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Question-55561




Question Number 55561 by otchereabdullai@gmail.com last updated on 26/Feb/19
Commented by otchereabdullai@gmail.com last updated on 26/Feb/19
prof W please am learning this question  solved for me on the 21st but i dont   understand this part : if n=16:α_n =−5<0  and if n=18:α_n =355>180  and how you got the n=17 .   please help me prof W
$${prof}\:{W}\:{please}\:{am}\:{learning}\:{this}\:{question} \\ $$$${solved}\:{for}\:{me}\:{on}\:{the}\:\mathrm{21}{st}\:{but}\:{i}\:{dont}\: \\ $$$${understand}\:{this}\:{part}\::\:{if}\:{n}=\mathrm{16}:\alpha_{{n}} =−\mathrm{5}<\mathrm{0} \\ $$$${and}\:{if}\:{n}=\mathrm{18}:\alpha_{{n}} =\mathrm{355}>\mathrm{180} \\ $$$${and}\:{how}\:{you}\:{got}\:{the}\:{n}=\mathrm{17}\:.\: \\ $$$${please}\:{help}\:{me}\:{prof}\:{W} \\ $$
Commented by mr W last updated on 27/Feb/19
we have got  α_n =(n−2)×180°−2525°  we want to find how large n is such  that 0<α_n <180°.  if we put (n−2)×180°−2525°=0, we  get n≈16.03. now we try with n=16,  we get α_n =(16−2)×180−2525=−5°,  which is not ok, i.e. n≠16.  then we try with n=17, we get  α_n =(17−2)×180−2525=175°, this is  ok. but is n=17 the only one solution?  let′s try with n=18, and we get  α_n =(18−2)×180−2525=355°, this is  not ok. that means n=17 is the only  one solution.
$${we}\:{have}\:{got} \\ $$$$\alpha_{{n}} =\left({n}−\mathrm{2}\right)×\mathrm{180}°−\mathrm{2525}° \\ $$$${we}\:{want}\:{to}\:{find}\:{how}\:{large}\:{n}\:{is}\:{such} \\ $$$${that}\:\mathrm{0}<\alpha_{{n}} <\mathrm{180}°. \\ $$$${if}\:{we}\:{put}\:\left({n}−\mathrm{2}\right)×\mathrm{180}°−\mathrm{2525}°=\mathrm{0},\:{we} \\ $$$${get}\:{n}\approx\mathrm{16}.\mathrm{03}.\:{now}\:{we}\:{try}\:{with}\:{n}=\mathrm{16}, \\ $$$${we}\:{get}\:\alpha_{{n}} =\left(\mathrm{16}−\mathrm{2}\right)×\mathrm{180}−\mathrm{2525}=−\mathrm{5}°, \\ $$$${which}\:{is}\:{not}\:{ok},\:{i}.{e}.\:{n}\neq\mathrm{16}. \\ $$$${then}\:{we}\:{try}\:{with}\:{n}=\mathrm{17},\:{we}\:{get} \\ $$$$\alpha_{{n}} =\left(\mathrm{17}−\mathrm{2}\right)×\mathrm{180}−\mathrm{2525}=\mathrm{175}°,\:{this}\:{is} \\ $$$${ok}.\:{but}\:{is}\:{n}=\mathrm{17}\:{the}\:{only}\:{one}\:{solution}? \\ $$$${let}'{s}\:{try}\:{with}\:{n}=\mathrm{18},\:{and}\:{we}\:{get} \\ $$$$\alpha_{{n}} =\left(\mathrm{18}−\mathrm{2}\right)×\mathrm{180}−\mathrm{2525}=\mathrm{355}°,\:{this}\:{is} \\ $$$${not}\:{ok}.\:{that}\:{means}\:{n}=\mathrm{17}\:{is}\:{the}\:{only} \\ $$$${one}\:{solution}. \\ $$
Commented by otchereabdullai@gmail.com last updated on 26/Feb/19
wow! wow! In fact you are an ideal  prof!
$${wow}!\:{wow}!\:{In}\:{fact}\:{you}\:{are}\:{an}\:{ideal} \\ $$$${prof}! \\ $$$$ \\ $$

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