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Category: Arithmetic

A-car-starts-from-rest-and-uniformly-accelerates-for-1-km-travels-with-uniform-velocity-for-98-km-and-brakes-and-stop-after-travelling-another-1-km-Consider-the-above-experiment-being-done-on-2-diff

Question Number 3463 by prakash jain last updated on 13/Dec/15 $$\mathrm{A}\:\mathrm{car}\:\mathrm{starts}\:\mathrm{from}\:\mathrm{rest}\:\mathrm{and}\:\mathrm{uniformly} \\ $$$$\mathrm{accelerates}\:\mathrm{for}\:\mathrm{1}\:\mathrm{km},\:\mathrm{travels}\:\mathrm{with}\:\mathrm{uniform} \\ $$$$\mathrm{velocity}\:\mathrm{for}\:\mathrm{98}\:\mathrm{km}\:\mathrm{and}\:\mathrm{brakes}\:\mathrm{and}\:\mathrm{stop} \\ $$$$\mathrm{after}\:\mathrm{travelling}\:\mathrm{another}\:\mathrm{1}\:\mathrm{km}. \\ $$$$\mathrm{Consider}\:\mathrm{the}\:\mathrm{above}\:\mathrm{experiment}\:\mathrm{being}\:\mathrm{done} \\ $$$$\mathrm{on}\:\mathrm{2}\:\mathrm{different}\:\mathrm{roads}\:\mathrm{1st}\:\mathrm{roads}\:\mathrm{has}\:\mathrm{higher} \\ $$$$\mathrm{coefficient}\:\mathrm{of}\:\mathrm{friction}\:\mathrm{for}\:\mathrm{car}\:\mathrm{for}\:\mathrm{all}\:\mathrm{types} \\ $$$$\mathrm{than}\:\mathrm{2nd}\:\mathrm{road}.…

Can-someone-show-me-how-i-x-a-v-k-0-v-v-k-x-v-k-a-k-ii-Does-k-0-v-v-k-x-v-k-a-k-k-0-v-v-k-x-k-a-v-k-

Question Number 3411 by Filup last updated on 13/Dec/15 $$\mathrm{Can}\:\mathrm{someone}\:\mathrm{show}\:\mathrm{me}\:\mathrm{how}: \\ $$$$\left({i}\right)\:\:\:\:\left({x}+{a}\right)^{{v}} =\underset{{k}=\mathrm{0}} {\overset{{v}} {\sum}}\begin{pmatrix}{{v}}\\{{k}}\end{pmatrix}\:{x}^{{v}−{k}} {a}^{{k}} \\ $$$$\left({ii}\right)\:\:\mathrm{Does}: \\ $$$$\:\:\:\:\:\underset{{k}=\mathrm{0}} {\overset{{v}} {\sum}}\begin{pmatrix}{{v}}\\{{k}}\end{pmatrix}\:{x}^{{v}−{k}} {a}^{{k}} =\underset{{k}=\mathrm{0}} {\overset{{v}}…

let-S-i-a-n-x-i-prove-or-disprove-that-d-dx-i-a-n-x-i-i-a-n-d-dx-x-i-i-a-n-x-i-

Question Number 3385 by Filup last updated on 12/Dec/15 $$\mathrm{let}: \\ $$$$\:\:\:\:\:\:\:\:{S}=\underset{{i}={a}} {\overset{{n}} {\sum}}{x}_{{i}} \\ $$$$\mathrm{prove}\:\mathrm{or}\:\mathrm{disprove}\:\mathrm{that}: \\ $$$$\:\:\:\:\:\:\frac{{d}}{{dx}}\left(\underset{{i}={a}} {\overset{{n}} {\sum}}{x}_{{i}} \right)=\underset{{i}={a}} {\overset{{n}} {\sum}}\left(\frac{{d}}{{dx}}\left\{{x}_{{i}} \right\}\right) \\…

Question-68775

Question Number 68775 by rajesh4661kumar@gmail.com last updated on 15/Sep/19 Answered by $@ty@m123 last updated on 15/Sep/19 $${Let}\:{a}\:{be}\:\:{the}\:{first}\:{term}\:{and}\:{d}\:{be}\:{the} \\ $$$${common}\:{difference}\:{of}\:{AP}. \\ $$$${a}+\left({p}−\mathrm{1}\right){d}={A}\:…\left(\mathrm{1}\right) \\ $$$${a}+\left({q}−\mathrm{1}\right){d}={AR}\:\:….\left(\mathrm{2}\right) \\ $$$${a}+\left({r}−\mathrm{1}\right){d}={AR}^{\mathrm{2}}…