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Question Number 146876 Answers: 1 Comments: 0

if the maximum value of 4sin^2 x+3cos^2 x+sin (x/2)+cos (x/2)+3 is a+(√b) then find a+b

$${if}\:{the}\:{maximum}\:{value}\:{of}\: \\ $$$$\mathrm{4sin}\:^{\mathrm{2}} {x}+\mathrm{3cos}\:^{\mathrm{2}} {x}+\mathrm{sin}\:\frac{{x}}{\mathrm{2}}+\mathrm{cos}\:\frac{{x}}{\mathrm{2}}+\mathrm{3} \\ $$$${is}\:{a}+\sqrt{{b}}\:{then}\:{find}\:{a}+{b} \\ $$

Question Number 146875 Answers: 0 Comments: 0

In a triangle ABC, if ((sin A)/(5−x))=((sin B)/(3x−1))=((sin C)/(2x+5)) then find integral solutions x?

$${In}\:{a}\:{triangle}\:{ABC},\:{if}\: \\ $$$$\frac{\mathrm{sin}\:{A}}{\mathrm{5}−{x}}=\frac{\mathrm{sin}\:{B}}{\mathrm{3}{x}−\mathrm{1}}=\frac{\mathrm{sin}\:{C}}{\mathrm{2}{x}+\mathrm{5}}\:{then}\:{find} \\ $$$$\:{integral}\:{solutions}\:{x}? \\ $$

Question Number 146874 Answers: 0 Comments: 0

let the line joining through orthocenter and circumcenter of a triangle ABC is parallel to the base BC then find tan B.tan C

$${let}\:{the}\:{line}\:{joining}\:{through}\: \\ $$$${orthocenter}\:{and}\:{circumcenter}\: \\ $$$${of}\:{a}\:{triangle}\:{ABC}\:{is}\:{parallel}\:{to}\: \\ $$$${the}\:{base}\:{BC}\:{then}\:{find}\:\:\mathrm{tan}\:{B}.\mathrm{tan}\:{C} \\ $$

Question Number 146865 Answers: 1 Comments: 0

arcsin(x^2 −4) = arcsin(2x + 4) ⇒ x = ?

$${arcsin}\left({x}^{\mathrm{2}} −\mathrm{4}\right)\:=\:{arcsin}\left(\mathrm{2}{x}\:+\:\mathrm{4}\right) \\ $$$$\Rightarrow\:{x}\:=\:? \\ $$

Question Number 146866 Answers: 1 Comments: 0

((sin^6 𝛂 + cos^6 𝛂 - 1)/(sin^4 𝛂 - sin^2 𝛂)) = ?

$$\frac{{sin}^{\mathrm{6}} \boldsymbol{\alpha}\:+\:{cos}^{\mathrm{6}} \boldsymbol{\alpha}\:-\:\mathrm{1}}{{sin}^{\mathrm{4}} \boldsymbol{\alpha}\:-\:{sin}^{\mathrm{2}} \boldsymbol{\alpha}}\:=\:? \\ $$

Question Number 146863 Answers: 1 Comments: 1

Question Number 146910 Answers: 1 Comments: 0

Question Number 146911 Answers: 0 Comments: 0

(dy/dx) = ((2cos^2 x−sin^2 x+y^2 )/(2cos x)) y(0)=−1 & y(1)=sin x

$$\:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{2cos}\:^{\mathrm{2}} \mathrm{x}−\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{y}^{\mathrm{2}} }{\mathrm{2cos}\:\mathrm{x}} \\ $$$$\:\:\:\mathrm{y}\left(\mathrm{0}\right)=−\mathrm{1}\:\&\:\mathrm{y}\left(\mathrm{1}\right)=\mathrm{sin}\:\mathrm{x}\: \\ $$

Question Number 147008 Answers: 0 Comments: 1

find the number of values of cot θ where θ∈[(π/(12)) (π/2)] satisfying the equation [tan θ.[cot θ]]=1 ? (where [x] is greatest integer less than or equal to x)

$${find}\:{the}\:{number}\:{of}\:{values}\:{of}\:\mathrm{cot}\:\theta\: \\ $$$${where}\:\theta\in\left[\frac{\pi}{\mathrm{12}}\:\frac{\pi}{\mathrm{2}}\right]\:{satisfying}\:{the}\: \\ $$$${equation}\:\left[\mathrm{tan}\:\theta.\left[\mathrm{cot}\:\theta\right]\right]=\mathrm{1}\:?\: \\ $$$$\left({where}\:\left[{x}\right]\:{is}\:{greatest}\:{integer}\right. \\ $$$$\left.{less}\:{than}\:{or}\:{equal}\:{to}\:{x}\right) \\ $$

Question Number 147007 Answers: 1 Comments: 0

Question Number 146860 Answers: 2 Comments: 0

∫sin(x) cos(x) dx = ?

$$\int{sin}\left({x}\right)\:{cos}\left({x}\right)\:{dx}\:=\:? \\ $$

Question Number 146859 Answers: 1 Comments: 0

∫_( 0) ^3 (√((x+2)^2 −8x)) = ?

$$\underset{\:\mathrm{0}} {\overset{\mathrm{3}} {\int}}\sqrt{\left({x}+\mathrm{2}\right)^{\mathrm{2}} −\mathrm{8}{x}}\:=\:? \\ $$

Question Number 146854 Answers: 1 Comments: 2

Solve for real numbers the following system of equations { ((a(a+1) = b−1)),((a^2 (b+3)+2a = −1)) :}

$${Solve}\:{for}\:{real}\:{numbers}\:{the}\:{following} \\ $$$${system}\:{of}\:{equations} \\ $$$$\begin{cases}{{a}\left({a}+\mathrm{1}\right)\:=\:{b}−\mathrm{1}}\\{{a}^{\mathrm{2}} \left({b}+\mathrm{3}\right)+\mathrm{2}{a}\:=\:−\mathrm{1}}\end{cases} \\ $$

Question Number 146853 Answers: 0 Comments: 0

Question Number 146850 Answers: 0 Comments: 0

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Question Number 146849 Answers: 1 Comments: 1

Question Number 146840 Answers: 2 Comments: 0

Question Number 146839 Answers: 0 Comments: 0

Question Number 146838 Answers: 1 Comments: 0

Given 4^x +4^(−x) −2^(2−x) +2^(2+x) −7=0 ,x>0 find 2^x +2^(−x) . if x∈[ −(π/6),0 ] then minimum value of function f(x)=cot (x+(π/3))−tan (((2π)/3)−x) when x = ?

$$\mathrm{Given}\:\mathrm{4}^{\mathrm{x}} +\mathrm{4}^{−\mathrm{x}} −\mathrm{2}^{\mathrm{2}−\mathrm{x}} +\mathrm{2}^{\mathrm{2}+\mathrm{x}} −\mathrm{7}=\mathrm{0}\:,\mathrm{x}>\mathrm{0} \\ $$$$\:\mathrm{find}\:\mathrm{2}^{\mathrm{x}} +\mathrm{2}^{−\mathrm{x}} . \\ $$$$\: \\ $$$$\:\mathrm{if}\:\mathrm{x}\in\left[\:−\frac{\pi}{\mathrm{6}},\mathrm{0}\:\right]\:\mathrm{then}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{cot}\:\left(\mathrm{x}+\frac{\pi}{\mathrm{3}}\right)−\mathrm{tan}\:\left(\frac{\mathrm{2}\pi}{\mathrm{3}}−\mathrm{x}\right)\: \\ $$$$\mathrm{when}\:\mathrm{x}\:=\:?\: \\ $$

Question Number 146837 Answers: 0 Comments: 0

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Question Number 146836 Answers: 0 Comments: 0

Σ_(n=1) ^∞ (1/(ϕ^( n) F_n )) =?

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\varphi^{\:{n}} \:\mathrm{F}_{{n}} }\:=? \\ $$

Question Number 146835 Answers: 2 Comments: 0

calculate ∫_0 ^∞ (dx/((x^2 +3)^2 (x^2 +4)^2 ))

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{4}\right)^{\mathrm{2}} } \\ $$

Question Number 146824 Answers: 1 Comments: 0

Question Number 146868 Answers: 1 Comments: 0

if tan^2 x+sec x=a+1 has at least one solution then find the complete set of values of ′a′?

$${if}\:\mathrm{tan}\:^{\mathrm{2}} {x}+\mathrm{sec}\:{x}={a}+\mathrm{1}\:{has}\:{at}\:{least}\: \\ $$$${one}\:{solution}\:{then}\:{find}\:{the}\:{complete}\:{set} \\ $$$${of}\:{values}\:{of}\:\:'{a}'? \\ $$

Question Number 146817 Answers: 1 Comments: 0

Question Number 146856 Answers: 0 Comments: 0

3. Calcula mediante una suma de Riemann una aproximaci´on al ´area limitada por la funci´on f(x) = −2x 2 − 4x + 30 y el eje x en el intervalo [−5, 3] con n rect´angulos. Δx=((3−(−5))/n) ⇒(8/n) ∴ x_0 =−5 ∴ a=x_0 =−5 x_1 =−5+1Δx x_2 =−5+2Δx x_3 =−5+3Δx ⋮ x_n =−5+nΔx

$$ \\ $$3. Calcula mediante una suma de Riemann una aproximaci´on al ´area limitada por la funci´on f(x) = −2x 2 − 4x + 30 y el eje x en el intervalo [−5, 3] con n rect´angulos. $$ \\ $$$$\Delta{x}=\frac{\mathrm{3}−\left(−\mathrm{5}\right)}{{n}}\:\Rightarrow\frac{\mathrm{8}}{{n}} \\ $$$$\therefore\:{x}_{\mathrm{0}} =−\mathrm{5} \\ $$$$ \\ $$$$\therefore\:{a}={x}_{\mathrm{0}} =−\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{x}_{\mathrm{1}} =−\mathrm{5}+\mathrm{1}\Delta{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{x}_{\mathrm{2}} =−\mathrm{5}+\mathrm{2}\Delta{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{x}_{\mathrm{3}} =−\mathrm{5}+\mathrm{3}\Delta{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\vdots \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{x}_{{n}} =−\mathrm{5}+{n}\Delta{x} \\ $$$$ \\ $$

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