Menu Close

Author: Tinku Tara

If-you-had-a-rectangle-with-side-lengths-h-and-b-the-area-is-given-by-A-h-b-hb-If-I-were-to-change-increase-or-decrease-the-value-of-one-or-both-of-the-variables-in-A-how-can-I-write-the-chang

Question Number 3330 by Filup last updated on 11/Dec/15 $$\mathrm{If}\:\mathrm{you}\:\mathrm{had}\:\mathrm{a}\:\mathrm{rectangle}\:\mathrm{with}\:\mathrm{side}\:\mathrm{lengths} \\ $$$${h}\:\mathrm{and}\:{b},\:\mathrm{the}\:\mathrm{area}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}: \\ $$$${A}\left({h},\:{b}\right)={hb} \\ $$$$ \\ $$$$\mathrm{If}\:\mathrm{I}\:\mathrm{were}\:\mathrm{to}\:\mathrm{change}\:\left(\mathrm{increase}\:\mathrm{or}\:\mathrm{decrease}\right) \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{one}\:\mathrm{or}\:\mathrm{both}\:\mathrm{of}\:\mathrm{the}\:\mathrm{variables} \\ $$$$\mathrm{in}\:{A},\:\mathrm{how}\:\mathrm{can}\:\mathrm{I}\:\mathrm{write}\:\mathrm{the}\:\mathrm{change}\:\mathrm{in}\:\mathrm{area}? \\ $$ Answered…

Question-68860

Question Number 68860 by ramirez105 last updated on 16/Sep/19 Commented by kaivan.ahmadi last updated on 16/Sep/19 $${set}\:{M}={x}+\sqrt{{y}^{\mathrm{2}} +\mathrm{1}}\:\:{and}\:\:\:{N}=−{y}+\frac{{xy}}{\:\sqrt{{y}^{\mathrm{2}} +\mathrm{1}}} \\ $$$$\frac{\partial{M}}{\partial{y}}=\frac{{y}}{\:\sqrt{{y}^{\mathrm{2}} +\mathrm{1}}}=\frac{\partial{N}}{\partial{x}} \\ $$$$\begin{cases}{\frac{\partial{u}}{\partial{x}}={x}+\sqrt{{y}^{\mathrm{2}} +\mathrm{1}}}\\{\frac{\partial{u}}{\partial{y}}=−{y}+\frac{{xy}}{\:\sqrt{{y}^{\mathrm{2}}…

Prove-that-among-all-triangle-of-equal-perimeter-equilateral-triangle-has-the-largest-area-

Question Number 3324 by prakash jain last updated on 10/Dec/15 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{among}\:\mathrm{all}\:\mathrm{triangle}\:\mathrm{of}\:\mathrm{equal} \\ $$$$\mathrm{perimeter},\:\mathrm{equilateral}\:\mathrm{triangle}\:\mathrm{has}\:\mathrm{the} \\ $$$$\mathrm{largest}\:\mathrm{area}. \\ $$ Commented by 123456 last updated on 10/Dec/15 $$\mathrm{2}{s}\left({x},{y},{z}\right)={x}+{y}+{z}…

k-0-4-k-k-2-2k-1-2-2k-

Question Number 134393 by liberty last updated on 03/Mar/21 $$\:\underset{\mathrm{k}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{4}^{\mathrm{k}} \:\left(\mathrm{k}!\right)^{\mathrm{2}} }{\left(\mathrm{2k}+\mathrm{1}\right)^{\mathrm{2}} \:\left(\mathrm{2k}\right)!}\:=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Eight-dice-are-tossed-If-the-dice-are-identical-in-appearance-how-many-different-looking-distinguishable-occurrences-are-there-

Question Number 134389 by EDWIN88 last updated on 03/Mar/21 $$\mathrm{Eight}\:\mathrm{dice}\:\mathrm{are}\:\mathrm{tossed}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{dice}\:\mathrm{are}\:\mathrm{identical}\:\mathrm{in} \\ $$$$\mathrm{appearance}\:,\:\mathrm{how}\:\mathrm{many}\:\mathrm{different}−\mathrm{looking}\: \\ $$$$\left(\mathrm{distinguishable}\right)\:\mathrm{occurrences}\:\mathrm{are}\:\mathrm{there}? \\ $$ Answered by bramlexs22 last updated on 03/Mar/21 $$\mathrm{Theorem}\: \\…

Question-68855

Question Number 68855 by ramirez105 last updated on 16/Sep/19 Commented by kaivan.ahmadi last updated on 16/Sep/19 $${set}\:{M}=\mathrm{6}{x}+{y}^{\mathrm{2}} \:\:{and}\:{N}={y}\left(\mathrm{2}{x}−\mathrm{3}{y}\right) \\ $$$$\frac{\partial{M}}{\partial{y}}=\mathrm{2}{y}\:=\frac{\partial{N}}{\partial{x}}\Rightarrow{the}\:{equation}\:{is}\:{exact} \\ $$$$\frac{\partial{u}}{\partial{x}}=\mathrm{6}{x}+{y}^{\mathrm{2}} \:\:\:{and}\:\:\frac{\partial{u}}{\partial{y}}={y}\left(\mathrm{2}{x}−\mathrm{3}{y}\right)=\mathrm{2}{xy}−\mathrm{3}{y}^{\mathrm{2}} \\ $$$$\Rightarrow{u}\left({x},{y}\right)=\int\left(\mathrm{6}{x}+{y}^{\mathrm{2}}…

Given-f-x-0-x-t-4-t-2-t-2-1-dt-Find-minimum-value-of-f-x-

Question Number 134391 by bramlexs22 last updated on 03/Mar/21 $$\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)=\int_{\mathrm{0}} ^{\:{x}} \:\left(\frac{{t}^{\mathrm{4}} −{t}^{\mathrm{2}} }{{t}^{\mathrm{2}} +\mathrm{1}}\right)\:{dt}. \\ $$$$\mathrm{Find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right). \\ $$ Answered by liberty last updated on…