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Question Number 65239 Answers: 1 Comments: 8

Question Number 65217 Answers: 0 Comments: 1

Question Number 65170 Answers: 0 Comments: 0

three forces F_1 , F_2 and F_3 acts through the points with position vectors r_1 ,r_2 and r_3 respectively where F_1 =(3i −2j−4k)N, r_1 = (i +k)m F_2 =(−i+j)N, r_2 =(j+k)m F_3 =(−i+4k)N, r_3 =(i+j+k)m a. show that this system does not reduce to a single force. When a fourth force F is added, the system of forces is in equilibrium b. Show that F acts through the point with vectors (3k)m.

$${three}\:{forces}\:{F}_{\mathrm{1}} ,\:{F}_{\mathrm{2}} \:{and}\:{F}_{\mathrm{3}} \:{acts}\:{through}\:{the}\:{points}\:{with}\:{position}\:{vectors} \\ $$$$\boldsymbol{{r}}_{\mathrm{1}} ,{r}_{\mathrm{2}} \:{and}\:{r}_{\mathrm{3}} \:{respectively}\:{where} \\ $$$$\:{F}_{\mathrm{1}} \:=\left(\mathrm{3}{i}\:−\mathrm{2}{j}−\mathrm{4}{k}\right){N},\:\:\:{r}_{\mathrm{1}} =\:\left({i}\:+{k}\right){m} \\ $$$${F}_{\mathrm{2}} =\left(−{i}+{j}\right){N},\:\:{r}_{\mathrm{2}} =\left({j}+{k}\right){m} \\ $$$${F}_{\mathrm{3}} =\left(−{i}+\mathrm{4}{k}\right){N},\:{r}_{\mathrm{3}} =\left({i}+{j}+{k}\right){m} \\ $$$${a}.\:{show}\:{that}\:{this}\:{system}\:{does}\:{not}\:{reduce}\:{to}\:{a}\:{single}\:{force}. \\ $$$$\:{When}\:{a}\:{fourth}\:{force}\:{F}\:{is}\:{added},\:{the}\:{system}\:{of}\:{forces}\:{is}\:{in}\:{equilibrium} \\ $$$${b}.\:{Show}\:{that}\:{F}\:{acts}\:{through}\:\:{the}\:{point}\:{with}\:{vectors}\:\left(\mathrm{3}{k}\right){m}. \\ $$

Question Number 65168 Answers: 2 Comments: 0

z = 1− i(√3) express z in the form r(cosθ +isinθ) also express z^7 in the form re^(iθ) .

$${z}\:=\:\mathrm{1}−\:\mathrm{i}\sqrt{\mathrm{3}} \\ $$$${express}\:{z}\:{in}\:{the}\:{form}\:\:{r}\left({cos}\theta\:+\mathrm{i}{sin}\theta\right)\:{also}\:{express}\:{z}^{\mathrm{7}} \:{in}\:{the}\:{form} \\ $$$${re}^{\mathrm{i}\theta} . \\ $$

Question Number 65166 Answers: 2 Comments: 1

Given that f(x) = (2/(x^2 −1)) a) Express f(x) in partial fraction. b.Evaluate ∫_3 ^5 f (x) dx

$${Given}\:{that}\:\:{f}\left({x}\right)\:=\:\frac{\mathrm{2}}{{x}^{\mathrm{2}} −\mathrm{1}} \\ $$$$\left.{a}\right)\:{Express}\:{f}\left({x}\right)\:{in}\:{partial}\:{fraction}. \\ $$$${b}.{Evaluate}\:\:\int_{\mathrm{3}} ^{\mathrm{5}} {f}\:\left({x}\right)\:{dx} \\ $$

Question Number 65113 Answers: 0 Comments: 1

Question Number 65052 Answers: 4 Comments: 0

A.Evaluate: (i)∫((sin x+cos x)/(9+16sin 2x))dx (ii)∫((1+x^2 )/((1−x^2 )(√(1+x^2 +x^4 ))))dx (iii)∫((x−1)/((x+1)(√(x^3 +x+x^2 ))))dx

$${A}.\mathrm{Evaluate}: \\ $$$$\left(\mathrm{i}\right)\int\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{9}+\mathrm{16sin}\:\mathrm{2}{x}}{dx} \\ $$$$\left(\mathrm{ii}\right)\int\frac{\mathrm{1}+{x}^{\mathrm{2}} }{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)\sqrt{\mathrm{1}+{x}^{\mathrm{2}} +{x}^{\mathrm{4}} }}{dx} \\ $$$$\left(\mathrm{iii}\right)\int\frac{{x}−\mathrm{1}}{\left({x}+\mathrm{1}\right)\sqrt{{x}^{\mathrm{3}} +{x}+{x}^{\mathrm{2}} }}{dx} \\ $$

Question Number 65013 Answers: 1 Comments: 0

why do we divide each term by n when given the question lim_(x→∞) ((3 +2n)/(1+n)) ?

$${why}\:{do}\:{we}\:{divide}\:{each}\:{term}\:{by}\:{n}\:{when}\:{given}\:{the}\:{question} \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\mathrm{3}\:+\mathrm{2}{n}}{\mathrm{1}+{n}}\:? \\ $$

Question Number 65011 Answers: 5 Comments: 1

1.(i)Evaluate:∫(1/(sin x−cos x+(√2)))dx (ii)Evaluate:∫2^2^2^x 2^2^x 2^x dx (iii)Evaluate:∫((cos^3 x)/(sin^2 x+sin x))dx 2.cosec [tan^(−1) {cos (cot^(−1) (sec(sin^(−1) a)))}]=What? 3.Prove that, sin [cot^(−1) {cos (tan^(−1) x)}]=(√((x^2 +1)/(x^2 +2))) 4.Mention Order and Degree and state also if it is linear or non-linear. y+(d^2 y/dx^2 )=((19)/(25))∫y^2 dx

$$\mathrm{1}.\left(\mathrm{i}\right)\mathrm{Evaluate}:\int\frac{\mathrm{1}}{\mathrm{sin}\:{x}−\mathrm{cos}\:{x}+\sqrt{\mathrm{2}}}{dx} \\ $$$$\left(\mathrm{ii}\right)\mathrm{Evaluate}:\int\mathrm{2}^{\mathrm{2}^{\mathrm{2}^{{x}} } } \mathrm{2}^{\mathrm{2}^{{x}} } \mathrm{2}^{{x}} \:{dx} \\ $$$$\left(\mathrm{iii}\right)\mathrm{Evaluate}:\int\frac{\mathrm{cos}\:^{\mathrm{3}} {x}}{\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{sin}\:{x}}{dx} \\ $$$$\mathrm{2}.\mathrm{cosec}\:\left[\mathrm{tan}^{−\mathrm{1}} \left\{\mathrm{cos}\:\left(\mathrm{cot}^{−\mathrm{1}} \left(\mathrm{sec}\left(\mathrm{sin}^{−\mathrm{1}} {a}\right)\right)\right)\right\}\right]=\mathrm{What}? \\ $$$$\mathrm{3}.\mathrm{Prove}\:\mathrm{that},\:\:\mathrm{sin}\:\left[\mathrm{cot}^{−\mathrm{1}} \left\{\mathrm{cos}\:\left(\mathrm{tan}^{−\mathrm{1}} {x}\right)\right\}\right]=\sqrt{\frac{{x}^{\mathrm{2}} +\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{2}}} \\ $$$$\mathrm{4}.\mathrm{Mention}\:\mathrm{Order}\:\mathrm{and}\:\mathrm{Degree}\:\mathrm{and}\:\:\mathrm{state}\:\mathrm{also}\:\mathrm{if}\:\mathrm{it}\:\mathrm{is}\:\mathrm{linear}\:\mathrm{or}\:\mathrm{non}-{l}\mathrm{inear}. \\ $$$$\:\:\:\:\:{y}+\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }=\frac{\mathrm{19}}{\mathrm{25}}\int{y}^{\mathrm{2}} \:{dx} \\ $$

Question Number 64966 Answers: 0 Comments: 0