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If-function-f-x-log-x-2-log-1-3-log-4-x-exist-find-the-domain-of-f-

Question Number 165805 by ZiYangLee last updated on 08/Feb/22 $$\mathrm{If}\:\:\mathrm{function}\:{f}\left({x}\right)=\mathrm{log}_{\frac{{x}}{\mathrm{2}}} \mathrm{log}_{\frac{\mathrm{1}}{\mathrm{3}}} \mathrm{log}\:_{\mathrm{4}} \:{x}\:\mathrm{exist}, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{of}\:{f}\:. \\ $$ Answered by ZiYangLee last updated on 08/Feb/22 $$\mathrm{Ans}:\:\left(\mathrm{1},\mathrm{2}\right)\cup\left(\mathrm{2},\mathrm{4}\right)…

given-the-sum-of-the-first-n-terms-of-an-AP-is-x-2-the-sum-of-the-first-2n-terms-of-the-same-AP-is-x-2-x-show-that-the-sum-of-the-first-4n-terms-is-4x-2-8x-4-

Question Number 34734 by mondodotto@gmail.com last updated on 10/May/18 $$\boldsymbol{\mathrm{given}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{first}}\:\boldsymbol{\mathrm{n}}\:\boldsymbol{\mathrm{terms}}\: \\ $$$$\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{an}}\:\boldsymbol{\mathrm{AP}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{{x}}^{\mathrm{2}} \:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}} \\ $$$$\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{first}}\:\mathrm{2}\boldsymbol{\mathrm{n}}\:\boldsymbol{\mathrm{terms}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{same}}\:\boldsymbol{\mathrm{AP}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{x}} \\ $$$$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{first}}\:\mathrm{4}\boldsymbol{\mathrm{n}}\:\boldsymbol{\mathrm{terms}}\:\mathrm{is} \\ $$$$\mathrm{4}\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{8}\boldsymbol{{x}}+\mathrm{4} \\ $$ Commented by…

use-bernoulli-methods-sec-2-y-dy-dx-xtany-x-3-

Question Number 34724 by mondodotto@gmail.com last updated on 10/May/18 $$\boldsymbol{\mathrm{use}}\:\boldsymbol{\mathrm{bernoulli}}\:\boldsymbol{\mathrm{methods}} \\ $$$$\boldsymbol{\mathrm{sec}}^{\mathrm{2}} \boldsymbol{{y}}\frac{\boldsymbol{{dy}}}{\boldsymbol{{dx}}}+\boldsymbol{{x}\mathrm{tan}{y}}=\boldsymbol{{x}}^{\mathrm{3}} \\ $$ Commented by mondodotto@gmail.com last updated on 10/May/18 $$\mathrm{please}\:\mathrm{someone}\:\mathrm{solve}\:\mathrm{this}\: \\ $$…

t-e-2t-dt-

Question Number 165794 by SANOGO last updated on 08/Feb/22 $$\int\frac{{t}}{{e}^{−\mathrm{2}{t}} }{dt} \\ $$ Answered by TheSupreme last updated on 08/Feb/22 $$\int{te}^{\mathrm{2}{t}} =\frac{{te}^{{t}} }{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{4}}{e}^{\mathrm{2}{t}} +{c} \\…

Question-165791

Question Number 165791 by aurpeyz last updated on 08/Feb/22 Answered by ghchoi0707 last updated on 08/Feb/22 $${m}=\mathrm{Mass}\:\mathrm{of}\:\mathrm{roller}\:\mathrm{coaster}\:\left(\mathrm{any}\:\mathrm{unit}\right) \\ $$$${g}=\mathrm{Acceleration}\:\mathrm{by}\:\mathrm{Gravity}\fallingdotseq\mathrm{9}.\mathrm{8m}/\mathrm{s}^{\mathrm{2}} \\ $$$${z}=\mathrm{Position}\:\mathrm{of}\:\mathrm{roller}\:\mathrm{coaster}\:\left(\mathrm{m}\right) \\ $$$${v}_{{i}} /{v}_{{f}} =\mathrm{Initial}/\mathrm{Final}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{roller}\:\mathrm{coaster}\:\left(\mathrm{m}/\mathrm{s}\right)…

How-many-numbers-greater-than-350-can-be-formed-from-1-2-3-4-and-5-

Question Number 34718 by tawa tawa last updated on 10/May/18 $$\mathrm{How}\:\mathrm{many}\:\mathrm{numbers}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{350}\:\mathrm{can}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{from}\:\:\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4}\:\mathrm{and}\:\mathrm{5} \\ $$ Answered by Rasheed.Sindhi last updated on 10/May/18 $$\mathrm{1dd}<\mathrm{350} \\ $$$$\mathrm{2dd}<\mathrm{350} \\ $$$$\mathrm{3dd}:\mathrm{355}\:\left(\mathrm{One}\:\mathrm{number}\right)…

Mr-and-Mr-young-borrowed-Z-amount-of-money-from-a-bank-at-a-daily-interest-rate-r-The-youngs-make-the-same-micro-payment-of-D-amount-to-the-bank-each-day-Set-up-a-differential-equation-for-amount-x

Question Number 165780 by MWSuSon last updated on 08/Feb/22 $$\mathrm{Mr}\:\mathrm{and}\:\mathrm{Mr}\:\mathrm{young}\:\mathrm{borrowed}\:\mathrm{Z}\:\mathrm{amount}\:\mathrm{of}\:\mathrm{money}\:\mathrm{from} \\ $$$$\mathrm{a}\:\mathrm{bank}\:\mathrm{at}\:\mathrm{a}\:\mathrm{daily}\:\mathrm{interest}\:\mathrm{rate}\:\mathrm{r}.\:\mathrm{The}\:\mathrm{youngs}\:\mathrm{make}\:\mathrm{the} \\ $$$$\mathrm{same}\:\mathrm{micro}\:\mathrm{payment}\:\mathrm{of}\:\mathrm{D}\:\mathrm{amount}\:\mathrm{to}\:\mathrm{the}\:\mathrm{bank}\:\mathrm{each}\:\mathrm{day}. \\ $$$$\:\mathrm{Set}\:\mathrm{up}\:\mathrm{a}\:\mathrm{differential}\:\mathrm{equation}\:\mathrm{for}\:\mathrm{amount}\:\mathrm{x}\:\mathrm{owed} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{bank}\:\mathrm{at}\:\mathrm{the}\:\mathrm{end}\:\mathrm{of}\:\mathrm{the}\:\mathrm{each}\:\mathrm{day}\:\mathrm{after}\:\mathrm{the}\:\mathrm{loan} \\ $$$$\mathrm{closing}. \\ $$ Commented by MWSuSon…

Solve-the-equation-x-1-x-1-x-1-x-1-1-

Question Number 165776 by ZiYangLee last updated on 08/Feb/22 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\:\:\:\sqrt{\frac{\sqrt{{x}}+\mathrm{1}^{} }{\:\sqrt{{x}}−\mathrm{1}\:}}−\sqrt{\frac{\sqrt{{x}}−\mathrm{1}^{} }{\:\sqrt{{x}}+\mathrm{1}\:}}\:=\:\mathrm{1} \\ $$ Answered by Rasheed.Sindhi last updated on 08/Feb/22 $$\:\:\:\sqrt{\frac{\sqrt{{x}}+\mathrm{1}^{} }{\:\sqrt{{x}}−\mathrm{1}\:}}−\sqrt{\frac{\sqrt{{x}}−\mathrm{1}^{}…

The-sum-of-first-the-n-terms-of-a-series-a-n-is-given-by-S-n-3n-2-n-find-k-10-20-a-k-A-910-B-913-C-968-D-1256-

Question Number 165777 by ZiYangLee last updated on 08/Feb/22 $$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{first}\:\mathrm{the}\:{n}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{series} \\ $$$$\left\{{a}_{{n}} \right\}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:{S}_{{n}} =\mathrm{3}{n}^{\mathrm{2}} +{n},\:\mathrm{find}\:\underset{{k}=\mathrm{10}} {\overset{\mathrm{20}} {\sum}}{a}_{{k}} \:. \\ $$$$\left.\mathrm{A}\right)\:\mathrm{910} \\ $$$$\left.\mathrm{B}\right)\:\mathrm{913} \\ $$$$\left.\mathrm{C}\right)\:\mathrm{968} \\…