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AllQuestion and Answers: Page 76

Question Number 208782    Answers: 1   Comments: 0

Question Number 208783    Answers: 0   Comments: 3

Solve for x and y. x^y − y^x = 17

$$\mathrm{Solve}\:\mathrm{for}\:\:\mathrm{x}\:\:\mathrm{and}\:\:\mathrm{y}. \\ $$$$\:\:\:\:\mathrm{x}^{\mathrm{y}} \:\:−\:\:\mathrm{y}^{\mathrm{x}} \:\:=\:\:\mathrm{17} \\ $$

Question Number 208772    Answers: 2   Comments: 0

Question Number 208759    Answers: 0   Comments: 5

Question Number 208756    Answers: 0   Comments: 0

Question Number 208755    Answers: 1   Comments: 0

Question Number 208743    Answers: 1   Comments: 10

Question Number 208741    Answers: 1   Comments: 0

Question Number 208742    Answers: 0   Comments: 0

Question Number 208739    Answers: 0   Comments: 0

Question Number 208738    Answers: 1   Comments: 0

sum: (1/(1.4.7)) + (1/(4.7.10)) + (1/(7.10.13)) + (1/(10.13.16)) + (1/(13.16.19)) + ... + (1/(94.97.100))

$$\mathrm{sum}: \\ $$$$\:\:\:\frac{\mathrm{1}}{\mathrm{1}.\mathrm{4}.\mathrm{7}}\:\:\:+\:\:\frac{\mathrm{1}}{\mathrm{4}.\mathrm{7}.\mathrm{10}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{7}.\mathrm{10}.\mathrm{13}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{10}.\mathrm{13}.\mathrm{16}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{13}.\mathrm{16}.\mathrm{19}}\:\:+\:\:...\:\:+\:\:\frac{\mathrm{1}}{\mathrm{94}.\mathrm{97}.\mathrm{100}} \\ $$

Question Number 208733    Answers: 1   Comments: 0

2∫_(1/3) ^1 ((x(√(−3x^2 +4x−1)))/(7x^2 −4x+1))dx=? Exact solution needed.

$$\mathrm{2}\underset{\frac{\mathrm{1}}{\mathrm{3}}} {\overset{\mathrm{1}} {\int}}\frac{{x}\sqrt{−\mathrm{3}{x}^{\mathrm{2}} +\mathrm{4}{x}−\mathrm{1}}}{\mathrm{7}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{1}}{dx}=? \\ $$$$\mathrm{Exact}\:\mathrm{solution}\:\mathrm{needed}. \\ $$

Question Number 208704    Answers: 1   Comments: 2

Find: arccos (arctg (5/(12)) + arcsin (4/5)) = ?

$$\mathrm{Find}: \\ $$$$\mathrm{arccos}\:\left(\mathrm{arctg}\:\frac{\mathrm{5}}{\mathrm{12}}\:\:+\:\:\mathrm{arcsin}\:\frac{\mathrm{4}}{\mathrm{5}}\right)\:=\:? \\ $$

Question Number 208692    Answers: 1   Comments: 0

∫_0 ^(π/2) xln sin x dx=?

$$\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}{x}\mathrm{ln}\:\mathrm{sin}\:{x}\:{dx}=? \\ $$

Question Number 208690    Answers: 1   Comments: 0

Question Number 208686    Answers: 1   Comments: 0

cos^2 2x = sin^2 2x + ((√3)/2) x = ?

$$\mathrm{cos}^{\mathrm{2}} \:\mathrm{2x}\:=\:\mathrm{sin}^{\mathrm{2}} \:\mathrm{2x}\:+\:\frac{\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$$$\mathrm{x}\:=\:? \\ $$

Question Number 208685    Answers: 1   Comments: 0

25 tan x = 3 x = ?

$$\mathrm{25}\:\mathrm{tan}\:\mathrm{x}\:=\:\mathrm{3} \\ $$$$\mathrm{x}\:=\:? \\ $$

Question Number 208681    Answers: 2   Comments: 0

Question Number 208676    Answers: 1   Comments: 0

Question Number 208670    Answers: 2   Comments: 1

Find: ∫_0 ^( 5) (√((1/2) (x^2 − 2x + 1))) dx = ?

$$\mathrm{Find}:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{5}} \:\sqrt{\frac{\mathrm{1}}{\mathrm{2}}\:\left(\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{2x}\:+\:\mathrm{1}\right)}\:\mathrm{dx}\:\:=\:\:? \\ $$

Question Number 208662    Answers: 2   Comments: 0

(( ((n),(0) ) +3 ((n),(1) ) +5 ((n),(2) ) +...+(2n+1) ((n),(n) ))/( ((n),(1) ) +2 ((n),(2) ) + 3 ((n),(3) ) +...+n ((n),(n) ))) =((23)/(11)) n=?

$$\:\:\frac{\begin{pmatrix}{\mathrm{n}}\\{\mathrm{0}}\end{pmatrix}\:+\mathrm{3}\begin{pmatrix}{\mathrm{n}}\\{\mathrm{1}}\end{pmatrix}\:+\mathrm{5}\begin{pmatrix}{\mathrm{n}}\\{\mathrm{2}}\end{pmatrix}\:+...+\left(\mathrm{2n}+\mathrm{1}\right)\begin{pmatrix}{\mathrm{n}}\\{\mathrm{n}}\end{pmatrix}}{\begin{pmatrix}{\mathrm{n}}\\{\mathrm{1}}\end{pmatrix}\:+\mathrm{2}\begin{pmatrix}{\mathrm{n}}\\{\mathrm{2}}\end{pmatrix}\:+\:\mathrm{3}\begin{pmatrix}{\mathrm{n}}\\{\mathrm{3}}\end{pmatrix}\:+...+\mathrm{n}\begin{pmatrix}{\mathrm{n}}\\{\mathrm{n}}\end{pmatrix}}\:=\frac{\mathrm{23}}{\mathrm{11}} \\ $$$$\:\mathrm{n}=? \\ $$

Question Number 208661    Answers: 1   Comments: 0

⇃

$$\:\:\downharpoonleft\underline{\:} \\ $$

Question Number 208652    Answers: 1   Comments: 0

Question Number 208647    Answers: 1   Comments: 0

(tan^2 x − 3) ∙ sinx = 0 Find: x = ?

$$\left(\mathrm{tan}^{\mathrm{2}} \boldsymbol{\mathrm{x}}\:−\:\mathrm{3}\right)\:\centerdot\:\mathrm{sin}\boldsymbol{\mathrm{x}}\:=\:\mathrm{0} \\ $$$$\mathrm{Find}:\:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$

Question Number 208646    Answers: 1   Comments: 0

y = ∣x − 2∣ + ∣x + 4∣ Find: min(y) and max(y)

$$\mathrm{y}\:=\:\mid\mathrm{x}\:−\:\mathrm{2}\mid\:+\:\mid\mathrm{x}\:+\:\mathrm{4}\mid \\ $$$$\mathrm{Find}:\:\:\:\mathrm{min}\left(\mathrm{y}\right)\:\:\:\mathrm{and}\:\:\:\mathrm{max}\left(\mathrm{y}\right) \\ $$

Question Number 208645    Answers: 1   Comments: 0

Solve : 2x_1 − λ_1 − 5λ_2 = 0 2x_2 − λ_1 − 2λ_2 = 0 2x_3 − 3λ_1 − λ_2 = 0 Find the values of x_1 , x_2 , x_3 , λ_1 , and λ_2

$$\mathrm{Solve}\:: \\ $$$$\mathrm{2x}_{\mathrm{1}} \:−\:\lambda_{\mathrm{1}} \:−\:\mathrm{5}\lambda_{\mathrm{2}} \:=\:\mathrm{0} \\ $$$$\mathrm{2x}_{\mathrm{2}} \:−\:\lambda_{\mathrm{1}} \:−\:\mathrm{2}\lambda_{\mathrm{2}} \:=\:\mathrm{0} \\ $$$$\mathrm{2x}_{\mathrm{3}} \:−\:\mathrm{3}\lambda_{\mathrm{1}} \:−\:\lambda_{\mathrm{2}} \:=\:\mathrm{0} \\ $$$$ \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}_{\mathrm{1}} ,\:\mathrm{x}_{\mathrm{2}} ,\:\mathrm{x}_{\mathrm{3}} ,\:\lambda_{\mathrm{1}} ,\:\mathrm{and}\:\lambda_{\mathrm{2}} \\ $$

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