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Category: Mensuration

Question-120790

Question Number 120790 by peter frank last updated on 02/Nov/20 Commented by TANMAY PANACEA last updated on 02/Nov/20 $${eqn}\:{big}\:{circle}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} ={R}^{\mathrm{2}} \:\:{and}\:{area}\:\pi{R}^{\mathrm{2}} \\ $$$${small}\:{circle}\:{centre}\left(−{a},\mathrm{0}\right)\:{radius}\:{r} \\…

Prove-that-P-n-z-a-0-z-n-a-1-z-n-1-a-n-1-z-a-n-at-least-have-one-value-of-zero-

Question Number 55058 by gunawan last updated on 16/Feb/19 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{P}_{{n}} \left({z}\right)={a}_{\mathrm{0}} {z}^{{n}} +{a}_{\mathrm{1}} {z}^{{n}−\mathrm{1}} +…+{a}_{{n}−\mathrm{1}} {z}+{a}_{{n}} \\ $$$$\mathrm{at}\:\mathrm{least}\:\mathrm{have}\:\mathrm{one}\:\:\mathrm{value}\:\mathrm{of}\:\mathrm{zero} \\ $$ Terms of Service…

Question-55055

Question Number 55055 by peter frank last updated on 16/Feb/19 Answered by mr W last updated on 16/Feb/19 $${T}_{{n}} =\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)=\frac{\left({n}−\mathrm{1}\right)}{{n}}×\frac{\left({n}+\mathrm{1}\right)}{{n}}×\frac{\left({n}+\mathrm{1}\right)}{{n}} \\ $$$${T}_{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{3}}{\mathrm{2}}×\frac{\mathrm{3}}{\mathrm{2}} \\…

Question-186030

Question Number 186030 by Rupesh123 last updated on 31/Jan/23 Answered by ajfour last updated on 31/Jan/23 $${x}^{\mathrm{2}} +{y}^{\mathrm{2}} ={d}^{\mathrm{2}} \\ $$$$\left({a}−{x}\right){y}={d}^{\mathrm{2}} \\ $$$$\left({b}−{y}\right){x}={d}^{\mathrm{2}} \\ $$$${d}\left(\frac{{x}}{{y}}+\mathrm{1}+\frac{{y}}{{x}}\right)={c}…