Find a parametrization of the line in which the planes x + y + z = -6 and y + z = -8 intersect.
1 answer:
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Check the picture drawn
Consider the line segment AB,
let M be the midpoint of AB, so AM=MA
erect the perpendicular MT to AB from point M. Pick a point P on MT and join it to the points A and B
The triangles PMA and PMB are congruent from the Side Angle Side congruence postulate:
AM=MA, PM is common and m(PMA)=m(PMB)=90°, as MT is perpendicular to AB
so PA=PB
Consider the line segment AB,
let M be the midpoint of AB, so AM=MA
erect the perpendicular MT to AB from point M. Pick a point P on MT and join it to the points A and B
The triangles PMA and PMB are congruent from the Side Angle Side congruence postulate:
AM=MA, PM is common and m(PMA)=m(PMB)=90°, as MT is perpendicular to AB
so PA=PB
The asymptote for f(x) is y = 0
Notice the asymptote for g(x) is y = -1, which shift f(x) down 1
apply this to f(x)'s rule:
Notice the graph of f(x) is shifted right 2 units...this horizontal movement must be applied to the x in f(x)'s rule:
The piece-wise function is defined as follows:
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.
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A piece-wise function is a function that has multiple definitions, depending on the input.
In this graph, for x at least 0 and less than 3, the parabolic curve passes through (0,0), (1,1), (2,4) and has an open interval at (3,9), hence the definition is:
For x greater than 3 and at most 6, it is a line going through (3,9) and (6,4), hence:
Goes through (3,9), hence:
b = 14.
So
For x between 6 and 10, it is a line going through (6,4) and (10,10), hence:
Then:
When x = 10, f(x) = 10, hence:
10 = 15 + b
b = -5.
Hence:
More can be learned about piece-wise functions at brainly.com/question/24734454
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