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Question Number 216827 Answers: 1 Comments: 1

Question Number 216821 Answers: 0 Comments: 0

Question Number 216820 Answers: 2 Comments: 0

f(x) = ax^4 + bx^3 + cx^2 + dx + e f(1) = 2 f(2) = 3 f(3) = 4 f(4) = 5 f(0) = 25 Then f(5) = ? Help me, please

$$ \\ $$$$\:\:\:{f}\left({x}\right)\:=\:{ax}^{\mathrm{4}} \:+\:{bx}^{\mathrm{3}} \:+\:{cx}^{\mathrm{2}} \:+\:{dx}\:+\:{e} \\ $$$$\:\:\:{f}\left(\mathrm{1}\right)\:=\:\mathrm{2} \\ $$$$\:\:\:{f}\left(\mathrm{2}\right)\:=\:\mathrm{3} \\ $$$$\:\:\:{f}\left(\mathrm{3}\right)\:=\:\mathrm{4} \\ $$$$\:\:\:{f}\left(\mathrm{4}\right)\:=\:\mathrm{5}\: \\ $$$$\:\:\:{f}\left(\mathrm{0}\right)\:=\:\mathrm{25} \\ $$$$\:\:\:\mathcal{T}{hen}\:\:{f}\left(\mathrm{5}\right)\:=\:? \\ $$$$\:\:\:\mathcal{H}{elp}\:{me},\:\:{please} \\ $$$$ \\ $$

Question Number 216819 Answers: 1 Comments: 0

Prove:∫_(0 ) ^1 ((K(x))/( (√(3−x))))dx=(1/(96π(√3)))×Γ((1/(24)))Γ((3/(24)))Γ((7/(24)))Γ(((11)/(24)))

$$\mathrm{Prove}:\int_{\mathrm{0}\:} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{K}}\left({x}\right)}{\:\sqrt{\mathrm{3}−{x}}}{dx}=\frac{\mathrm{1}}{\mathrm{96}\pi\sqrt{\mathrm{3}}}×\Gamma\left(\frac{\mathrm{1}}{\mathrm{24}}\right)\Gamma\left(\frac{\mathrm{3}}{\mathrm{24}}\right)\Gamma\left(\frac{\mathrm{7}}{\mathrm{24}}\right)\Gamma\left(\frac{\mathrm{11}}{\mathrm{24}}\right) \\ $$

Question Number 216810 Answers: 0 Comments: 1

40 random numbers picked from 0 to 100. what is the probability that at least half of them has the range of 10.

$$ \\ $$40 random numbers picked from 0 to 100. what is the probability that at least half of them has the range of 10.

Question Number 216800 Answers: 1 Comments: 0

Question Number 216799 Answers: 1 Comments: 1

Question Number 216807 Answers: 1 Comments: 0

Uh guys is the speed formula (d/t) or lim_(Δt→0) ((Δd)/(Δt))

$$\mathrm{Uh}\:\mathrm{guys}\:\mathrm{is}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{formula} \\ $$$$\frac{{d}}{{t}} \\ $$$$\mathrm{or} \\ $$$$\mathrm{li}\underset{\Delta{t}\rightarrow\mathrm{0}} {\mathrm{m}}\frac{\Delta{d}}{\Delta{t}} \\ $$

Question Number 216792 Answers: 0 Comments: 0

Question Number 216788 Answers: 1 Comments: 1

Question Number 216787 Answers: 1 Comments: 0

form the differential equationfrom the following 1) y=Ae^(3x) +Be^(5x) 2) y^2 =(x−1) 3) c(y+c)^2 +x^3 =0

$${form}\:{the}\:{differential}\:{equationfrom}\:{the}\:{following} \\ $$$$\left.\mathrm{1}\right)\:{y}={Ae}^{\mathrm{3}{x}} +{Be}^{\mathrm{5}{x}} \\ $$$$\left.\mathrm{2}\right)\:{y}^{\mathrm{2}} =\left({x}−\mathrm{1}\right) \\ $$$$\left.\mathrm{3}\right)\:{c}\left({y}+{c}\right)^{\mathrm{2}} +{x}^{\mathrm{3}} =\mathrm{0} \\ $$

Question Number 216786 Answers: 1 Comments: 0

Question Number 216785 Answers: 0 Comments: 0

given the recursive {a_n } define by setting a_(1 ) ∈ (0,1) , a_(n+1) = a_n (1−a_n ) , n≥1 prove that (1) lim_(n→∞) na_n = 1 (2) b_n = n(1−na_n ) is a incresing sequence and diverge to ∞ (3) lim_(n→∞) ((n(1−na_n ))/(ln(n))) = 1

$$\:\:\:\mathrm{given}\:\mathrm{the}\:\mathrm{recursive}\:\left\{\mathrm{a}_{\mathrm{n}} \right\}\:\mathrm{define}\:\mathrm{by}\:\mathrm{setting} \\ $$$$\:\:\mathrm{a}_{\mathrm{1}\:} \:\in\:\left(\mathrm{0},\mathrm{1}\right)\:\:\:,\:\:\:\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:=\:\mathrm{a}_{\mathrm{n}} \left(\mathrm{1}−\mathrm{a}_{\mathrm{n}} \right)\:\:\:,\:\mathrm{n}\geqslant\mathrm{1} \\ $$$$\:\:\mathrm{prove}\:\mathrm{that}\:\:\left(\mathrm{1}\right)\:\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{na}_{\mathrm{n}} =\:\mathrm{1} \\ $$$$\:\:\left(\mathrm{2}\right)\:\:\mathrm{b}_{\mathrm{n}} \:=\:\mathrm{n}\left(\mathrm{1}−\mathrm{na}_{\mathrm{n}} \right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{incresing}\:\mathrm{sequence} \\ $$$$\:\:\:\mathrm{and}\:\mathrm{diverge}\:\mathrm{to}\:\infty \\ $$$$\:\:\:\left(\mathrm{3}\right)\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{n}\left(\mathrm{1}−\mathrm{na}_{\mathrm{n}} \right)}{\mathrm{ln}\left(\mathrm{n}\right)}\:=\:\mathrm{1} \\ $$

Question Number 216783 Answers: 3 Comments: 0

Find all positive integers n such that n^2 +7n+6 is perfect square.

$${Find}\:{all}\:{positive}\:{integers}\:{n}\:{such}\:{that} \\ $$$${n}^{\mathrm{2}} +\mathrm{7}{n}+\mathrm{6}\:{is}\:{perfect}\:{square}. \\ $$

Question Number 216776 Answers: 1 Comments: 0

Question Number 216774 Answers: 1 Comments: 0

find ∫ ((tan^2 (x) )/(1+sec^4 (x))) .dx

$$\:\:\boldsymbol{{find}}\:\int\:\frac{\boldsymbol{{tan}}^{\mathrm{2}} \left(\boldsymbol{{x}}\right)\:}{\mathrm{1}+\boldsymbol{{sec}}^{\mathrm{4}} \left(\boldsymbol{{x}}\right)}\:.\boldsymbol{{dx}}\: \\ $$

Question Number 216772 Answers: 2 Comments: 0

find ∫((tan^2 (x) )/(1−sec^4 (x))) .dx

$$\:\:\boldsymbol{{find}}\:\int\frac{\boldsymbol{{tan}}^{\mathrm{2}} \left(\boldsymbol{{x}}\right)\:}{\mathrm{1}−\boldsymbol{{sec}}^{\mathrm{4}} \left(\boldsymbol{{x}}\right)}\:.\boldsymbol{{dx}}\:\: \\ $$

Question Number 216769 Answers: 1 Comments: 0

Solve for integer k,m and n: k^2 m−n^2 =8

$${Solve}\:{for}\:{integer}\:{k},{m}\:{and}\:{n}: \\ $$$${k}^{\mathrm{2}} {m}−{n}^{\mathrm{2}} =\mathrm{8} \\ $$

Question Number 216764 Answers: 1 Comments: 0

solve x? (√x) + 11 = 0

$${solve}\:{x}? \\ $$$$\sqrt{{x}}\:+\:\mathrm{11}\:=\:\mathrm{0} \\ $$

Question Number 216755 Answers: 1 Comments: 0

Question Number 216754 Answers: 2 Comments: 0

∫_( 0) ^( 1) ((x ln^2 (x))/(1 + x^2 )) dx

$$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{x}\:\mathrm{ln}^{\mathrm{2}} \left(\mathrm{x}\right)}{\mathrm{1}\:+\:\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$

Question Number 216751 Answers: 0 Comments: 0

Find Card{(A,B,C)∈P(E)^3 / AUBUC=E}

$${Find}\:\:\:{Card}\left\{\left({A},{B},{C}\right)\in{P}\left({E}\right)^{\mathrm{3}} /\:{AUBUC}={E}\right\} \\ $$

Question Number 216750 Answers: 1 Comments: 0

If a−b=(√(ab)) find the value of ((a−b)/(a+b))

$${If}\:\:{a}−{b}=\sqrt{{ab}}\:\:\:{find}\:\:\:{the}\:{value}\:{of}\:\frac{{a}−{b}}{{a}+{b}} \\ $$

Question Number 216749 Answers: 2 Comments: 0

Find ∫_0 ^∞ (((−1)^(E(x)) )/(E(−x)))dx

$${Find}\:\:\int_{\mathrm{0}} ^{\infty} \frac{\left(−\mathrm{1}\right)^{{E}\left({x}\right)} }{{E}\left(−{x}\right)}{dx} \\ $$

Question Number 216748 Answers: 1 Comments: 0

Find ∫_(−1) ^1 ln∣Γ((1/2)+it)∣dt

$${Find}\:\:\int_{−\mathrm{1}} ^{\mathrm{1}} {ln}\mid\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}+{it}\right)\mid{dt} \\ $$

Question Number 216746 Answers: 0 Comments: 0

Calculate (((5+i)^4 )/(239+i)) Then Prove the Machin formula 4arctan((1/5))−arctan((1/(239)))=(π/4)

$${Calculate}\:\frac{\left(\mathrm{5}+{i}\right)^{\mathrm{4}} }{\mathrm{239}+{i}}\:{Then}\: \\ $$$${Prove}\:{the}\:{Machin}\:{formula} \\ $$$$\mathrm{4}{arctan}\left(\frac{\mathrm{1}}{\mathrm{5}}\right)−{arctan}\left(\frac{\mathrm{1}}{\mathrm{239}}\right)=\frac{\pi}{\mathrm{4}} \\ $$

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