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elena-14-01-66 [18.8K]

3 years ago

13

A line segment has (x1, y1) as one endpoint and (xm, ym) as its midpoint. Find the other endpoint (x2, y2) of the line segment i

n terms of x1, y1, xm, and ym.

1 answer:

N76 [4]3 years ago

5 0

Midpoint (xm, ym) = ((x1 + x2)/2, (y1 + y2)/2)
xm = (x1 + x2)/2
2xm = x1 + x2
x2 = 2xm - x1
y2 = 2ym - y1

Therefore, (x2, y2) = (2xm - x1, 2ym - y1)

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Step-by-step explanation:

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3 years ago

Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 4 at x = −3 and a local minimum value of 0 at

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The formula is f(x) = a x ^ 3 + b x ^ 2 + c x + d
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f(- 3) = 3 ==> - 27a + 9b - 3c + d = 3
f '(- 3) = 0 (being a most extreme) ==> 27a - 6b + c = 0.
f(1) = 0 ==> a + b + c + d = 0
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Along these lines, we have the four conditions
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a + b + c + d = 0
27a - 6b + c = 0
3a + 2b + c = 0
Subtracting the last two conditions yields 24a - 8b = 0 ==> b = 3a.
Along these lines, the last condition yields 3a + 6a + c = 0 ==> c = - 9a.
Consequently, we have from the initial two conditions:
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Answer:

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(3)

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