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Question Number 114922 Answers: 2 Comments: 0

find minimum value of function y=(√((x+6)^2 +25)) +(√((x−6)^2 +121))

$${find}\:{minimum}\:{value}\:{of}\:{function} \\ $$$${y}=\sqrt{\left({x}+\mathrm{6}\right)^{\mathrm{2}} +\mathrm{25}}\:+\sqrt{\left({x}−\mathrm{6}\right)^{\mathrm{2}} +\mathrm{121}} \\ $$

Question Number 114919 Answers: 0 Comments: 0

Question Number 114912 Answers: 0 Comments: 0

Question Number 114917 Answers: 0 Comments: 3

Question Number 114906 Answers: 3 Comments: 1

Question Number 114880 Answers: 1 Comments: 1

∫ln (sin (x))dx=?

$$\int\mathrm{ln}\:\left(\mathrm{sin}\:\left({x}\right)\right){dx}=? \\ $$

Question Number 114879 Answers: 1 Comments: 0

If the product of the matrices (((1 1)),((0 1)) ) (((1 2)),((0 1)) ) (((1 3)),((0 1)) )... (((1 k)),((0 1)) )= (((1 378)),((0 1)) ) then k =

$${If}\:{the}\:{product}\:{of}\:{the}\:{matrices}\: \\ $$$$\begin{pmatrix}{\mathrm{1}\:\:\:\mathrm{1}}\\{\mathrm{0}\:\:\:\mathrm{1}}\end{pmatrix}\begin{pmatrix}{\mathrm{1}\:\:\:\:\mathrm{2}}\\{\mathrm{0}\:\:\:\:\mathrm{1}}\end{pmatrix}\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\mathrm{3}}\\{\mathrm{0}\:\:\:\:\:\mathrm{1}}\end{pmatrix}...\begin{pmatrix}{\mathrm{1}\:\:\:\:\:{k}}\\{\mathrm{0}\:\:\:\:\:\mathrm{1}}\end{pmatrix}=\begin{pmatrix}{\mathrm{1}\:\:\:\:\mathrm{378}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$${then}\:{k}\:=\: \\ $$

Question Number 114878 Answers: 2 Comments: 0

Given f(x) = ∫_0 ^x (dt/( (√(1+t^3 )))) and g(x) be the inverse function of f(x), then g ′′(x)=λg^2 (x). then the value of λ =

$${Given}\:{f}\left({x}\right)\:=\:\underset{\mathrm{0}} {\overset{{x}} {\int}}\:\frac{{dt}}{\:\sqrt{\mathrm{1}+{t}^{\mathrm{3}} }}\:{and}\:{g}\left({x}\right)\:{be}\:{the} \\ $$$${inverse}\:{function}\:{of}\:{f}\left({x}\right),\:{then}\:{g}\:''\left({x}\right)=\lambda{g}^{\mathrm{2}} \left({x}\right). \\ $$$${then}\:{the}\:{value}\:{of}\:\lambda\:= \\ $$

Question Number 114876 Answers: 2 Comments: 1

Question Number 114875 Answers: 2 Comments: 0

A man sent 7 letters to his 7 friend . the letters are kept in addressed envelopes at random. the probability that 3 friends receive correct letters and 4 letters go to wrong destination is _ (old question unanswered)

$${A}\:{man}\:{sent}\:\mathrm{7}\:{letters}\:{to}\:{his}\:\mathrm{7}\:{friend}\:. \\ $$$${the}\:{letters}\:{are}\:{kept}\:{in}\:{addressed}\:{envelopes} \\ $$$${at}\:{random}.\:{the}\:{probability}\:{that}\:\mathrm{3}\:{friends} \\ $$$${receive}\:{correct}\:{letters}\:{and}\:\mathrm{4}\:{letters}\:{go} \\ $$$${to}\:{wrong}\:{destination}\:{is}\:\_ \\ $$$$ \\ $$$$\left({old}\:{question}\:{unanswered}\right) \\ $$

Question Number 114863 Answers: 1 Comments: 0

find four consecutive multiples of 5 such that twice the sum of the two greatest integer exceed five times the least by 5

$${find}\:{four}\:{consecutive}\:{multiples}\:{of}\:\mathrm{5} \\ $$$${such}\:{that}\:{twice}\:{the}\:{sum}\:{of}\:{the}\:{two} \\ $$$${greatest}\:{integer}\:{exceed}\:{five}\:{times}\:{the} \\ $$$${least}\:{by}\:\mathrm{5} \\ $$

Question Number 114860 Answers: 0 Comments: 3

Question Number 114858 Answers: 0 Comments: 0

prove Σ_(k=1) ^∞ (((H_k )^2 )/(k2^k ))=((7ζ(3))/8)

$${prove} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left({H}_{{k}} \right)^{\mathrm{2}} }{{k}\mathrm{2}^{{k}} }=\frac{\mathrm{7}\zeta\left(\mathrm{3}\right)}{\mathrm{8}} \\ $$

Question Number 114857 Answers: 0 Comments: 7

we know that e^(πi) = −1 ⇒ ln (e^(πi) ) = ln(−1) πi = ln (−1). How good is this prove?

$$\mathrm{we}\:\mathrm{know}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:{e}^{\pi{i}} \:=\:−\mathrm{1}\: \\ $$$$\Rightarrow\:\mathrm{ln}\:\left({e}^{\pi{i}} \right)\:=\:\mathrm{ln}\left(−\mathrm{1}\right) \\ $$$$\:\:\pi{i}\:=\:\mathrm{ln}\:\left(−\mathrm{1}\right).\: \\ $$$$\mathrm{How}\:\mathrm{good}\:\mathrm{is}\:\mathrm{this}\:\mathrm{prove}? \\ $$

Question Number 114850 Answers: 2 Comments: 1

a man hits a golf ball at the top of a cliff which is 40.0 m high. given that the ball falls into a water down cliff and he hears the sound 3 s after he hit the ball. what is the initial speed of the ball. take the speed of sound in air as 343 m/s. neglect air resistance.

$$\mathrm{a}\:\mathrm{man}\:\mathrm{hits}\:\mathrm{a}\:\mathrm{golf}\:\mathrm{ball}\:\mathrm{at}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{a}\:\mathrm{cliff} \\ $$$$\mathrm{which}\:\mathrm{is}\:\mathrm{40}.\mathrm{0}\:\mathrm{m}\:\mathrm{high}.\:\mathrm{given}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{ball}\:\mathrm{falls}\:\mathrm{into}\:\mathrm{a}\:\mathrm{water}\:\mathrm{down}\:\mathrm{cliff}\:\mathrm{and}\:\mathrm{he} \\ $$$$\mathrm{hears}\:\mathrm{the}\:\mathrm{sound}\:\mathrm{3}\:\mathrm{s}\:\mathrm{after}\:\mathrm{he}\:\mathrm{hit}\:\mathrm{the}\:\mathrm{ball}. \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{initial}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ball}.\:\mathrm{take} \\ $$$$\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{sound}\:\mathrm{in}\:\mathrm{air}\:\mathrm{as}\:\mathrm{343}\:\mathrm{m}/\mathrm{s}.\:\mathrm{neglect} \\ $$$$\mathrm{air}\:\mathrm{resistance}. \\ $$

Question Number 114840 Answers: 1 Comments: 0