
To maximize profit we need to minimize the term (2x-1)^2 as it is always positive (or zero) and subtracts from the number 4. The minimum of (2x -1)^2 occurs when 2x -1 = 0 or x = 1/2. Since x is the number of speakers in thousands, (1/2)x = 500 speakers.
Note: this problem can be more easily addressed in a Calculus course by taking the first derivative of p(x), setting it to zero, and solving for x (which yields x = 1/2 too)
Thank you,
MrB
Answer:
System of Linear Equations entered :
[1] 6x-2y=8
[2] 3x-4=y
Equations Simplified or Rearranged :
[1] 6x - 2y = 8
[2] 3x - y = 4
Solve by Substitution :
// Solve equation [2] for the variable y
[2] y = 3x - 4
// Plug this in for variable y in equation [1]
[1] 6x - 2•(3x-4) = 8
[1] 0 = 0 => Infinitely many solutions
Answer:
I honestly don't know how to solve anything like this but my best guess is 135
Step-by-step explanation:
I used the area of a circle formula to find the area of the two semi-circles, and then added it to the area of the rectangle. (Once again, I really do not know xD)
Answer:
Step-by-step explanation:
Diameter = 72 inches
radius r = 72/2 = 36 inches
Area = πr²
= 3.14* 36 * 36
=4069.44 inches²²