2 years ago

USING the Midpoint Formula , POINT A is at (-3,-5) and point M is at (-0.5,0). what are the coordinates of point B

1 answer:

7 0

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-5})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x-3}{2}~~,~~\cfrac{y-5}{2} \right)~~=~~\stackrel{\stackrel{Midpoint}{M}}{(-0.5~,~0)}\implies \begin{cases} \cfrac{x-3}{2}=-0.5\\[1em] x-3=-1\\ \boxed{x= 2}\\ \cline{1-1} \cfrac{y-5}{2}=0\\[1em] y-5=0\\ \boxed{y=5} \end{cases}$

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Suppose p" must approximate p with relative error at most 10-3 . Find the largest interval in which p* must lie for each value o

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Answer:

$[p-|p|*10^{-3} \, , \, p+|p|* 10^-3]$

Step-by-step explanation

The relative error is the absolute error divided by the absolute value of p. for an approximation p*, the relative error is

r = |p*-p|/|p|

we want r to be at most 10⁻³, thus

|p*-p|/|p| ≤ 10⁻³

|p*-p| ≤ |p|* 10⁻³

therefore, p*-p should lie in the interval [ - |p| * 10⁻³ , |p| * 10⁻³ ], and as a consecuence, p* should be in the interval [p - |p| * 10⁻³ , p + |p| * 10⁻³ ]

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Helga [31]

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