Question Number 139959 by Engr_Jidda last updated on 02/May/21
$${If}\:{W}\:{varies}\:{jointly}\:{as}\:{L}\:{and}\:{the} \\ $$$${square}\:{of}\:{R}.\:{Find}\:{the}\:{percentage} \\ $$$${change}\:{in}\:{W}\:{if}\:{L}\:{increases}\:{by}\:\mathrm{20\%} \\ $$$${and}\:{R}\:{increases}\:{by}\:\mathrm{50\%}. \\ $$$${If}\:{W}=\mathrm{15}\:{when}\:{H}=\mathrm{3}\:{and}\:{R}=\mathrm{2}\frac{\mathrm{1}}{\mathrm{3}}.\:{find}\: \\ $$$${W}\:{when}\:{H}=\mathrm{1}\:{and}\:{R}=\mathrm{10}. \\ $$$${Find}\:{also}\:{W}\:{interms}\:\:{of}\:{H}\:{and}\:{R}. \\ $$
Answered by TheSupreme last updated on 02/May/21
$${w}={klr}^{\mathrm{2}} \\ $$$${w}'={k}\left(\mathrm{1}.\mathrm{2}{l}\right)\left(\mathrm{1}.\mathrm{5}{r}\right)^{\mathrm{2}} =\mathrm{1}.\mathrm{2}×\mathrm{2}.\mathrm{25}{krl}^{\mathrm{2}} =\mathrm{2}.\mathrm{7}{w} \\ $$$$\frac{{w}'}{{w}}×\mathrm{100}=\mathrm{270\%} \\ $$$${assuming}\:\mathrm{2}\frac{\mathrm{1}}{\mathrm{3}}=\frac{\mathrm{7}}{\mathrm{3}} \\ $$$$\mathrm{15}={k}\mathrm{3}\left(\frac{\mathrm{7}}{\mathrm{3}}\right)^{\mathrm{2}} ={k}\frac{\mathrm{49}}{\mathrm{3}}\rightarrow{k}=\frac{\mathrm{45}}{\mathrm{49}} \\ $$$${W}=\frac{\mathrm{45}}{\mathrm{49}}×\mathrm{1}×\mathrm{10}^{\mathrm{2}} =\frac{\mathrm{4500}}{\mathrm{49}}=\mathrm{91}.\mathrm{8367}... \\ $$
Commented by Engr_Jidda last updated on 02/May/21
$${thank}\:{you}\:{sir} \\ $$