Y=-1/2x+3
y=-1/2x-5 is parallel:
y=-1/2x-1 is parallel: x+2y=-2
y=2x-4 is perpendicular: -2x+y=-4
y=1/2x+2 is parallel: -x+2y=2
The Lagrangian is
It has critical points where the first order derivatives vanish:
From the first two equations we get
Then
At these critical points, we have
(maximum)
(minimum)
Answer:
Step-by-step explanation:
Company A's equation is 900+0.50x5,000
Company B's equation is 1,500+0.38x5,000
Both equal 3,400 and have to be multiplied by 5,000
Answer:
x = y = 22
Step-by-step explanation:
It would help to know your math course. Do you know any calculus? I'll assume not.
Equations
x + y = 44
Max = xy
Solution
y = 44 - x
Max = x (44 - x) Remove the brackets
Max = 44x - x^2 Use the distributive property to take out - 1 on the right.
Max = - (x^2 - 44x ) Complete the square inside the brackets.
Max = - (x^2 - 44x + (44/2)^2 ) + (44 / 2)^2 . You have to understand this step. What you have done is taken 1/2 the x term and squared it. You are trying to complete the square. You must compensate by adding that amount on the end of the equation. You add because of that minus sign outside the brackets. The number inside will be minus when the brackets are removed.
Max = -(x - 22)^2 + 484
The maximum occurs when x = 22. That's because - (x - 22) becomes 0.
If it is not zero it will be minus and that will subtract from 484
x + y = 44
xy = 484
When you solve this, you find that x = y = 22 If you need more detail, let me know.
Answer:
Step-by-step explanation:
(-3/4)x + 9 = (-1/2)x + 8
9 - 8 = (-1/2)x + (3/4)x
1 = (1/4)x
x = 4
y = (-3/4)4 + 9
y = -3 + 9
y = 6
