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AllQuestion and Answers: Page 651

Question Number 153050 Answers: 1 Comments: 0

Question Number 153046 Answers: 2 Comments: 1

Question Number 153041 Answers: 3 Comments: 0

A ball is thrown vertically upwards with a velocity of 10 ms^(−1) from a point 75m above the ground. How long will it take the ball to strike the ground?

$$\mathrm{A}\:\mathrm{ball}\:\mathrm{is}\:\mathrm{thrown}\:\mathrm{vertically}\:\mathrm{upwards} \\ $$$$\mathrm{with}\:\mathrm{a}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{10}\:{ms}^{−\mathrm{1}} \:\mathrm{from}\:\mathrm{a}\:\mathrm{point} \\ $$$$\mathrm{75}{m}\:\mathrm{above}\:\mathrm{the}\:\mathrm{ground}.\:\mathrm{How}\:\mathrm{long}\:\mathrm{will} \\ $$$$\mathrm{it}\:\mathrm{take}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{to}\:\mathrm{strike}\:\mathrm{the}\:\mathrm{ground}? \\ $$

Question Number 153040 Answers: 0 Comments: 0

prove that.. Ω =∫_0 ^( ∞) (( sin (x ))/(sinh(x)))dx =(π/2) tanh ((π/2))

$$ \\ $$$$\:{prove}\:{that}.. \\ $$$$ \\ $$$$\Omega\:=\int_{\mathrm{0}} ^{\:\infty} \frac{\:{sin}\:\left({x}\:\right)}{{sinh}\left({x}\right)}{dx}\:=\frac{\pi}{\mathrm{2}}\:{tanh}\:\left(\frac{\pi}{\mathrm{2}}\right)\:\: \\ $$

Question Number 153039 Answers: 1 Comments: 0

lim_(x→0) ((x(e^x +1)−2(e^x −1))/x^3 ) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\left({e}^{{x}} +\mathrm{1}\right)−\mathrm{2}\left({e}^{{x}} −\mathrm{1}\right)}{{x}^{\mathrm{3}} }\:=\:? \\ $$

Question Number 153038 Answers: 1 Comments: 0

Question Number 153033 Answers: 2 Comments: 0

y=log (1+cos x) (dy/dx)=

$${y}=\mathrm{log}\:\left(\mathrm{1}+\mathrm{cos}\:{x}\right) \\ $$$$\frac{{dy}}{{dx}}= \\ $$

Question Number 153030 Answers: 0 Comments: 0

Question Number 153108 Answers: 1 Comments: 0

∫(dθ/(sin^2 θ(3−sin θ)))

$$\int\frac{\mathrm{d}\theta}{\mathrm{sin}\:^{\mathrm{2}} \theta\left(\mathrm{3}−\mathrm{sin}\:\theta\right)} \\ $$

Question Number 153109 Answers: 0 Comments: 1

∫(dx/(x^2 +2x+2(√(x^2 +2x−4))))

$$\int\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{2}\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}−\mathrm{4}}} \\ $$

Question Number 153019 Answers: 0 Comments: 0

Determine all functions f:R→(1;+∞) continuous such that f(4x) ∙ f(3x) = 2^x ; ∀x∈R

$$\mathrm{Determine}\:\mathrm{all}\:\mathrm{functions}\:\:\mathrm{f}:\mathbb{R}\rightarrow\left(\mathrm{1};+\infty\right) \\ $$$$\mathrm{continuous}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{f}\left(\mathrm{4x}\right)\:\centerdot\:\mathrm{f}\left(\mathrm{3x}\right)\:=\:\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:\:;\:\:\forall\mathrm{x}\in\mathbb{R} \\ $$

Question Number 153016 Answers: 1 Comments: 2

∫_0 ^2 xe^(4−x^2 ) dx

$$\int_{\mathrm{0}} ^{\mathrm{2}} \mathrm{xe}^{\mathrm{4}−\mathrm{x}^{\mathrm{2}} } \mathrm{dx} \\ $$

Question Number 153012 Answers: 0 Comments: 1

Find all ordered pairs of real numbers (x,y) for which { (((1+x^4 )(1+x^2 )(1+x)=1+y^7 )),(((1+y^4 )(1+y^2 )(1+y)=1+x^7 )) :}

$$\:{Find}\:{all}\:{ordered}\:{pairs}\:{of}\:{real}\: \\ $$$$\:{numbers}\:\left({x},{y}\right)\:{for}\:{which} \\ $$$$\:\:\begin{cases}{\left(\mathrm{1}+{x}^{\mathrm{4}} \right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}\right)=\mathrm{1}+{y}^{\mathrm{7}} }\\{\left(\mathrm{1}+{y}^{\mathrm{4}} \right)\left(\mathrm{1}+{y}^{\mathrm{2}} \right)\left(\mathrm{1}+{y}\right)=\mathrm{1}+{x}^{\mathrm{7}} }\end{cases} \\ $$

Question Number 153009 Answers: 3 Comments: 2

montrer que: 2cos(π/2^n )=(√(2 +(√(2+...+(√2)))))

$${montrer}\:{que}: \\ $$$$\mathrm{2}{cos}\frac{\pi}{\mathrm{2}^{{n}} }=\sqrt{\mathrm{2}\:+\sqrt{\mathrm{2}+...+\sqrt{\mathrm{2}}}} \\ $$$$ \\ $$

Question Number 153006 Answers: 1 Comments: 8

prove that 4!!=8 please help

$${prove}\:{that}\: \\ $$$$\mathrm{4}!!=\mathrm{8} \\ $$$${please}\:{help} \\ $$

Question Number 152993 Answers: 3 Comments: 1

Question Number 152985 Answers: 0 Comments: 2

Question Number 152976 Answers: 0 Comments: 0

Question Number 152974 Answers: 0 Comments: 6

Question Number 153093 Answers: 1 Comments: 1

Find the solution of three variables equality system x, y, z . a^3 + a^2 x + ay + z = 0 b^3 + b^2 x + by + z = 0 c^3 + c^2 x + cy + z = 0 Thank you so much

$${Find}\:\:{the}\:\:{solution}\:\:{of}\:\:{three}\:\:{variables}\:\:{equality}\:\:{system}\:\:{x},\:{y},\:{z}\:. \\ $$$$\:\:{a}^{\mathrm{3}} \:+\:{a}^{\mathrm{2}} {x}\:+\:{ay}\:+\:{z}\:=\:\mathrm{0} \\ $$$$\:\:{b}^{\mathrm{3}} \:+\:{b}^{\mathrm{2}} {x}\:+\:{by}\:+\:{z}\:=\:\mathrm{0} \\ $$$$\:\:{c}^{\mathrm{3}} \:+\:{c}^{\mathrm{2}} {x}\:+\:{cy}\:+\:{z}\:=\:\mathrm{0} \\ $$$$ \\ $$$${Thank}\:\:{you}\:\:{so}\:\:{much} \\ $$

Question Number 152971 Answers: 0 Comments: 0

Question Number 152960 Answers: 1 Comments: 0

Find the values for b and c given that the quadratic expression x^2 +bx+c<0 {x:−1<x>3}

$$\:\: \\ $$$$\:\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{for}\:\mathrm{b}\:\mathrm{and}\:\mathrm{c}\:\mathrm{given} \\ $$$$\:\:\:\:\mathrm{that}\:\mathrm{the}\:\mathrm{quadratic}\:\mathrm{expression} \\ $$$$\:\:\:\:{x}^{\mathrm{2}} +\mathrm{b}{x}+\mathrm{c}<\mathrm{0}\: \\ $$$$\:\:\:\:\left\{{x}:−\mathrm{1}<{x}>\mathrm{3}\right\} \\ $$$$\: \\ $$

Question Number 153392 Answers: 0 Comments: 1

Σ_(k=1) ^n k^a =?

$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}^{{a}} =?\:\:\: \\ $$

Question Number 152950 Answers: 0 Comments: 1

((1/2))+((1/3)+(2/3))+((1/4)+(2/4)+(3/4))+...+((1/8)+(2/8)+...+(7/8))=?

$$\left(\frac{\mathrm{1}}{\mathrm{2}}\right)+\left(\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{2}}{\mathrm{3}}\right)+\left(\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{2}}{\mathrm{4}}+\frac{\mathrm{3}}{\mathrm{4}}\right)+...+\left(\frac{\mathrm{1}}{\mathrm{8}}+\frac{\mathrm{2}}{\mathrm{8}}+...+\frac{\mathrm{7}}{\mathrm{8}}\right)=? \\ $$

Question Number 152949 Answers: 1 Comments: 0

Question Number 152947 Answers: 1 Comments: 0

prove :: 𝛗=∫_(−∞) ^( ∞) (( e^( −(1/x^( 2) )) )/x^( 4) ) dx =^? (1/2) Γ ((1/2) )

$$ \\ $$$$\:\:\:{prove}\::: \\ $$$$\:\:\:\boldsymbol{\phi}=\int_{−\infty} ^{\:\infty} \:\frac{\:{e}^{\:−\frac{\mathrm{1}}{{x}^{\:\mathrm{2}} }} }{{x}^{\:\mathrm{4}} }\:{dx}\:\overset{?} {=}\:\frac{\mathrm{1}}{\mathrm{2}}\:\Gamma\:\left(\frac{\mathrm{1}}{\mathrm{2}}\:\right) \\ $$$$ \\ $$

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