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Question Number 69231 Answers: 0 Comments: 1

Prove that Σ_(p=0) ^∞ (((−1)^p )/(4p+1)) = ((π−argcoth((√2) ))/(4(√2))) and Σ_(p=0) ^(∞ ) (((−1)^p )/(4p+3)) = ((π+argcoth((√2) ))/(4(√2) ))

$${Prove}\:{that}\:\:\underset{{p}=\mathrm{0}} {\overset{\infty} {\sum}}\:\:\frac{\left(−\mathrm{1}\right)^{{p}} }{\mathrm{4}{p}+\mathrm{1}}\:=\:\frac{\pi−{argcoth}\left(\sqrt{\mathrm{2}}\:\right)}{\mathrm{4}\sqrt{\mathrm{2}}}\:\:{and} \\ $$$$\underset{{p}=\mathrm{0}} {\overset{\infty\:} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{{p}} }{\mathrm{4}{p}+\mathrm{3}}\:=\:\frac{\pi+{argcoth}\left(\sqrt{\mathrm{2}}\:\right)}{\mathrm{4}\sqrt{\mathrm{2}}\:}\:\:\: \\ $$

Question Number 69230 Answers: 0 Comments: 0

Question Number 69229 Answers: 0 Comments: 0

a, b, c ∈ nonnegative real numbers (√(a^2 + b^2 + 1)) + (√(b^2 + c^2 + 1)) + (√(c^2 + a^2 + 1)) ≥ 2 + (√(2(a^2 + b^2 + c^2 ) + 1)) Find all triplets (a, b, c) so that inequality above hold .

$${a},\:{b},\:{c}\:\:\in\:\:{nonnegative}\:\:{real}\:\:{numbers} \\ $$$$\sqrt{{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:+\:\mathrm{1}}\:+\:\sqrt{{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} \:+\:\mathrm{1}}\:+\:\sqrt{{c}^{\mathrm{2}} \:+\:{a}^{\mathrm{2}} \:+\:\mathrm{1}}\:\:\geqslant\:\:\mathrm{2}\:+\:\sqrt{\mathrm{2}\left({a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} \right)\:+\:\mathrm{1}} \\ $$$${Find}\:\:{all}\:\:{triplets}\:\left({a},\:{b},\:{c}\right)\:\:{so}\:\:{that}\:\:{inequality}\:\:{above}\:\:{hold}\:. \\ $$

Question Number 69226 Answers: 0 Comments: 0

Question Number 69222 Answers: 0 Comments: 1

Question Number 69212 Answers: 1 Comments: 0

use limit comparison test to determine the series converge or diverge Σ_(k=1) ^∞ ln(1+(1/k^2 ))

$${use}\:{limit}\:{comparison}\:{test}\:{to}\:{determine} \\ $$$${the}\:{series}\:{converge}\:{or}\:{diverge} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{{k}^{\mathrm{2}} }\right) \\ $$

Question Number 69207 Answers: 1 Comments: 3

help please. A river is 5m wide and flows at 3.0ms^(−1) . A man can swim at 2.0ms^(−1) in still water. if he sets off at an angle of 90° to the bank calculate a) the mans time and velocity b) his distance downstream from the starting point till when he reaches the other side of the river bank c) the actual distance he swims through the water.

$${help}\:{please}. \\ $$$$ \\ $$$${A}\:{river}\:{is}\:\mathrm{5}{m}\:{wide}\:{and}\:{flows}\:{at}\:\mathrm{3}.\mathrm{0}{ms}^{−\mathrm{1}} .\:{A}\:{man}\:{can}\:{swim}\:{at}\:\mathrm{2}.\mathrm{0}{ms}^{−\mathrm{1}} \\ $$$${in}\:{still}\:{water}.\:{if}\:{he}\:{sets}\:{off}\:{at}\:{an}\:{angle}\:{of}\:\mathrm{90}°\:{to}\:{the}\:{bank} \\ $$$${calculate} \\ $$$$\left.{a}\right)\:{the}\:{mans}\:{time}\:{and}\:{velocity} \\ $$$$\left.{b}\right)\:{his}\:{distance}\:{downstream}\:{from}\:{the}\:{starting}\:{point}\:{till} \\ $$$${when}\:{he}\:{reaches}\:{the}\:{other}\:{side}\:{of}\:{the}\:{river}\:{bank} \\ $$$$\left.{c}\right)\:{the}\:{actual}\:{distance}\:{he}\:{swims}\:{through}\:{the}\:{water}. \\ $$

Question Number 69211 Answers: 0 Comments: 0

To conserve rice from a cooperative there is a foil of area A=24cm^2 . The cooperatives want to build a barn in the shape of a parallelopiped square rectangle without cover. What should be the symmetrical dimensions for the volume to be maximum?

$${To}\:{conserve}\:{rice}\:{from}\:{a}\:{cooperative}\:{there}\:{is} \\ $$$${a}\:{foil}\:{of}\:{area}\:{A}=\mathrm{24}{cm}^{\mathrm{2}} .\:{The}\:{cooperatives} \\ $$$${want}\:{to}\:{build}\:{a}\:{barn}\:{in}\:{the}\:{shape}\:{of}\:{a}\:{parallelopiped} \\ $$$${square}\:{rectangle}\:{without}\:{cover}. \\ $$$${What}\:{should}\:{be}\:{the}\:{symmetrical}\:{dimensions}\:{for} \\ $$$${the}\:{volume}\:{to}\:{be}\:{maximum}? \\ $$

Question Number 69201 Answers: 2 Comments: 0

Question Number 69198 Answers: 0 Comments: 0

please someone check Q69159

$$\:{please}\:{someone}\:{check}\:\:{Q}\mathrm{69159} \\ $$

Question Number 69192 Answers: 1 Comments: 0

Question Number 69188 Answers: 2 Comments: 2

Question Number 69183 Answers: 1 Comments: 2

Question Number 69162 Answers: 1 Comments: 0

Find the local extreme values of the function : f(x,y)= xy−x^2 −y^2 −2x−2y+4.

$${Find}\:{the}\:{local}\:{extreme}\:{values}\:{of} \\ $$$${the}\:{function}\:: \\ $$$${f}\left({x},{y}\right)=\:{xy}−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{2}{y}+\mathrm{4}. \\ $$

Question Number 69159 Answers: 0 Comments: 0

please help A 7.38 g sample of magnesium sulfate MgSO_4 . X H_2 O lost 3.78g of water on heating, find the value of X.

$${please}\:{help}\: \\ $$$$\:{A}\:\mathrm{7}.\mathrm{38}\:{g}\:{sample}\:{of}\:{magnesium}\:{sulfate}\:{MgSO}_{\mathrm{4}} .\:{X}\:{H}_{\mathrm{2}} {O}\:{lost}\:\mathrm{3}.\mathrm{78}{g}\:{of} \\ $$$${water}\:{on}\:{heating},\:{find}\:{the}\:{value}\:{of}\:{X}. \\ $$

Question Number 69143 Answers: 0 Comments: 0

x^4 +ax^3 +bx^2 +cx+d=0 let x=f(t) linear perhaps t^4 +At^3 +Bt^2 +Ct+D=0 can we have 4AB=A^3 +8C solving at most a degree three polynomial ?

$${x}^{\mathrm{4}} +{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$$${let}\:\:{x}={f}\left({t}\right)\:\:{linear}\:{perhaps} \\ $$$${t}^{\mathrm{4}} +{At}^{\mathrm{3}} +{Bt}^{\mathrm{2}} +{Ct}+{D}=\mathrm{0} \\ $$$${can}\:{we}\:{have}\:\: \\ $$$$\:\:\:\mathrm{4}{AB}={A}^{\mathrm{3}} +\mathrm{8}{C}\:\:{solving}\:{at}\:{most} \\ $$$${a}\:{degree}\:{three}\:{polynomial}\:? \\ $$

Question Number 69176 Answers: 0 Comments: 1

difference of two complementary angles is 102^° .find two angles

$${difference}\:{of}\:{two}\:{complementary}\: \\ $$$${angles}\:{is}\:\mathrm{102}^{°} .{find}\:{two}\:{angles} \\ $$

Question Number 69175 Answers: 1 Comments: 0

if two finite sets have m and n term.if the no of subset of first set is 112 more then the no of subset of second set.find m and n?

$${if}\:{two}\:{finite}\:{sets}\:{have}\:{m}\:{and}\:{n}\:{term}.{if}\:{the}\:{no}\:{of}\:{subset}\:{of}\:{first}\:{set}\:{is}\:\mathrm{112}\:{more}\:{then}\:{the}\:{no}\:{of}\:{subset}\:{of}\:{second}\:{set}.{find}\:{m}\:{and}\:{n}? \\ $$

Question Number 69168 Answers: 0 Comments: 0

Question Number 69167 Answers: 1 Comments: 0

Question Number 69133 Answers: 0 Comments: 1

∫(x − tanx)^2 dx = ?

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\int\left(\boldsymbol{\mathrm{x}}\:−\:\boldsymbol{\mathrm{tanx}}\right)^{\mathrm{2}} \:\boldsymbol{\mathrm{dx}}\:\:=\:? \\ $$$$ \\ $$

Question Number 69130 Answers: 0 Comments: 3

9Σ_(k=4) ^n (1/(k^3 −6k^2 +11k−6))=?

$$\mathrm{9}\underset{\mathrm{k}=\mathrm{4}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{k}^{\mathrm{3}} −\mathrm{6k}^{\mathrm{2}} +\mathrm{11k}−\mathrm{6}}=? \\ $$$$\:\:\:\:\: \\ $$

Question Number 69123 Answers: 1 Comments: 0

Question Number 69116 Answers: 0 Comments: 0

Here are three propositions: − This sentence has exactly six words −There are two wrong propositions −The two previous sentences are correct Among that propositions ,how many are wrong? list them!

$$\:{Here}\:\:{are}\:{three}\:{propositions}:\: \\ $$$$−\:{This}\:{sentence}\:{has}\:{exactly}\:{six}\:{words} \\ $$$$−{There}\:{are}\:{two}\:{wrong}\:{propositions} \\ $$$$−{The}\:{two}\:{previous}\:{sentences}\:{are}\:{correct} \\ $$$$ \\ $$$${Among}\:{that}\:{propositions}\:,{how}\:{many}\:{are}\:{wrong}?\:{list}\:{them}! \\ $$

Question Number 69092 Answers: 1 Comments: 0

Question Number 69082 Answers: 1 Comments: 1

Solve x^2 = 16^x

$$\boldsymbol{{Solve}}\:\:\boldsymbol{{x}}^{\mathrm{2}} \:=\:\mathrm{16}^{\boldsymbol{{x}}} \\ $$

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