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Question Number 116902 Answers: 0 Comments: 0

Question Number 116900 Answers: 0 Comments: 0

Question Number 116891 Answers: 2 Comments: 0

Proof that ((4(cos^4 (a)+sin^4 (a)))/(cos^4 (a)−sin^4 (a))) = (3+cos (4a))sec (2a)

$$\mathrm{Proof}\:\mathrm{that}\:\frac{\mathrm{4}\left(\mathrm{cos}\:^{\mathrm{4}} \left({a}\right)+\mathrm{sin}\:^{\mathrm{4}} \left({a}\right)\right)}{\mathrm{cos}\:^{\mathrm{4}} \left({a}\right)−\mathrm{sin}\:^{\mathrm{4}} \left({a}\right)}\:=\:\left(\mathrm{3}+\mathrm{cos}\:\left(\mathrm{4}{a}\right)\right)\mathrm{sec}\:\left(\mathrm{2}{a}\right)\: \\ $$

Question Number 116887 Answers: 2 Comments: 1

Let k=sin 1°×sin 3°×sin 5°×…×sin 89° Find log_2 k^2 .

$$\mathrm{Let}\:{k}=\mathrm{sin}\:\mathrm{1}°×\mathrm{sin}\:\mathrm{3}°×\mathrm{sin}\:\mathrm{5}°×\ldots×\mathrm{sin}\:\mathrm{89}° \\ $$$$\mathrm{Find}\:\mathrm{log}_{\mathrm{2}} {k}^{\mathrm{2}} . \\ $$

Question Number 116884 Answers: 1 Comments: 0

Question Number 116883 Answers: 1 Comments: 0

Find the number m of ways to partition 10 students into four team so that two team contains 3 students and two team contains 2 students .

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{m}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{to} \\ $$$$\mathrm{partition}\:\mathrm{10}\:\mathrm{students}\:\mathrm{into}\:\mathrm{four}\:\mathrm{team} \\ $$$$\mathrm{so}\:\mathrm{that}\:\mathrm{two}\:\mathrm{team}\:\mathrm{contains}\:\mathrm{3}\:\mathrm{students} \\ $$$$\mathrm{and}\:\mathrm{two}\:\mathrm{team}\:\mathrm{contains}\:\mathrm{2}\:\mathrm{students}\:. \\ $$

Question Number 116881 Answers: 3 Comments: 0

Find the number m of non negative integer solution of x+y+z=18

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{m}\:\mathrm{of}\:\mathrm{non}\:\mathrm{negative} \\ $$$$\mathrm{integer}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{18} \\ $$$$ \\ $$

Question Number 116859 Answers: 2 Comments: 1

lim_(x→∞) ((3x^2 )/5^x )=?

$${li}\underset{{x}\rightarrow\infty} {{m}}\frac{\mathrm{3}{x}^{\mathrm{2}} }{\mathrm{5}^{{x}} }=? \\ $$

Question Number 116854 Answers: 4 Comments: 0

... calculus elementary algebra ... please solve :: ((6x+9))^(1/3) +((7−7x))^(1/3) +((x−8))^(1/3) =2 ...m.n.july.1970...

$$\:\:\:...\:\:\:{calculus}\:\:\:{elementary}\:\:{algebra}\:...\:\: \\ $$$$ \\ $$$$ \\ $$$$\:{please}\:{solve}\::: \\ $$$$ \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{6}{x}+\mathrm{9}}\:+\sqrt[{\mathrm{3}}]{\mathrm{7}−\mathrm{7}{x}}\:+\sqrt[{\mathrm{3}}]{{x}−\mathrm{8}}\:=\mathrm{2} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:...{m}.{n}.{july}.\mathrm{1970}... \\ $$$$\: \\ $$

Question Number 116853 Answers: 0 Comments: 0

Question Number 116847 Answers: 1 Comments: 1

Question Number 116846 Answers: 0 Comments: 2

...nice calculus... prove that :: ∫_0 ^( (π/2)) (√(((2^x −1)sin^3 (x))/((2^x +1)(sin^3 (x)+cos^3 (x))))) dx<(π/8) ...m.n.1970...

$$\:\:\:\:\:\:\:\:\:\:\:\:\:...{nice}\:\:{calculus}... \\ $$$$\:\:\:{prove}\:\:{that}\::: \\ $$$$ \\ $$$$\:\: \\ $$$$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \sqrt{\frac{\left(\mathrm{2}^{{x}} −\mathrm{1}\right){sin}^{\mathrm{3}} \left({x}\right)}{\left(\mathrm{2}^{{x}} +\mathrm{1}\right)\left({sin}^{\mathrm{3}} \left({x}\right)+{cos}^{\mathrm{3}} \left({x}\right)\right)}}\:\:{dx}<\frac{\pi}{\mathrm{8}} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:...{m}.{n}.\mathrm{1970}... \\ $$$$ \\ $$

Question Number 116845 Answers: 1 Comments: 1

Question Number 116844 Answers: 1 Comments: 0

∫ ((8x+sin^(−1) (2x))/( (√(1−4x^2 )))) dx

$$\int\:\frac{\mathrm{8x}+\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{2x}\right)}{\:\sqrt{\mathrm{1}−\mathrm{4x}^{\mathrm{2}} }}\:\mathrm{dx}\: \\ $$

Question Number 116843 Answers: 0 Comments: 1

Question Number 116841 Answers: 0 Comments: 1

Question Number 116832 Answers: 3 Comments: 0

If 19 sin 2x = 37 cos 2x+38 sin^2 x then tan x = __

$$\mathrm{If}\:\mathrm{19}\:\mathrm{sin}\:\mathrm{2x}\:=\:\mathrm{37}\:\mathrm{cos}\:\mathrm{2x}+\mathrm{38}\:\mathrm{sin}\:^{\mathrm{2}} \mathrm{x} \\ $$$$\mathrm{then}\:\mathrm{tan}\:\mathrm{x}\:=\:\_\_ \\ $$

Question Number 116824 Answers: 2 Comments: 0

Given a>b>0 , a&b real number such that a^2 −ab+b^2 =7 and a−ab+b=−1. find the value of a^2 −b^2

$$\mathrm{Given}\:\mathrm{a}>\mathrm{b}>\mathrm{0}\:,\:\mathrm{a\&b}\:\mathrm{real}\:\mathrm{number}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{a}^{\mathrm{2}} −\mathrm{ab}+\mathrm{b}^{\mathrm{2}} =\mathrm{7}\:\mathrm{and}\:\mathrm{a}−\mathrm{ab}+\mathrm{b}=−\mathrm{1}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}^{\mathrm{2}} −\mathrm{b}^{\mathrm{2}} \\ $$

Question Number 116822 Answers: 3 Comments: 1

what the value of (√i) =?

$$\:\mathrm{what}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\sqrt{{i}}\:=? \\ $$

Question Number 116820 Answers: 0 Comments: 0

prove that lim f(x)=L and lim f(x)=M, then L=M

$${prove}\:{that}\:{lim}\:{f}\left({x}\right)={L}\:{and}\:{lim}\:{f}\left({x}\right)={M}, \\ $$$${then}\:{L}={M} \\ $$

Question Number 116819 Answers: 1 Comments: 0

prove the limit lim_(x−⟩2) (√(2x))=2

$${prove}\:{the}\:{limit} \\ $$$${li}\underset{{x}−\rangle\mathrm{2}} {{m}}\sqrt{\mathrm{2}{x}}=\mathrm{2} \\ $$

Question Number 116872 Answers: 1 Comments: 0

Question Number 116815 Answers: 2 Comments: 0

∫ (dx/((x−2)(x^2 +4))) =?

$$\int\:\frac{\mathrm{dx}}{\left(\mathrm{x}−\mathrm{2}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{4}\right)}\:=? \\ $$

Question Number 116813 Answers: 2 Comments: 0

∫_1 ^(√3) ((√(1+x^2 ))/x^2 ) dx ?

$$\:\:\:\:\:\:\underset{\mathrm{1}} {\overset{\sqrt{\mathrm{3}}} {\int}}\:\frac{\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }}{\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}\:? \\ $$

Question Number 116803 Answers: 0 Comments: 0

Solve for X(x,y,z), Y(x,y,z), Z(x,y,z) { (((∂Z/∂y)−(∂Y/∂z)=1−x^2 )),(((∂Z/∂x)−(∂X/∂z)=−(y^2 /2))),(((∂Y/∂x)−(∂X/∂y)=z(2x−y))) :} where { ((X(x,y,0)=0)),((Y(x,y,0)=0)),((Z(x,y,z)=0)) :}

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{X}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right),\:\mathrm{Y}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right),\:\mathrm{Z}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right) \\ $$$$\begin{cases}{\frac{\partial\mathrm{Z}}{\partial\mathrm{y}}−\frac{\partial\mathrm{Y}}{\partial\mathrm{z}}=\mathrm{1}−\mathrm{x}^{\mathrm{2}} }\\{\frac{\partial\mathrm{Z}}{\partial\mathrm{x}}−\frac{\partial\mathrm{X}}{\partial\mathrm{z}}=−\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{2}}}\\{\frac{\partial\mathrm{Y}}{\partial\mathrm{x}}−\frac{\partial\mathrm{X}}{\partial\mathrm{y}}=\mathrm{z}\left(\mathrm{2x}−\mathrm{y}\right)}\end{cases}\:\mathrm{where}\:\begin{cases}{\mathrm{X}\left(\mathrm{x},\mathrm{y},\mathrm{0}\right)=\mathrm{0}}\\{\mathrm{Y}\left(\mathrm{x},\mathrm{y},\mathrm{0}\right)=\mathrm{0}}\\{\mathrm{Z}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=\mathrm{0}}\end{cases} \\ $$

Question Number 116806 Answers: 2 Comments: 0

Hi Prove that: ∫_(-∞) ^(+∞) -e^(-x^2 ) dx=(√π) Thanks beforehand

$$\mathrm{Hi} \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\:\int_{-\infty} ^{+\infty} -\mathrm{e}^{-\mathrm{x}^{\mathrm{2}} } \mathrm{dx}=\sqrt{\pi} \\ $$$$\mathrm{Thanks}\:\mathrm{beforehand} \\ $$$$ \\ $$

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