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Category: Arithmetic

A-truck-P-travelling-at-54km-h-passes-a-point-at-10-30-am-while-another-truck-Q-travelling-at-90km-h-passes-through-this-same-point-30-minutes-later-At-what-time-will-truck-Q-overtake-P-

Question Number 201433 by necx122 last updated on 06/Dec/23 $${A}\:{truck},\:{P},\:{travelling}\:{at}\:\mathrm{54}{km}/{h}\:{passes} \\ $$$${a}\:{point}\:{at}\:\mathrm{10}:\mathrm{30}\:{am}\:{while}\:{another}\:{truck}, \\ $$$${Q}\:{travelling}\:{at}\:\mathrm{90}{km}/{h}\:{passes}\:{through} \\ $$$${this}\:{same}\:{point}\:\mathrm{30}\:{minutes}\:{later}.\:{At} \\ $$$${what}\:{time}\:{will}\:{truck}\:{Q}\:{overtake}\:{P}? \\ $$ Answered by Rasheed.Sindhi last updated…

Biggest-prime-factor-of-3-14-3-13-12-

Question Number 201257 by BaliramKumar last updated on 02/Dec/23 $$\mathrm{Biggest}\:\mathrm{prime}\:\mathrm{factor}\:\mathrm{of}\:\left(\mathrm{3}^{\mathrm{14}} \:+\:\mathrm{3}^{\mathrm{13}} \:−\:\mathrm{12}\right)\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated on 02/Dec/23 $$\mathrm{Biggest}\:\mathrm{prime}\:\mathrm{factor}\:\mathrm{of}\:\left(\mathrm{3}^{\mathrm{14}} \:+\:\mathrm{3}^{\mathrm{13}} \:−\:\mathrm{12}\right)\:=\:? \\…

Question-201139

Question Number 201139 by cherokeesay last updated on 30/Nov/23 Commented by Frix last updated on 30/Nov/23 $${x}\approx\mathrm{6395}.\mathrm{12283}\wedge{y}\approx\mathrm{171}.\mathrm{458282} \\ $$$$\mathrm{Exact}\:\mathrm{solution}: \\ $$$${x}=\mathrm{32}\left(\mathrm{8}\left(\mathrm{5}{r}^{\mathrm{2}} +\mathrm{6}{r}+\mathrm{9}\right)\sqrt{{r}−\mathrm{1}}+\mathrm{16}{r}^{\mathrm{2}} +\mathrm{29}{r}+\mathrm{38}\right) \\ $$$${y}=\mathrm{16}\left(\mathrm{4}\left({r}^{\mathrm{2}}…

Question-200972

Question Number 200972 by Mingma last updated on 27/Nov/23 Answered by AST last updated on 27/Nov/23 $${a}^{\mathrm{2}} ={b}^{\mathrm{2}} \left({b}+\mathrm{2}\right);{a}={b}\sqrt{{b}+\mathrm{2}} \\ $$$${b}=\left(\frac{{x}}{{y}}\right)^{\mathrm{2}} −\mathrm{2}\Rightarrow\left({a},{b}\right)=\left(\frac{{x}^{\mathrm{3}} −\mathrm{2}{xy}^{\mathrm{2}} }{{y}^{\mathrm{3}} },\frac{{x}^{\mathrm{2}}…

Question-200627

Question Number 200627 by cherokeesay last updated on 21/Nov/23 Answered by Frix last updated on 21/Nov/23 $$\mathrm{The}\:\mathrm{1}^{\mathrm{st}} \:\mathrm{equation}\:\mathrm{is}\:\mathrm{true}\:\mathrm{for}\:{y}=\frac{\mathrm{1}}{{x}} \\ $$$$\Rightarrow\:{x}=\mathrm{2}\wedge{y}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Commented by cherokeesay…

Question-200657

Question Number 200657 by cherokeesay last updated on 21/Nov/23 Answered by Frix last updated on 21/Nov/23 $$\mathrm{3}\sqrt[{\mathrm{4}}]{\mathrm{27}{x}^{\mathrm{2}} +\mathrm{24}{x}+\frac{\mathrm{28}}{\mathrm{3}}}=\mathrm{4}+\sqrt[{\mathrm{3}}]{\frac{\mathrm{81}{x}}{\mathrm{2}}−\mathrm{1}} \\ $$$$\mathrm{3}\sqrt[{\mathrm{4}}]{\frac{\mathrm{81}{x}^{\mathrm{2}} +\mathrm{72}{x}+\mathrm{28}}{\mathrm{3}}}=\mathrm{4}+\sqrt[{\mathrm{3}}]{\frac{\mathrm{81}{x}−\mathrm{2}}{\mathrm{2}}} \\ $$$${x}=\frac{{t}}{\mathrm{9}} \\ $$$$\mathrm{3}\sqrt[{\mathrm{4}}]{\frac{{t}^{\mathrm{2}}…