Square OABC is drawn on a centimetre grid. O is (0,0) A is (3,0) B is (3,3) C is (0,3) Write down how many invariant points ther
e are on the perimeter of the square when OABC is translated by the vector [1 3]
1 answer:
Answer:
No invariant point
Step-by-step explanation:
Hello!
When we translate a form, in this case a polygon We must observe the direction of the vector. Since our vector is:
1) Let's apply that translation to this polygon, a square. Check it below:
2) The invariant points are the points that didn't change after the transformation, simply put the points that haven't changed.
Examining the graph, we can see that no, there is not an invariant point, after the translation. There is no common point that belongs to OABC and O'A'B'C' simultaneously. All points moved.
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Answer:
1. Objective function is a maximum at (16,0), Z = 4x+4y = 4(16) + 4(0) = 64
2. Objective function is at a maximum at (5,3), Z=3x+2y=3(5)+2(3)=21
Step-by-step explanation:
1. Maximize: P = 4x +4y
Subject to: 2x + y ≤ 20
x + 2y ≤ 16
x, y ≥ 0
Plot the constraints and the objective function Z, or P=4x+4y)
Push the objective function to the limit permitted by the feasible region to find the maximum.
Answer: Objective function is a maximum at (16,0),
Z = 4x+4y = 4(16) + 4(0) = 64
2. Maximize P = 3x + 2y
Subject to x + y ≤ 8
2x + y ≤ 13
x ≥ 0, y ≥ 0
Plot the constraints and the objective function Z, or P=3x+2y.
Push the objective function to the limit in the increase + direction permitted by the feasible region to find the maximum intersection.
Answer: Objective function is at a maximum at (5,3),
Z = 3x+2y = 3(5)+2(3) = 21
