A point lies in quadrant 2. If it is rotated 180 degrees counterclockwise, which quadrant will the point come to rest?
1 answer:
A point (a, b) in the second Quadrant, is any point where a is negative and b is positive.
For example (-3, 5), (-189, 14) etc are all points in the 2.Quadrant
Rotating a point P(x, y) in the second Quadrant 180° counterclockwise, means rotating 180° counterclockwise about the origin, which maps point P to P'(-a, -b) in the fourth Quadrant.
For example (-3, 5), (-189, 14) etc are all points in the 2.Quadrant
Rotating a point P(x, y) in the second Quadrant 180° counterclockwise, means rotating 180° counterclockwise about the origin, which maps point P to P'(-a, -b) in the fourth Quadrant.
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Answer:
24 trees per acre
Step-by-step explanation:
Let x be the optimal tree density per acre and y be the number of bushels yield per tree
Since for each unit change of x from 28 trees/acre, we have 2 unit change of y from 40 bushels per tree in the reversed direction
Change of x from 28 is x - 28
Change of y from 40 is y - 40
Therefore we have y - 40 = -2(x - 28) or y = 40 - 2(x - 28) = -2x + 96
The total bushels per acre should be y bushels/tree * x tree/acre. We want to optimize this. Substitute the above equation in for y and we have
To find the maximum value of this, we can take the first derivative and set it to 0
We know this is a maxima because . So T is maximum when x = 24 trees per acre