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expeople1 [14]
2 years ago
5

How would i rewrite this equation so it is not in fraction form-5/(1-cos(-x))

Mathematics
1 answer:
Lynna [10]2 years ago
8 0

\bf -\cfrac{5}{1-cos(-x)}\implies -\cfrac{5}{\underset{\textit{symmetry identity}}{1-cos(x)}}\impliedby \begin{array}{llll} \textit{let's multiply top/bottom}\\ \textit{by the conjugate 1+cos(x)} \end{array} \\\\\\ \cfrac{-5}{1-cos(x)}\cdot \cfrac{1+cos(x)}{1+cos(x)}\implies \cfrac{-5(1+cos(x))}{\underset{\textit{difference of squares}}{[1-cos(x)][1+cos(x)]}} \\\\\\

\bf \cfrac{-5[1+cos(x)]}{1^2-cos^2(x)}\implies \cfrac{-5-5cos(x)}{\underset{\textit{pythagorean identity}}{1-cos^2(x)}}\implies \cfrac{-5-5cos(x)}{sin^2(x)} \\\\\\ \cfrac{-5}{sin^2(x)}-\cfrac{5cos(x)}{sin^2(x)}\implies -5\cdot \cfrac{1}{sin^2(x)}-5\cdot \cfrac{1}{sin(x)}\cdot \cfrac{cos(x)}{sin(x)} \\\\\\ -5\cdot csc^2(x)-5\cdot csc(x)\cdot cot(x)\implies \boxed{-5csc^2(x)-5csc(x)cot(x)}

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Answer and explanation:

Given : Strands Copper wire from a manufacturer are analyzed forstrenghth and conductivity. The Results from 100 strands are as follows :

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Low conductivity                         15                3

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P(A\cup B)=0.18+0.11-0.03

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c) Consider the event that a strand low conductivity and the event that the strand has a low strength. Are these tow events mutually exclusive?

Since the events the stand has low conductivity and the stand has low strength  are not mutually exclusive, since there exists some cases in which both the  events coincide. i.e. Intersection of both the events exists with probability 0.03.

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