Answer:
The maximum is P=112.4 at (23.4,7)
Step-by-step explanation:
From the graph, the coordinates of the vertices of the feasible region are:
(0,25)
(9,7)
(23.4, 7)
(15,17.5)
Substituting these values in the objective function, P.
At (0,25), P = 6x − 4y=6(0)-4(25)=-100
At (9,7), P = 6x − 4y=6(9)-4(7)=26
At (23.4,7), P = 6x − 4y=6(23.4)-4(7)=112.4
At (15,17.5), P = 6x − 4y=6(15)-4(17.5)=20
Since the objective is to maximize,
The maximum is P=112.4 at (23.4,7)
To solve the linear programming problem, graph the inequalities to find the feasible region, then compute the function P = 6x − 4y at each corner point of the feasible region to find the maximum value. The values of x and y must also uphold all the inequalities.
The subject of the problem is a linear programming problem, and to solve it, we first identify the feasible region by graphing inequalities. This involves graphing x + 2y ≤ 50, 5x + 4y ≤ 145, 2x + y ≥ 25, y ≥ 7, and x ≥ 0. The feasible region would be formed by the area enclosed within those lines.
Next, we find the corner points of the feasible region because, in a linear programming problem, the maximum and minimum always occur at the vertices or corner points. Let's calculate these corner points.
Finally, we evaluate the function P = 6x − 4y at each corner point and find the value of P that would be maximized. It's crucial to remember that the values of x and y must satisfy all the given inequalities.
#SPJ11
The solutions of the quadratic equation x² + 13 = 8x + 37 are x = 4 + 2√10 and x = 4 - 2√10.
The quadratic equation is defined as a function containing the highest power of a variable is two.
The given equation as:
x² - 8x + 13 = 37
Subtracting 37 from both sides, we get:
x² - 8x - 24 = 0
Now, we have the equation in standard form, so we can use the quadratic formula to find the solutions:
x = (-b ± √(b² - 4ac)) / 2a
Here, a = 1, b = -8, and c = -24.
Substitute these values into the quadratic formula, and we get:
x = (-(-8) ± √((-8)² - 4(1)(-24))) / 2(1)
x = (8 ± √(64 + 96)) / 2
x = (8 ± √160) / 2
x = (8 ± 4√10) / 2
Simplifying, we get:
x = 4 ± 2√10
Therefore, the solutions of the quadratic equation x² + 13 = 8x + 37 are x = 4 + 2√10 and x = 4 - 2√10.
Learn more about quadratic function here:
#SPJ3
Answer:
Step-by-step explanation:
Area of prism = base area × altitude
1. (2x²-10)(x+4)
= 3x³-2x - 40
2. Base area = 2πr
Volume = (2πr)(r²+ 5r)
=2πr³ + 10πr²
3. Base area=½(6)(x-4)(x+3)=3(x-4)(x+3)
Volume= 3(x-4)(x+3)(⅓)
=(x-4)(x+3)= x² - x -12
4. Base circumference= 10π
Base radius = 10π/(2π) = 5
Base area = πr² = 25π
Volume = 25π(3x²-2x)
=125πx²-50πx
5. Volume = 3π√50
=15π√2
6. Base diameter = 16
Base radius = 16/2 = 8
Base area = 2πr = 16π
Volume = 16π(23a²)
=368πa²
Answer:
Step-by-step explanation:
The statement that is not true (an exception is easily created) is C
Draw a 1 by 4 rectangle.
Underneath it draw a 2 by 2 rectangle.
They both have the same area (4 units) but they are not congruent. The corresponding lengths are not equal and that is another condition that must be met for there to be congruence. There are many others.
Draw a 2 by 2 square.
draw a triangle with a base of 1 and a height of 8. These two figures have the same area, but they don't even have the same number of sides.
C is simply not true.
3 is the correct answer