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Question Number 165653 Answers: 1 Comments: 2

Question Number 165651 Answers: 1 Comments: 5

If the equation (2x−1)−p(x^2 +2)=0, where p is constant, has imaginary roots, deduce that 2p^2 +p−1≥0.

$${If}\:{the}\:{equation}\:\left(\mathrm{2}{x}−\mathrm{1}\right)−{p}\left({x}^{\mathrm{2}} +\mathrm{2}\right)=\mathrm{0}, \\ $$$${where}\:{p}\:{is}\:{constant},\:{has}\:{imaginary} \\ $$$${roots},\:{deduce}\:{that}\:\mathrm{2}{p}^{\mathrm{2}} +{p}−\mathrm{1}\geqslant\mathrm{0}. \\ $$

Question Number 165650 Answers: 0 Comments: 0

Question Number 165649 Answers: 0 Comments: 0

Question Number 165648 Answers: 0 Comments: 0

Question Number 165639 Answers: 1 Comments: 1

Question Number 165692 Answers: 1 Comments: 0

why we use the current as conventional in a circuit?

$${why}\:{we}\:{use}\:{the}\:{current}\:{as}\:{conventional}\:{in} \\ $$$${a}\:{circuit}? \\ $$

Question Number 165691 Answers: 1 Comments: 0

why can′t birds catch by the AC current?

$${why}\:{can}'{t}\:{birds}\:{catch}\:{by}\:{the}\:{AC}\:{current}? \\ $$

Question Number 165637 Answers: 1 Comments: 0

37tanx =11tan3x solve it

$$\mathrm{37}{tanx}\:=\mathrm{11}{tan}\mathrm{3}{x} \\ $$$${solve}\:{it} \\ $$

Question Number 165620 Answers: 1 Comments: 0

solve z^7 =−4

$${solve} \\ $$$${z}^{\mathrm{7}} =−\mathrm{4} \\ $$

Question Number 165617 Answers: 1 Comments: 0

what is the focal length formula for combined lenses? if lenses more than tow?

$${what}\:{is}\:{the}\:{focal}\:{length}\:{formula}\:{for}\: \\ $$$${combined}\:{lenses}?\:{if}\:{lenses}\:{more}\:{than}\: \\ $$$${tow}? \\ $$

Question Number 165616 Answers: 2 Comments: 1

Question Number 165615 Answers: 1 Comments: 0

∫_( 0) ^( 1) (dx/( (√x) ((x)^(1/3) +(x)^(1/4) )))=?

$$\:\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{{dx}}{\:\sqrt{{x}}\:\left(\sqrt[{\mathrm{3}}]{{x}}+\sqrt[{\mathrm{4}}]{{x}}\right)}=? \\ $$

Question Number 165641 Answers: 2 Comments: 0

Given that y = (1/x) (a) Show that y^((n)) = (((−1)^n n!)/x^(n+1) ) (b) Find an expression for y^((n−1)) + y^((n))

$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Given}\:\mathrm{that}\:\:{y}\:=\:\frac{\mathrm{1}}{{x}}\: \\ $$$$\left({a}\right)\:\mathrm{Show}\:\mathrm{that}\:\:{y}^{\left({n}\right)} \:=\:\frac{\left(−\mathrm{1}\right)^{{n}} \:{n}!}{{x}^{{n}+\mathrm{1}} } \\ $$$$\left({b}\right)\:\mathrm{Find}\:\mathrm{an}\:\mathrm{expression}\:\mathrm{for}\:{y}^{\left({n}−\mathrm{1}\right)} +\:{y}^{\left({n}\right)} \\ $$$$ \\ $$

Question Number 165608 Answers: 0 Comments: 0

Reupload unanswered question. sec^2 1° + sec^2 2° + sec^2 3° + …+ sec^2 89° = ?

$$\mathrm{Reupload}\:\:\mathrm{unanswered}\:\:\mathrm{question}. \\ $$$$\mathrm{sec}^{\mathrm{2}} \mathrm{1}°\:+\:\mathrm{sec}^{\mathrm{2}} \:\mathrm{2}°\:+\:\mathrm{sec}^{\mathrm{2}} \:\mathrm{3}°\:+\:\ldots+\:\mathrm{sec}^{\mathrm{2}} \:\mathrm{89}°\:\:=\:\:? \\ $$

Question Number 165600 Answers: 0 Comments: 19

Question Number 165599 Answers: 1 Comments: 0

Question Number 165597 Answers: 0 Comments: 0

prove that Σ_(n=1) ^∞ (( ψ^( (1)) (n))/n^( 2) ) =(7/4) ζ (4) ■ m.n

$$ \\ $$$$\:\:\:\:{prove}\:{that} \\ $$$$\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\psi^{\:\left(\mathrm{1}\right)} \left({n}\right)}{{n}^{\:\mathrm{2}} }\:=\frac{\mathrm{7}}{\mathrm{4}}\:\zeta\:\left(\mathrm{4}\right)\:\:\:\blacksquare\:{m}.{n} \\ $$$$ \\ $$

Question Number 165581 Answers: 2 Comments: 0

ϕ(t)=∫_0 ^( (π/2)) ( sin(x)+t cos(x))^( 2) dx find the value of the extermum of ϕ (t).

$$ \\ $$$$\varphi\left({t}\right)=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \left(\:{sin}\left({x}\right)+{t}\:{cos}\left({x}\right)\right)^{\:\mathrm{2}} {dx} \\ $$$${find}\:\:{the}\:\:{value}\:{of}\:{the}\:{extermum} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{of}\:\:\:\varphi\:\left({t}\right). \\ $$

Question Number 165574 Answers: 0 Comments: 0

Question Number 165570 Answers: 2 Comments: 0

Question Number 165568 Answers: 0 Comments: 0

Question Number 165567 Answers: 0 Comments: 0

Question Number 165576 Answers: 2 Comments: 0

Given f: E→F ; g: F→G . E; F and G are sets. Show that if f and g are bijectives then g○f is bijective and (g○f)^(−1) =f^(−1) ○g^(−1)

$${Given}\:{f}:\:{E}\rightarrow{F}\:;\:{g}:\:{F}\rightarrow{G}\:. \\ $$$${E};\:{F}\:\:{and}\:{G}\:{are}\:{sets}. \\ $$$${Show}\:{that}\:{if}\:{f}\:{and}\:{g}\:{are}\:{bijectives} \\ $$$${then}\:{g}\circ{f}\:{is}\:{bijective}\:{and}\: \\ $$$$\left({g}\circ{f}\right)^{−\mathrm{1}} ={f}^{−\mathrm{1}} \circ{g}^{−\mathrm{1}} \\ $$

Question Number 165565 Answers: 2 Comments: 0

Question Number 165561 Answers: 2 Comments: 0

I=∫(dx/(x^8 +x^6 )) J=∫((1−x^7 )/(x(1+x^7 )))dx Calculate I and J

$${I}=\int\frac{{dx}}{{x}^{\mathrm{8}} +{x}^{\mathrm{6}} } \\ $$$${J}=\int\frac{\mathrm{1}−{x}^{\mathrm{7}} }{{x}\left(\mathrm{1}+{x}^{\mathrm{7}} \right)}{dx} \\ $$$${Calculate}\:{I}\:{and}\:{J} \\ $$

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