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Question Number 117781 Answers: 1 Comments: 0

Log (cosβ) = p ⇒ cos β = 10^p ∴ secβ = (1/(cosβ)) = (1/(10^p )) = 10^(−p) ∴ Log (secβ) = Log 10^(−p) = −p Log 10 = −p

$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{Log}\:\left(\mathrm{cos}\beta\right)\:=\:\mathrm{p}\:\:\:\:\:\Rightarrow\:\:\:\mathrm{cos}\:\beta\:=\:\mathrm{10}^{\mathrm{p}} \:\: \\ $$$$\:\:\:\:\:\:\:\therefore\:\:\:\mathrm{sec}\beta\:=\:\:\frac{\mathrm{1}}{\mathrm{cos}\beta}\:\:=\:\:\frac{\mathrm{1}}{\mathrm{10}^{\mathrm{p}} }\:\:=\:\mathrm{10}^{−\mathrm{p}} \\ $$$$\:\:\:\:\:\:\:\therefore\:\:\:\mathrm{Log}\:\left(\mathrm{sec}\beta\right)\:=\:\:\mathrm{Log}\:\mathrm{10}^{−\mathrm{p}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:−\mathrm{p}\:\mathrm{Log}\:\mathrm{10} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:−\mathrm{p} \\ $$

Question Number 117791 Answers: 3 Comments: 0

If k is an integer which satisfies 2sin^2 θ+10cos^2 (θ/2)=7−2k, then k∈? A.{0,1,2,3} B.{−1,0,1,2,3} C.{(−2,−1,0,1,2,3} D.{−3,−2,−1,0}

$$\mathrm{If}\:{k}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integer}\:\mathrm{which}\:\mathrm{satisfies}\: \\ $$$$\mathrm{2sin}^{\mathrm{2}} \theta+\mathrm{10cos}^{\mathrm{2}} \frac{\theta}{\mathrm{2}}=\mathrm{7}−\mathrm{2}{k},\:\mathrm{then}\:{k}\in? \\ $$$${A}.\left\{\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3}\right\}\:\:\:{B}.\left\{−\mathrm{1},\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3}\right\} \\ $$$${C}.\left\{\left(−\mathrm{2},−\mathrm{1},\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3}\right\}\:\:{D}.\left\{−\mathrm{3},−\mathrm{2},−\mathrm{1},\mathrm{0}\right\}\right. \\ $$

Question Number 117767 Answers: 1 Comments: 1

x^2 +y_ ^2 =a^2 (√(2 )) x^2 +y^2 =a^2 what is intersection Angle=?

$${x}^{\mathrm{2}} +{y}_{} ^{\mathrm{2}} ={a}^{\mathrm{2}} \sqrt{\mathrm{2}\:} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} ={a}^{\mathrm{2}} \:\:\:\:\:\: \\ $$$$ \\ $$$${what}\:{is}\:{intersection}\:\:{Angle}=?\: \\ $$

Question Number 117759 Answers: 0 Comments: 1

(dθ/dx)=((√(1−(θ^2 /x^2 )))/(sin(θ+x)))

$$\frac{{d}\theta}{{dx}}=\frac{\sqrt{\mathrm{1}−\frac{\theta^{\mathrm{2}} }{{x}^{\mathrm{2}} }}}{{sin}\left(\theta+{x}\right)} \\ $$

Question Number 117754 Answers: 2 Comments: 1

Question Number 117739 Answers: 1 Comments: 0

what is the centre of the circle with radius 4(√2) that can be inscribed in the parabola y=x^2 −16x+128?

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{centre}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle} \\ $$$$\mathrm{with}\:\mathrm{radius}\:\mathrm{4}\sqrt{\mathrm{2}}\:\mathrm{that}\:\mathrm{can}\:\mathrm{be}\: \\ $$$$\mathrm{inscribed}\:\mathrm{in}\:\mathrm{the}\:\mathrm{parabola}\: \\ $$$$\mathrm{y}=\mathrm{x}^{\mathrm{2}} −\mathrm{16x}+\mathrm{128}? \\ $$

Question Number 117728 Answers: 3 Comments: 0

Solution (d^2 y/dx^2 ) + 3(dy/dx) − 4y = x^2

$${Solution}\:\:\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\mathrm{3}\frac{{dy}}{{dx}}\:−\:\mathrm{4}{y}\:=\:{x}^{\mathrm{2}} \\ $$

Question Number 117724 Answers: 2 Comments: 5

∫ ((sin^(−1) (x))/x^2 ) dx =?

$$\int\:\frac{\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}\:=? \\ $$

Question Number 117708 Answers: 2 Comments: 3

Find the number of all 5 digit numbers x_1 x_2 x_3 x_4 x_5 with x_1 ≥x_2 ≥x_3 ≥x_4 ≥x_5 .

$${Find}\:{the}\:{number}\:{of}\:{all}\:\mathrm{5}\:{digit} \\ $$$${numbers}\:{x}_{\mathrm{1}} {x}_{\mathrm{2}} {x}_{\mathrm{3}} {x}_{\mathrm{4}} {x}_{\mathrm{5}} \:{with} \\ $$$${x}_{\mathrm{1}} \geqslant{x}_{\mathrm{2}} \geqslant{x}_{\mathrm{3}} \geqslant{x}_{\mathrm{4}} \geqslant{x}_{\mathrm{5}} . \\ $$

Question Number 117704 Answers: 0 Comments: 7

Given a function ψ:R→R with ψ(θ) = θ^2 −x^2 . Find the value of ((d^2 ψ(θ))/dx^2 ) when θ=8

$$\mathrm{Given}\:\mathrm{a}\:\mathrm{function}\:\psi:\mathbb{R}\rightarrow\mathbb{R} \\ $$$$\mathrm{with}\:\psi\left(\theta\right)\:=\:\theta^{\mathrm{2}} −\mathrm{x}^{\mathrm{2}} .\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\frac{\mathrm{d}^{\mathrm{2}} \psi\left(\theta\right)}{\mathrm{dx}^{\mathrm{2}} }\:\:\mathrm{when}\:\theta=\mathrm{8} \\ $$

Question Number 117688 Answers: 1 Comments: 3

Question Number 117687 Answers: 2 Comments: 0

lim_(x→0) (((ln (cosh x)−ln (cos x))^2 )/( (√(cosh x))+(√(cos x))−2)) =?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{ln}\:\left(\mathrm{cosh}\:\mathrm{x}\right)−\mathrm{ln}\:\left(\mathrm{cos}\:\mathrm{x}\right)\right)^{\mathrm{2}} }{\:\sqrt{\mathrm{cosh}\:\mathrm{x}}+\sqrt{\mathrm{cos}\:\mathrm{x}}−\mathrm{2}}\:=?\: \\ $$

Question Number 117666 Answers: 0 Comments: 3

Question Number 117655 Answers: 0 Comments: 3

Question Number 117654 Answers: 0 Comments: 1

Question Number 117649 Answers: 1 Comments: 0

Let P(x) be a polynomial function of degree n such that P(k)=(k/(k+1)) for k=0,1,2,...,n. Then P(n+1) is equal to (A) −1 if n is even (B) 1 if n is odd (C) (n/(n+2)) if n is even (D) (n/(n+2)) if n is odd Which among the four proposals is/are correct ?

$$\mathrm{Let}\:\mathrm{P}\left({x}\right)\:\mathrm{be}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{function}\:\mathrm{of}\:\mathrm{degree}\:\mathrm{n}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{P}\left({k}\right)=\frac{{k}}{{k}+\mathrm{1}}\:\:\mathrm{for}\:{k}=\mathrm{0},\mathrm{1},\mathrm{2},...,\mathrm{n}.\:\mathrm{Then}\:\mathrm{P}\left(\mathrm{n}+\mathrm{1}\right)\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\: \\ $$$$\left(\mathrm{A}\right)\:−\mathrm{1}\:\mathrm{if}\:\mathrm{n}\:\mathrm{is}\:\mathrm{even}\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{1}\:\mathrm{if}\:{n}\:\mathrm{is}\:\mathrm{odd} \\ $$$$\left(\mathrm{C}\right)\:\frac{{n}}{{n}+\mathrm{2}}\:\mathrm{if}\:{n}\:\mathrm{is}\:\mathrm{even}\:\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\frac{{n}}{{n}+\mathrm{2}}\:\:\mathrm{if}\:{n}\:\mathrm{is}\:\mathrm{odd} \\ $$$$\mathrm{Which}\:\mathrm{among}\:\mathrm{the}\:\mathrm{four}\:\mathrm{proposals}\:\mathrm{is}/\mathrm{are}\:\mathrm{correct}\:? \\ $$

Question Number 117646 Answers: 2 Comments: 1