Menu Close

Category: Others

f-length-of-a-rectangle-is-reduced-by-5-umits-and-its-breadth-is-increasesd-3-units-then-area-of-rectangle-is-reduced-by-8-sq-units-if-lenghth-is-reduced-3-units-and-breadth-is-increased-by-2-units

Question Number 26528 by bbbbbb last updated on 26/Dec/17 $${f}\:{length}\:\:{of}\:{a}\:{rectangle}\:{is}\:{reduced}\:{by}\:\mathrm{5}\: \\ $$$${umits}\:{and}\:{its}\:{breadth}\:{is}\:{increasesd} \\ $$$$\mathrm{3}\:{units}\:{then}\:{area}\:{of}\:{rectangle}\:{is}\:{reduced} \\ $$$${by}\:\mathrm{8}\:{sq}\:{units}\:{if}\:{lenghth}\:{is}\:{reduced} \\ $$$$\mathrm{3}\:{units}\:{and}\:{breadth}\:{is}\:{increased}\:{by}\: \\ $$$$\mathrm{2}\:{units}\:{then}\:{area}\:{of}\:{rectangle} \\ $$$${will}\:{increased}\:{by}\:\mathrm{67}\:{sq}\:{units}\:.\: \\ $$$${then}\:{find}\:{length}\:{and}\:{breadth}\:{of}\:{rectangle} \\…

x-1-x-2-4x-5-2-dx-

Question Number 92055 by 675480065 last updated on 04/May/20 $$\int\left(\frac{\mathrm{x}+\mathrm{1}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{4x}+\mathrm{5}\right)^{\mathrm{2}} }\right)\mathrm{dx} \\ $$ Commented by Prithwish Sen 1 last updated on 04/May/20 $$\int\frac{\mathrm{x}+\mathrm{1}}{\left(\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}}…

let-n-be-a-fixed-positive-integer-How-many-ways-are-there-to-write-n-as-a-sum-of-positive-integers-n-a-1-a-2-a-k-with-k-arbitary-positive-integer-and-a-1-a-2-a-k-a-1-1-for-example-wi

Question Number 26513 by gunawan last updated on 26/Dec/17 $$\mathrm{let}\:{n}\:\mathrm{be}\:\mathrm{a}\:\mathrm{fixed}\:\mathrm{positive}\:\mathrm{integer}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{are}\:\mathrm{there}\:\mathrm{to}\:\mathrm{write}\:{n}\:\mathrm{as}\:\mathrm{a}\:\mathrm{sum}\:\mathrm{of} \\ $$$$\mathrm{positive}\:\mathrm{integers},\: \\ $$$${n}={a}_{\mathrm{1}} +{a}_{\mathrm{2}} +…+{a}_{{k}} \\ $$$$\mathrm{with}\:{k}\:\mathrm{arbitary}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{and}\:{a}_{\mathrm{1}} \leqslant{a}_{\mathrm{2}} …\leqslant{a}_{{k}} \leqslant{a}_{\mathrm{1}} +\mathrm{1}.\:\mathrm{for}\:\mathrm{example} \\ $$$$\mathrm{with}\:{n}=\mathrm{4},\:\mathrm{there}\:\mathrm{are}\:\mathrm{four}\:\mathrm{ways}\::\:\mathrm{4},\:\mathrm{2}+\mathrm{2},\:\mathrm{1}+\mathrm{1}+\mathrm{2},\mathrm{1}+\mathrm{1}+\mathrm{1}+\mathrm{1} \\…

x-1-x-2-x-1-dx-

Question Number 92025 by 675480065 last updated on 04/May/20 $$\int\left(\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}^{\mathrm{2}} −\mathrm{x}−\mathrm{1}}\right)\mathrm{dx} \\ $$ Commented by mathmax by abdo last updated on 04/May/20 $${I}\:=\int\:\frac{{x}−\mathrm{1}}{{x}^{\mathrm{2}} −{x}−\mathrm{1}}{dx}\:\Rightarrow\:{I}\:=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{2}{x}−\mathrm{1}−\mathrm{1}}{{x}^{\mathrm{2}} −{x}−\mathrm{1}}{dx}…