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Question Number 71239    Answers: 2   Comments: 3

∫(1/(2cosx−5sinx−3))dx

$$\int\frac{\mathrm{1}}{\mathrm{2cosx}−\mathrm{5sinx}−\mathrm{3}}\mathrm{dx} \\ $$

Question Number 71235    Answers: 2   Comments: 1

sinh[ln (x + (√(1 + x^2 ))) ] ≡ A. 2x B. (1/x) C. x^2 D. x

$${sinh}\left[{ln}\:\left({x}\:+\:\sqrt{\mathrm{1}\:+\:{x}^{\mathrm{2}} }\right)\:\right]\:\equiv\: \\ $$$$ \\ $$$${A}.\:\:\mathrm{2}{x} \\ $$$${B}.\:\:\frac{\mathrm{1}}{{x}} \\ $$$${C}.\:\:{x}^{\mathrm{2}} \\ $$$${D}.\:\:{x} \\ $$

Question Number 71233    Answers: 1   Comments: 3

Question Number 71229    Answers: 0   Comments: 1

Question Number 71220    Answers: 0   Comments: 0

Question Number 71216    Answers: 1   Comments: 0

Question Number 71206    Answers: 1   Comments: 0

Let p,q,r are positive real numbers . 0 < r < min{p,q}. Prove that (√(p−r)) + (√(q−r)) ≤ min{(√((pq)/r)) , (√(2(p+q − 2r))) }

$${Let}\:\:{p},{q},{r}\:\:{are}\:\:{positive}\:\:{real}\:\:{numbers}\:. \\ $$$$\mathrm{0}\:<\:{r}\:<\:{min}\left\{{p},{q}\right\}. \\ $$$${Prove}\:\:{that} \\ $$$$\:\:\:\:\:\sqrt{{p}−{r}}\:+\:\sqrt{{q}−{r}}\:\:\leqslant\:\:{min}\left\{\sqrt{\frac{{pq}}{{r}}}\:,\:\sqrt{\mathrm{2}\left({p}+{q}\:−\:\mathrm{2}{r}\right)}\:\right\} \\ $$

Question Number 71196    Answers: 1   Comments: 0

the curve y = f(x), when f(x) is a quadratic expression has a maximum value point at (1,4). The curve touches the line 6x + y = 13. Find the value of x for which y = 8

$${the}\:{curve}\:{y}\:=\:{f}\left({x}\right),\:{when}\:{f}\left({x}\right)\:{is}\:{a}\:{quadratic}\:{expression}\:{has}\: \\ $$$${a}\:{maximum}\:{value}\:{point}\:{at}\:\left(\mathrm{1},\mathrm{4}\right).\:{The}\:{curve}\:{touches}\:{the}\:{line} \\ $$$$\mathrm{6}{x}\:+\:{y}\:=\:\mathrm{13}.\:{Find}\:{the}\:{value}\:{of}\:{x}\:{for}\:{which}\:{y}\:=\:\mathrm{8} \\ $$

Question Number 71184    Answers: 1   Comments: 4

Question Number 71198    Answers: 0   Comments: 0

A particle P is projected from a point O at the edge of a cliff 60m from the sea with a velocity of 30ms^(−1) . When P is at a point B where OB is a horizontal, another particle Qsuch that P and Q hit the sea simultaneously at thesame point A. Gven that they strike the sea 6seconds after P was fired ^ calculate a) the sine of the angle of elevation of projection. b) the distance from A to O. c) the time of flight of Q. d) the Range . (take g = 10ms^(−2) ) please help

$${A}\:{particle}\:{P}\:{is}\:{projected}\:{from}\:\:{a}\:{point}\:{O}\:{at}\:\:{the}\:{edge}\:{of}\:{a}\:{cliff}\:\mathrm{60}{m} \\ $$$${from}\:{the}\:{sea}\:{with}\:{a}\:{velocity}\:{of}\:\mathrm{30}{ms}^{−\mathrm{1}} .\:{When}\:{P}\:{is}\:{at}\:{a}\:{point}\:{B} \\ $$$${where}\:{OB}\:{is}\:{a}\:{horizontal},\:{another}\:{particle}\:{Qsuch}\:{that}\: \\ $$$${P}\:{and}\:{Q}\:{hit}\:{the}\:{sea}\:{simultaneously}\:{at}\:{thesame}\:{point}\:{A}.\:{Gven}\:{that}\:{they} \\ $$$${strike}\:{the}\:{sea}\:\mathrm{6}{seconds}\:{after}\:{P}\:{was}\:{fired}\bar {\:}\:{calculate} \\ $$$$\left.{a}\right)\:{the}\:{sine}\:{of}\:{the}\:{angle}\:{of}\:{elevation}\:{of}\:{projection}. \\ $$$$\left.{b}\right)\:{the}\:{distance}\:{from}\:{A}\:{to}\:{O}. \\ $$$$\left.{c}\right)\:{the}\:{time}\:{of}\:{flight}\:{of}\:{Q}. \\ $$$$\left.{d}\right)\:{the}\:{Range}\:. \\ $$$$\left({take}\:{g}\:=\:\mathrm{10}{ms}^{−\mathrm{2}} \right)\: \\ $$$${please}\:{help}\: \\ $$

Question Number 71197    Answers: 0   Comments: 0

Question Number 71175    Answers: 1   Comments: 3

∫(1/(x^2 +2016x))dx

$$\int\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} +\mathrm{2016x}}\mathrm{dx} \\ $$

Question Number 71172    Answers: 0   Comments: 2

find fhe range f(x)=(4/(1+(√x)))

$${find}\:{fhe}\:{range} \\ $$$$ \\ $$$${f}\left({x}\right)=\frac{\mathrm{4}}{\mathrm{1}+\sqrt{{x}}} \\ $$

Question Number 71149    Answers: 1   Comments: 4

Question Number 71147    Answers: 2   Comments: 1

Question Number 71146    Answers: 1   Comments: 1

sin α=((12)/(13)) and α is in the 2nd quadrent. prove cos α=−(5/(13))

$$\mathrm{sin}\:\alpha=\frac{\mathrm{12}}{\mathrm{13}}\:\:\mathrm{and}\:\alpha\:\mathrm{is}\:\mathrm{in}\:\mathrm{the}\:\mathrm{2nd}\:\mathrm{quadrent}. \\ $$$$\mathrm{prove}\:\mathrm{cos}\:\alpha=−\frac{\mathrm{5}}{\mathrm{13}} \\ $$

Question Number 71143    Answers: 0   Comments: 1

let A_n =Σ_(k=0) ^n (1/(3k+1)) calculate A_n interms H_n =Σ_(k=1) ^n (1/k)

$${let}\:\:{A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{\mathrm{1}}{\mathrm{3}{k}+\mathrm{1}}\:{calculate}\:{A}_{{n}} \:{interms}\:{H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}} \\ $$

Question Number 71142    Answers: 0   Comments: 1

find ∫(√(x(x+1)(x+2)))dx

$${find}\:\int\sqrt{{x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)}{dx} \\ $$

Question Number 71141    Answers: 0   Comments: 6

(2x)^x =(1/(16))

$$\left(\mathrm{2}{x}\right)^{{x}} =\frac{\mathrm{1}}{\mathrm{16}} \\ $$

Question Number 71134    Answers: 1   Comments: 0

if a, b and c are positive, find: ((a/b))^(log_(10) c) ×((b/c))^(log_(10) a) ×((c/a))^(log_(10) b)

$${if}\:{a},\:{b}\:{and}\:{c}\:{are}\:{positive},\:{find}: \\ $$$$\left(\frac{{a}}{{b}}\right)^{{log}_{\mathrm{10}} {c}} ×\left(\frac{{b}}{{c}}\right)^{{log}_{\mathrm{10}} {a}} ×\left(\frac{{c}}{{a}}\right)^{{log}_{\mathrm{10}} {b}} \\ $$$$ \\ $$

Question Number 71117    Answers: 0   Comments: 0

Question Number 71114    Answers: 0   Comments: 0

Question Number 71096    Answers: 1   Comments: 0

Question Number 71091    Answers: 0   Comments: 3

Question Number 71115    Answers: 1   Comments: 0

Question Number 71089    Answers: 1   Comments: 0

((√((√2)−1)))^x +((√((√2)+1)))^x =4

$$\left(\sqrt{\sqrt{\mathrm{2}}−\mathrm{1}}\right)^{\mathrm{x}} +\left(\sqrt{\sqrt{\mathrm{2}}+\mathrm{1}}\right)^{\mathrm{x}} =\mathrm{4} \\ $$

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