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Question Number 205353    Answers: 2   Comments: 0

If ax^2 + bx + c = 0 had two roots p and q and p^2 + q^2 = p^3 + q^3 then show that b^3 − 2a^2 c + ab^2 = 3abc.

$$\mathrm{If}\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0}\:\mathrm{had}\:\mathrm{two}\:\mathrm{roots}\:{p}\:\mathrm{and}\:{q} \\ $$$$\mathrm{and}\:{p}^{\mathrm{2}} \:+\:{q}^{\mathrm{2}} \:=\:{p}^{\mathrm{3}} \:+\:{q}^{\mathrm{3}} \:\mathrm{then}\:\mathrm{show}\:\mathrm{that} \\ $$$${b}^{\mathrm{3}} \:−\:\mathrm{2}{a}^{\mathrm{2}} {c}\:+\:{ab}^{\mathrm{2}} \:=\:\mathrm{3}{abc}. \\ $$

Question Number 205350    Answers: 1   Comments: 2

A man invested U24000.00 in U5.00 shares of a firm. After a period of time, it appreciated to U5.50 per share. How much dividend did he receive, if the dividend declared is 50k per share?

$${A}\:{man}\:{invested}\:{U}\mathrm{24000}.\mathrm{00}\:{in}\:{U}\mathrm{5}.\mathrm{00} \\ $$$${shares}\:{of}\:{a}\:{firm}.\:{After}\:{a}\:{period}\:{of} \\ $$$${time},\:{it}\:{appreciated}\:{to}\:{U}\mathrm{5}.\mathrm{50}\:{per}\:{share}. \\ $$$${How}\:{much}\:{dividend}\:{did}\:{he}\:{receive},\:{if} \\ $$$${the}\:{dividend}\:{declared}\:{is}\:\mathrm{50}{k}\:{per}\:{share}? \\ $$

Question Number 205360    Answers: 2   Comments: 0

Question Number 205338    Answers: 2   Comments: 0

Question Number 205339    Answers: 1   Comments: 0

lim_(x→0) ((tan(tanx))/(sin(1−cosx)))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{tan}\left(\mathrm{tan}{x}\right)}{\mathrm{sin}\left(\mathrm{1}−\mathrm{cos}{x}\right)} \\ $$

Question Number 205335    Answers: 0   Comments: 0

∫((ax+b)/((x^2 −cx+d)^n ))dx

$$\int\frac{{ax}+{b}}{\left({x}^{\mathrm{2}} −{cx}+{d}\right)^{{n}} }{dx} \\ $$

Question Number 205334    Answers: 1   Comments: 1

Question Number 205332    Answers: 0   Comments: 0

determin a) U_(nεN^∗ ) (1,(1/n))

$${determin} \\ $$$$\left.{a}\right)\:\underset{{n}\epsilon{N}^{\ast} } {{U}}\left(\mathrm{1},\frac{\mathrm{1}}{{n}}\right) \\ $$

Question Number 205324    Answers: 3   Comments: 0

Compare: 37^(37) and 36^(38)

$$\mathrm{Compare}: \\ $$$$\mathrm{37}^{\mathrm{37}} \:\:\:\mathrm{and}\:\:\:\mathrm{36}^{\mathrm{38}} \\ $$

Question Number 205323    Answers: 0   Comments: 1

If log_(√((a^2 +b^2 )/2)) ((a+b)/b)≥log_(√(ab)) (2/((1/a)+(1/b))) when a>1 b>1

$${If}\:\:\:\:{log}_{\sqrt{\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }{\mathrm{2}}}} \frac{{a}+{b}}{{b}}\geqslant{log}_{\sqrt{{ab}}} \frac{\mathrm{2}}{\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}} \\ $$$${when}\:{a}>\mathrm{1}\:{b}>\mathrm{1} \\ $$

Question Number 205321    Answers: 1   Comments: 0

a^→ =i^ +3j^ +4k^ b^→ =2i^ −3j^ +4k^ c^→ =5i^ −2j^ +4k^ given that p^→ ×b^→ =b^→ ×c^→ and p^→ .b^→ =0 then the value of p^→ (i^ −j^ +k^ )is

$$\overset{\rightarrow} {{a}}=\hat {{i}}+\mathrm{3}\hat {{j}}+\mathrm{4}\hat {{k}}\:\overset{\rightarrow} {{b}}=\mathrm{2}\hat {{i}}−\mathrm{3}\hat {{j}}+\mathrm{4}\hat {{k}}\:\overset{\rightarrow} {{c}}=\mathrm{5}\hat {{i}}−\mathrm{2}\hat {{j}}+\mathrm{4}\hat {{k}}\:{given}\:{that}\:\overset{\rightarrow} {{p}}×\overset{\rightarrow} {{b}}=\overset{\rightarrow} {{b}}×\overset{\rightarrow} {{c}}\:{and}\:\overset{\rightarrow} {{p}}.\overset{\rightarrow} {{b}}=\mathrm{0}\:{then}\:{the}\:{value}\:{of}\:\overset{\rightarrow} {{p}}\left(\hat {{i}}−\hat {{j}}+\hat {{k}}\right){is} \\ $$

Question Number 205319    Answers: 0   Comments: 0

Question Number 205318    Answers: 0   Comments: 0

]^(]^ ]∡)

$$\left.\overset{\left.\overset{} {\right]}\left.\right]\measuredangle} {\right]} \\ $$

Question Number 205315    Answers: 1   Comments: 0

Question Number 205307    Answers: 1   Comments: 1

lim_(n→∞) ((⌊a⌋+⌊2a⌋+...+⌊na⌋)/n^2 ) where a∈R and ⌊x⌋ is the floor of x ∈ R

$$\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\lfloor{a}\rfloor+\lfloor\mathrm{2}{a}\rfloor+...+\lfloor{na}\rfloor}{{n}^{\mathrm{2}} }\:\mathrm{where}\:{a}\in\mathbb{R} \\ $$$$\:\:\:\mathrm{and}\:\lfloor{x}\rfloor\:\mathrm{is}\:\mathrm{the}\:\mathrm{floor}\:\mathrm{of}\:\mathrm{x}\:\in\:\mathbb{R} \\ $$

Question Number 205306    Answers: 1   Comments: 0

Question Number 205302    Answers: 1   Comments: 0

Question Number 205294    Answers: 1   Comments: 0

∫((3x−x^3 ))^(1/3) dx

$$\int\sqrt[{\mathrm{3}}]{\mathrm{3}{x}−{x}^{\mathrm{3}} }{dx} \\ $$

Question Number 205289    Answers: 0   Comments: 0

Question Number 205288    Answers: 0   Comments: 0

Question Number 205284    Answers: 0   Comments: 0

Question Number 205297    Answers: 2   Comments: 0

Find the′′ range ′′ of : i : f (x) =⌊ (( x)/( ⌊ x ⌋)) ⌋ ii: f(x) = (( x)/(⌊ x ⌋ + ⌊ −x ⌋))

$$ \\ $$$$\:\:\:{Find}\:\:{the}''\:{range}\:''\:{of}\:\:: \\ $$$$ \\ $$$$\:\:\:{i}\::\:\:\:{f}\:\left({x}\right)\:=\lfloor\:\frac{\:{x}}{\:\lfloor\:{x}\:\rfloor}\:\rfloor \\ $$$$\:\:\:{ii}:\:{f}\left({x}\right)\:=\:\frac{\:{x}}{\lfloor\:{x}\:\rfloor\:+\:\lfloor\:−{x}\:\rfloor} \\ $$$$\:\: \\ $$

Question Number 205280    Answers: 0   Comments: 1

Question Number 205279    Answers: 1   Comments: 0

∫^(π/2) _(-π/2) ((8(√2)cosx)/((1+e^(sinx) )(1+sin^4 x)))dx=aπ+blog(3+2(√2)) then find a+b

$$\underset{-\pi/\mathrm{2}} {\int}^{\pi/\mathrm{2}} \frac{\mathrm{8}\sqrt{\mathrm{2}}{cosx}}{\left(\mathrm{1}+\overset{{sinx}} {{e}}\right)\left(\mathrm{1}+{si}\overset{\mathrm{4}} {{n}x}\right)}{dx}={a}\pi+{blog}\left(\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}\right)\:{then}\:{find}\:{a}+{b} \\ $$

Question Number 205273    Answers: 3   Comments: 0

If f(x−1)=2x+2 Find f(x)=?

$$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}−\mathrm{1}\right)=\mathrm{2x}+\mathrm{2} \\ $$$$\mathrm{Find}\:\:\:\mathrm{f}\left(\mathrm{x}\right)=? \\ $$

Question Number 205269    Answers: 2   Comments: 0

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