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:
A. x < 3
B. X > 9
c. x < 1
d. x < -2
Step-by-step explanation:
For A. 2x+1 < 7
First, subtract 1 from both sides
Then, we will get
2x+1 -1 < 7 - 1
2x < 6
Now, divide both sides by 2
2x / 2 < 6/2
x < 3
For B. X-5 >4
Add 5 to both sides,
Then, we will get
X -5 +5 > 4 + 5
X > 9
For c. 2x+3 <5
Subtract 3 from both sides
2x +3 -3 < 5 - 3
2x < 2
Divide both sides by 2
2x / 2 < 2/2
x < 1
For d. 2x-3 x >2
First, evaluate 2x -3x
2x -3x = -x
Then, 2x-3 x >2 becomes
-x > 2
Now, divide both sides by -1
-x/-1 > 2/-1
x < -2
(NOTE: The sign changes when you divide or multiply by a negative sign)
Answer:
x=5, y=6
Step-by-step explanation:
By the HL theorem, if the corresponding hypotenuses and one side of two triangles are equal, they are congruent.
So put the hypotenuses equal to each other, and put the side lengths equal to each other.
3x-2=2y+1
x=y-1
Sub 'y-1' into the first equation for x:
3(y-1)-2=2y+1
3y-3-2=2y+1
y=6
x=y-1=6-1=5
The dude above me is wrong lol
Answer:
Hi! The answer is 9.7 / n :)
Answer:
28π
Step-by-step explanation:
A =2πrh+2π
r= ft = 2
h= 5ft
A = 2π (2* 5 )+ 2π(2*2)
A= 2π (10)+2π (4)
A= 20π + 8π
= 28π