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Question Number 87767 Answers: 0 Comments: 1

Question Number 87759 Answers: 0 Comments: 2

Question Number 87757 Answers: 0 Comments: 2

∫_a ^b ((√(x−a))/(√(b−x))) dx =?

$$\int_{\mathrm{a}} ^{\mathrm{b}} \:\frac{\sqrt{\mathrm{x}−\mathrm{a}}}{\sqrt{\mathrm{b}−\mathrm{x}}}\:\mathrm{dx}\:=?\: \\ $$

Question Number 87755 Answers: 0 Comments: 2

f(((x−3)/(x+1))) + f(((x+3)/(1−x))) = x find f(x)

$$\mathrm{f}\left(\frac{\mathrm{x}−\mathrm{3}}{\mathrm{x}+\mathrm{1}}\right)\:+\:\mathrm{f}\left(\frac{\mathrm{x}+\mathrm{3}}{\mathrm{1}−\mathrm{x}}\right)\:=\:\mathrm{x} \\ $$$$\mathrm{find}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$

Question Number 87754 Answers: 0 Comments: 0

Given that forces F_(1 ) and F_2 position vectors r_(1 ) and r_2 F_1 = (2i + 3j)N r_1 = i + 2j F_2 = (αi−7j) N r_2 = 3i + 4j Given that these system of forces form a couple find the value of α.

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{forces}\:\mathrm{F}_{\mathrm{1}\:} \:\mathrm{and}\:\mathrm{F}_{\mathrm{2}} \:\mathrm{position}\:\mathrm{vectors}\:\mathrm{r}_{\mathrm{1}\:} \mathrm{and}\:\mathrm{r}_{\mathrm{2}} \\ $$$$\:\:\boldsymbol{\mathrm{F}}_{\mathrm{1}} \:=\:\left(\mathrm{2}\boldsymbol{{i}}\:+\:\mathrm{3}\boldsymbol{{j}}\right)\mathrm{N}\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{r}}_{\mathrm{1}} =\:\boldsymbol{\mathrm{i}}\:+\:\mathrm{2}\boldsymbol{\mathrm{j}} \\ $$$$\:\:\:\boldsymbol{\mathrm{F}}_{\mathrm{2}} \:=\:\left(\alpha\boldsymbol{{i}}−\mathrm{7}\boldsymbol{{j}}\right)\:\mathrm{N}\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{r}}_{\mathrm{2}} \:=\:\mathrm{3}\boldsymbol{\mathrm{i}}\:+\:\mathrm{4}\boldsymbol{\mathrm{j}} \\ $$$$\mathrm{Given}\:\mathrm{that}\:\mathrm{these}\:\mathrm{system}\:\mathrm{of}\:\mathrm{forces}\:\mathrm{form}\:\mathrm{a}\:\mathrm{couple} \\ $$$$\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\alpha. \\ $$

Question Number 87752 Answers: 1 Comments: 0

A particle exhibits simple hamornic motion such that (d^2 x/dt^2 ) + 4x = 0 Calculate the period of the ocsillation

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{exhibits}\:\mathrm{simple}\:\mathrm{hamornic}\:\mathrm{motion}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\frac{{d}^{\mathrm{2}} {x}}{{dt}^{\mathrm{2}} }\:+\:\mathrm{4}{x}\:=\:\mathrm{0} \\ $$$$\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{period}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ocsillation}\: \\ $$

Question Number 87751 Answers: 0 Comments: 2

find in the form y= f(x) the general solution of the differentail equation (d^2 y/dx^2 ) −(dy/dx)−6y = e^(3x)

$$\mathrm{find}\:\mathrm{in}\:\mathrm{the}\:\mathrm{form}\:{y}=\:{f}\left({x}\right)\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\: \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{differentail}\:\mathrm{equation} \\ $$$$\:\:\:\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:−\frac{{dy}}{{dx}}−\mathrm{6}{y}\:=\:{e}^{\mathrm{3}{x}} \\ $$$$ \\ $$

Question Number 87737 Answers: 1 Comments: 0

solve sin((π/([(([x])/4)])))=(1/2)

$${solve} \\ $$$${sin}\left(\frac{\pi}{\left[\frac{\left[{x}\right]}{\mathrm{4}}\right]}\right)=\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 87733 Answers: 1 Comments: 2

Question Number 87732 Answers: 0 Comments: 1

Solve it in N C_n ^3 −C_n ^2 =5+((n^3 −6n^2 )/6)

$$\mathrm{Solve}\:\mathrm{it}\:\mathrm{in}\:\mathbb{N} \\ $$$$\mathrm{C}_{\mathrm{n}} ^{\mathrm{3}} −\mathrm{C}_{\mathrm{n}} ^{\mathrm{2}} =\mathrm{5}+\frac{\mathrm{n}^{\mathrm{3}} −\mathrm{6n}^{\mathrm{2}} }{\mathrm{6}} \\ $$

Question Number 87731 Answers: 0 Comments: 1

solve in N A_n ^4 =A_n ^3

$$\mathrm{solve}\:\mathrm{in}\:\mathbb{N} \\ $$$$\mathrm{A}_{\mathrm{n}} ^{\mathrm{4}} =\mathrm{A}_{\mathrm{n}} ^{\mathrm{3}} \\ $$

Question Number 87726 Answers: 0 Comments: 0

Question Number 87724 Answers: 1 Comments: 0

solve the equation sin^(−1) (cos ⌊x⌋)=1

$${solve}\:{the}\:{equation} \\ $$$$\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{sin}}^{−\mathrm{1}} \left(\boldsymbol{\mathrm{cos}}\:\lfloor\boldsymbol{{x}}\rfloor\right)=\mathrm{1} \\ $$

Question Number 87723 Answers: 1 Comments: 0

∫((1/(x−1))+((Σ_(k=0) ^(2018) (k+1)x^k )/(Σ_(k=0) ^(2019) x^k )))dx

$$\int\left(\frac{\mathrm{1}}{{x}−\mathrm{1}}+\frac{\underset{{k}=\mathrm{0}} {\overset{\mathrm{2018}} {\sum}}\left({k}+\mathrm{1}\right){x}^{{k}} }{\underset{{k}=\mathrm{0}} {\overset{\mathrm{2019}} {\sum}}{x}^{{k}} }\right){dx} \\ $$

Question Number 87716 Answers: 1 Comments: 1

Question Number 87711 Answers: 1 Comments: 2

∫_0 ^∞ ((1−xe^(−x) −e^(−x) )/(x(e^x −e^(−x) )))dx

$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}−{xe}^{−{x}} −{e}^{−{x}} }{{x}\left({e}^{{x}} −{e}^{−{x}} \right)}{dx} \\ $$

Question Number 87709 Answers: 0 Comments: 0

sbow that ∫_1 ^∞ (([3x])/(([x])!))dx=4e−1

$${sbow}\:{that} \\ $$$$\int_{\mathrm{1}} ^{\infty} \frac{\left[\mathrm{3}{x}\right]}{\left(\left[{x}\right]\right)!}{dx}=\mathrm{4}{e}−\mathrm{1} \\ $$

Question Number 87692 Answers: 0 Comments: 8

sir Ma?h+t?que you have posted ∫(dx/(((x+1)....(x+n))^2 ))=......can you reposted it please

$${sir}\:{Ma}?{h}+{t}?{que}\:{you}\:{have}\:{posted} \\ $$$$\int\frac{{dx}}{\left(\left({x}+\mathrm{1}\right)....\left({x}+{n}\right)\right)^{\mathrm{2}} }=......{can}\:{you}\:{reposted}\:{it}\:{please} \\ $$

Question Number 87690 Answers: 1 Comments: 4

lim_(x→0) ((2sin x−sin 2x)/(x−sin x))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2sin}\:\mathrm{x}−\mathrm{sin}\:\mathrm{2x}}{\mathrm{x}−\mathrm{sin}\:\mathrm{x}} \\ $$

Question Number 87687 Answers: 1 Comments: 0

Let w=[1;(π/n)] ,n∈N^∗ a_n =Σ_(p=0) ^(n−1) ((2p+1)/(1−w^(2p+1) )) and b_n =Σ_(p=0) ^(n−1) (n/(1+w^p )) Find all integer n such as a_n =b_n

$${Let}\:\:{w}=\left[\mathrm{1};\frac{\pi}{{n}}\right]\:,{n}\in\mathbb{N}^{\ast} \: \\ $$$$\:{a}_{{n}} =\underset{{p}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\sum}}\:\frac{\mathrm{2}{p}+\mathrm{1}}{\mathrm{1}−{w}^{\mathrm{2}{p}+\mathrm{1}} }\:\:\:\:{and}\:\:\:{b}_{{n}} =\underset{{p}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\sum}}\:\frac{{n}}{\mathrm{1}+{w}^{{p}} }\: \\ $$$${Find}\:\:{all}\:{integer}\:{n}\:{such}\:{as}\:\:{a}_{{n}} ={b}_{{n}} \: \\ $$

Question Number 87686 Answers: 3 Comments: 0

∫(√((ln(x+(√(1+x^2 ))))/(1+x^2 ))) dx

$$\int\sqrt{\frac{{ln}\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)}{\mathrm{1}+{x}^{\mathrm{2}} }}\:{dx} \\ $$

Question Number 87682 Answers: 0 Comments: 0

what is ▽^2 ((1/r^→ )) if ▽^→ = i^ (∂/∂x)+j^ (∂/∂y)+k^ (∂/∂z) and r^→ = i^ x + j^ y + k^ z

$$\mathrm{what}\:\mathrm{is}\:\bigtriangledown^{\mathrm{2}} \left(\frac{\mathrm{1}}{\overset{\rightarrow} {\mathrm{r}}}\right)\:\mathrm{if}\: \\ $$$$\overset{\rightarrow} {\bigtriangledown}\:=\:\hat {\mathrm{i}}\:\frac{\partial}{\partial\mathrm{x}}+\hat {\mathrm{j}}\frac{\partial}{\partial\mathrm{y}}+\hat {\mathrm{k}}\:\frac{\partial}{\partial\mathrm{z}} \\ $$$$\mathrm{and}\:\overset{\rightarrow} {\mathrm{r}}\:=\:\hat {\mathrm{i}x}\:+\:\hat {\mathrm{j}y}\:+\:\hat {\mathrm{k}z}\: \\ $$

Question Number 87671 Answers: 1 Comments: 3

Question Number 87669 Answers: 1 Comments: 4

∫_2 ^( e) ((1/(ln x))−(1/(ln^2 x))) dx?

$$\int_{\mathrm{2}} ^{\:\:\mathrm{e}} \left(\frac{\mathrm{1}}{\mathrm{ln}\:\mathrm{x}}−\frac{\mathrm{1}}{\mathrm{ln}^{\mathrm{2}} \mathrm{x}}\right)\:\mathrm{dx}? \\ $$

Question Number 87648 Answers: 0 Comments: 4

the sequence a_1 ,a_2 ,a_3 , ... satisfies the relation a_(n+1) = a_n +a_(n−1) , for n>1. given that a_(20) = 6765 and a_(18) = 2584 what is a_(16)

$$\mathrm{the}\:\mathrm{sequence}\:\mathrm{a}_{\mathrm{1}} ,\mathrm{a}_{\mathrm{2}} ,\mathrm{a}_{\mathrm{3}} ,\:...\:\mathrm{satisfies} \\ $$$$\mathrm{the}\:\mathrm{relation}\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:=\:\mathrm{a}_{\mathrm{n}} +\mathrm{a}_{\mathrm{n}−\mathrm{1}} \:,\:\mathrm{for} \\ $$$$\mathrm{n}>\mathrm{1}.\:\mathrm{given}\:\mathrm{that}\:\mathrm{a}_{\mathrm{20}} \:=\:\mathrm{6765}\:\mathrm{and} \\ $$$$\mathrm{a}_{\mathrm{18}} \:=\:\mathrm{2584}\:\mathrm{what}\:\mathrm{is}\:\mathrm{a}_{\mathrm{16}} \\ $$

Question Number 87647 Answers: 1 Comments: 0

If a_1 = 1 , a_(n+1 ) = 2a_n + 5 , n = 1,2,3,.... then a_(100) = ?

$$\mathrm{If}\:\mathrm{a}_{\mathrm{1}} \:=\:\mathrm{1}\:,\:\mathrm{a}_{\mathrm{n}+\mathrm{1}\:} =\:\mathrm{2a}_{\mathrm{n}} \:+\:\mathrm{5}\:,\:\mathrm{n}\:=\: \\ $$$$\mathrm{1},\mathrm{2},\mathrm{3},....\:\mathrm{then}\:\mathrm{a}_{\mathrm{100}} \:=\:? \\ $$

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