Question Number 55526 by alex26 last updated on 26/Feb/19 $$\mathrm{If}\:\underset{−\mathrm{1}} {\overset{\mathrm{4}} {\int}}\:{f}\left({x}\right)\:{dx}\:=\:\mathrm{4}\:\mathrm{and}\:\underset{\mathrm{2}} {\overset{\mathrm{4}} {\int}}\:\left(\mathrm{3}−{f}\left({x}\right)\right){dx}=\mathrm{7}, \\ $$$$\mathrm{then}\:\:\underset{\:\mathrm{2}} {\overset{−\mathrm{1}} {\int}}\:{f}\left({x}\right)\:{dx}\:= \\ $$ Commented by mr W last…
Question Number 55089 by eso last updated on 17/Feb/19 $$\:\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\:\frac{\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}/\mathrm{2}} }\:{dx}\:= \\ $$ Commented by maxmathsup by imad last updated on 17/Feb/19…
Question Number 54970 by Tip Top last updated on 15/Feb/19 $$\mathrm{If}\:\:\:{a}\:\mathrm{cos}\:{A}={b}\:\mathrm{cos}\:{B}\:\:\mathrm{in}\:\mathrm{a}\:\bigtriangleup{ABC},\: \\ $$$$\mathrm{then}\:\angle{C}\:\:\mathrm{is} \\ $$ Answered by $@ty@m last updated on 15/Feb/19 $${Given} \\ $$$$\frac{{a}}{{b}}=\frac{\mathrm{cos}\:{B}}{\mathrm{cos}\:{A}}\:\:…\left(\mathrm{1}\right)…
Question Number 54541 by Tip Top last updated on 05/Feb/19 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:{x}\:\mathrm{between}\:\:\:\mathrm{0}\:\:\mathrm{and}\:\:\:\mathrm{2}\pi\: \\ $$$$\mathrm{which}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\mathrm{sin}\:{x}\:\sqrt{\mathrm{8}\:\mathrm{cos}\:^{\mathrm{2}} {x}}\:=\:\mathrm{1}\:\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP}\: \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{common}\:\mathrm{difference}. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated…
Question Number 54468 by soksan last updated on 04/Feb/19 $$\mathrm{First}\:\mathrm{three}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{given} \\ $$$$\mathrm{by}\:\:{a}_{\mathrm{1}} =\mathrm{1},\:{a}_{{n}} ={a}_{{n}−\mathrm{1}} +\mathrm{2}{a}_{{n}−\mathrm{2}} \:\mathrm{are}\:\mathrm{in} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 54422 by gunawan last updated on 03/Feb/19 $$\mathrm{The}\:\mathrm{median}\:{AD}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:{ABC} \\ $$$$\mathrm{is}\:\mathrm{bisected}\:\mathrm{at}\:{E},\:{BE}\:\mathrm{meets}\:{AC}\:\mathrm{in}\:{F}, \\ $$$$\mathrm{then}\:{AF}\::\:{AC}\:= \\ $$ Commented by ajfour last updated on 03/Feb/19 Commented by…
Question Number 54421 by gunawan last updated on 03/Feb/19 $$\mathrm{If}\:\mathrm{the}\:\mathrm{vector}\:\boldsymbol{\mathrm{c}},\:\boldsymbol{\mathrm{a}}={x}\boldsymbol{\mathrm{i}}+{y}\boldsymbol{\mathrm{j}}+{z}\boldsymbol{\mathrm{k}}\:\mathrm{and}\:\boldsymbol{\mathrm{b}}=\boldsymbol{\mathrm{j}} \\ $$$$\mathrm{are}\:\mathrm{such}\:\mathrm{that}\:\boldsymbol{\mathrm{a}},\:\boldsymbol{\mathrm{c}}\:\mathrm{and}\:\boldsymbol{\mathrm{b}}\:\mathrm{form}\:\mathrm{a}\:\mathrm{right} \\ $$$$\mathrm{handed}\:\mathrm{system},\:\mathrm{then}\:\boldsymbol{\mathrm{c}}\:\mathrm{is} \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 04/Feb/19 $$\left.{p}\left.{ls}\:{carify}\:{i}\right)\left({a}\:,{b},{c}\:\right)\:\:\:{ii}\right)\left({a},{c},{b}\right)\:{which}\:{one}\:{form} \\…
Question Number 54420 by gunawan last updated on 03/Feb/19 $$\mathrm{Let}\:\boldsymbol{\mathrm{a}}=\boldsymbol{\mathrm{i}}+\boldsymbol{\mathrm{j}}\:\mathrm{and}\:\boldsymbol{\mathrm{b}}=\mathrm{2}\boldsymbol{\mathrm{i}}−\boldsymbol{\mathrm{k}},\:\mathrm{the}\:\mathrm{point}\:\mathrm{of} \\ $$$$\mathrm{intersection}\:\mathrm{of}\:\mathrm{the}\:\mathrm{lines}\:\boldsymbol{\mathrm{r}}×\boldsymbol{\mathrm{a}}=\boldsymbol{\mathrm{b}}×\boldsymbol{\mathrm{a}} \\ $$$$\mathrm{and}\:\boldsymbol{\mathrm{r}}×\boldsymbol{\mathrm{b}}=\boldsymbol{\mathrm{a}}×\boldsymbol{\mathrm{b}}\:\mathrm{is} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 03/Feb/19 $${r}={ix}+{jy}+{kz} \\…
Question Number 54419 by gunawan last updated on 03/Feb/19 $$\mathrm{If}\:\boldsymbol{\mathrm{a}}=\boldsymbol{\mathrm{i}}+\boldsymbol{\mathrm{j}}−\boldsymbol{\mathrm{k}},\:\boldsymbol{\mathrm{b}}=\boldsymbol{\mathrm{i}}−\boldsymbol{\mathrm{j}}+\boldsymbol{\mathrm{k}}\:\mathrm{and}\:\boldsymbol{\mathrm{c}}\:\mathrm{is}\:\mathrm{a}\:\mathrm{unit} \\ $$$$\mathrm{vector}\:\bot\:\mathrm{to}\:\mathrm{the}\:\mathrm{vector}\:\boldsymbol{\mathrm{a}}\:\mathrm{and}\:\mathrm{coplanar} \\ $$$$\mathrm{with}\:\boldsymbol{\mathrm{a}}\:\mathrm{and}\:\boldsymbol{\mathrm{b}},\:\mathrm{then}\:\mathrm{a}\:\mathrm{unit}\:\mathrm{vector}\:\boldsymbol{\mathrm{d}}\:\bot\:\mathrm{to} \\ $$$$\mathrm{both}\:\boldsymbol{\mathrm{a}}\:\mathrm{and}\:\boldsymbol{\mathrm{c}}\:\mathrm{is} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 03/Feb/19…
Question Number 54418 by gunawan last updated on 03/Feb/19 $$\mathrm{The}\:\mathrm{projection}\:\mathrm{of}\:\mathrm{the}\:\mathrm{vector}\:\boldsymbol{\mathrm{a}}=\mathrm{4}\boldsymbol{\mathrm{i}}−\mathrm{3}\boldsymbol{\mathrm{j}}+\mathrm{2}\boldsymbol{\mathrm{k}} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{axis}\:\mathrm{making}\:\mathrm{equal}\:\mathrm{acute}\:\mathrm{angles} \\ $$$$\mathrm{with}\:\mathrm{the}\:\mathrm{coordinate}\:\mathrm{axes}\:\mathrm{is} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 03/Feb/19 $$\boldsymbol{{a}}=\mathrm{4}\boldsymbol{{i}}−\mathrm{3}\boldsymbol{{j}}+\mathrm{2}\boldsymbol{{k}}\:\:\:{so}\:\:\mid\boldsymbol{{a}}\mid=\sqrt{\mathrm{4}^{\mathrm{2}} +\left(−\mathrm{3}\right)^{\mathrm{2}}…