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AlgebraQuestion and Answers: Page 271

Question Number 90318 Answers: 0 Comments: 0

Please can this be resolve in partial fraction? ((sec^2 x − (2/x^2 ))/((tan x + (1/x))^2 ))

$$\mathrm{Please}\:\mathrm{can}\:\mathrm{this}\:\mathrm{be}\:\mathrm{resolve}\:\mathrm{in}\:\mathrm{partial}\:\mathrm{fraction}? \\ $$$$\:\:\:\:\:\:\frac{\mathrm{sec}^{\mathrm{2}} \mathrm{x}\:\:−\:\:\frac{\mathrm{2}}{\mathrm{x}^{\mathrm{2}} }}{\left(\mathrm{tan}\:\mathrm{x}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{2}} } \\ $$

Question Number 90251 Answers: 1 Comments: 2

(1/(1!))+((1^2 +2^2 )/(2!))+((1^2 +2^2 +3^2 )/(3!))+.......= ???

$$\frac{\mathrm{1}}{\mathrm{1}!}+\frac{\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} }{\mathrm{2}!}+\frac{\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} }{\mathrm{3}!}+.......=\:??? \\ $$

Question Number 90240 Answers: 0 Comments: 0

solve (d^2 y/dx^2 )+x(dy/dx)+xy=x^3

$${solve} \\ $$$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+{x}\frac{{dy}}{{dx}}+{xy}={x}^{\mathrm{3}} \\ $$$$ \\ $$

Question Number 90225 Answers: 0 Comments: 3

x+y+z = 4 z+t+x = −3 y+z+t = 4 t+x+y = 1 find the value of x^2 +y^2 +z^2 +t^2

$$\mathrm{x}+\mathrm{y}+\mathrm{z}\:=\:\mathrm{4} \\ $$$$\mathrm{z}+\mathrm{t}+\mathrm{x}\:=\:−\mathrm{3} \\ $$$$\mathrm{y}+\mathrm{z}+\mathrm{t}\:=\:\mathrm{4} \\ $$$$\mathrm{t}+\mathrm{x}+\mathrm{y}\:=\:\mathrm{1} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} +\mathrm{t}^{\mathrm{2}} \: \\ $$

Question Number 90212 Answers: 0 Comments: 4

if x^2 = 5x+1 find E = (((x^3 −140) (x^(11) )^(1/(3 )) )/((x^4 +1))^(1/(3 )) )

$${if}\:{x}^{\mathrm{2}} \:=\:\mathrm{5}{x}+\mathrm{1}\: \\ $$$${find}\:{E}\:=\:\frac{\left({x}^{\mathrm{3}} −\mathrm{140}\right)\:\sqrt[{\mathrm{3}\:\:}]{{x}^{\mathrm{11}} }}{\sqrt[{\mathrm{3}\:\:}]{{x}^{\mathrm{4}} +\mathrm{1}}} \\ $$

Question Number 90195 Answers: 0 Comments: 0

Question Number 90194 Answers: 1 Comments: 0

(x^2 /(x+a))+(√x)=a (a∈R) solve for: x .

$$\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{a}}}+\sqrt{\boldsymbol{\mathrm{x}}}=\boldsymbol{\mathrm{a}}\:\:\:\:\:\left(\boldsymbol{\mathrm{a}}\in\boldsymbol{\mathrm{R}}\right) \\ $$$$\mathrm{solve}\:\mathrm{for}:\:\:\mathrm{x}\:\:. \\ $$

Question Number 90178 Answers: 1 Comments: 1

Question Number 90139 Answers: 0 Comments: 3

x = 2021^3 −2019^3 (√((x−2)/6)) = ?

$$\mathrm{x}\:=\:\mathrm{2021}^{\mathrm{3}} −\mathrm{2019}^{\mathrm{3}} \\ $$$$\sqrt{\frac{\mathrm{x}−\mathrm{2}}{\mathrm{6}}}\:=\:? \\ $$

Question Number 90162 Answers: 1 Comments: 0

Question Number 90160 Answers: 1 Comments: 0

Question Number 90103 Answers: 0 Comments: 1

Question Number 90097 Answers: 0 Comments: 1

((√(3+(√8))))^x +((√(3−(√8))))^x = 6

$$\left(\sqrt{\mathrm{3}+\sqrt{\mathrm{8}}}\right)^{\mathrm{x}} \:+\left(\sqrt{\mathrm{3}−\sqrt{\mathrm{8}}}\right)^{\mathrm{x}} \:=\:\mathrm{6} \\ $$

Question Number 90086 Answers: 0 Comments: 7

Question Number 90092 Answers: 0 Comments: 1

G((√(x+5))) = x G(x^2 ) = x^a −b find a+b

$$\mathrm{G}\left(\sqrt{\mathrm{x}+\mathrm{5}}\right)\:=\:\mathrm{x} \\ $$$$\mathrm{G}\left(\mathrm{x}^{\mathrm{2}} \right)\:=\:\mathrm{x}^{\mathrm{a}} −\mathrm{b} \\ $$$$\mathrm{find}\:\mathrm{a}+\mathrm{b}\: \\ $$

Question Number 90048 Answers: 1 Comments: 0

5^(√x) −5^(x−7) = 100

$$\mathrm{5}^{\sqrt{\mathrm{x}}} \:−\mathrm{5}^{\mathrm{x}−\mathrm{7}} \:=\:\mathrm{100} \\ $$

Question Number 90038 Answers: 0 Comments: 0

Σ_(n=1) ^∞ (H_n /n^k )=S_k H_q =Σ_(p=1) ^q (1/p) Is there a simple from for S_k

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{H}_{{n}} }{{n}^{{k}} }={S}_{{k}} \:\:\:\:\:\:\:{H}_{{q}} =\underset{{p}=\mathrm{1}} {\overset{{q}} {\sum}}\frac{\mathrm{1}}{{p}} \\ $$$${Is}\:{there}\:{a}\:{simple}\:{from}\:{for}\:{S}_{{k}} \\ $$

Question Number 90030 Answers: 0 Comments: 0

Question Number 89991 Answers: 0 Comments: 2

if a,b > 0 and (a^2 /b^2 ) = (5/3) find ((a^2 +b^2 )/(ab))

$$\mathrm{if}\:\mathrm{a},\mathrm{b}\:>\:\mathrm{0}\:\mathrm{and}\:\frac{\mathrm{a}^{\mathrm{2}} }{\mathrm{b}^{\mathrm{2}} }\:=\:\frac{\mathrm{5}}{\mathrm{3}} \\ $$$$\mathrm{find}\:\frac{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} }{\mathrm{ab}} \\ $$

Question Number 89977 Answers: 0 Comments: 2

Question Number 89955 Answers: 1 Comments: 2

9^(x+1) ∤28(3^x )+3=0

$$\mathrm{9}^{\mathrm{x}+\mathrm{1}} \nmid\mathrm{28}\left(\mathrm{3}^{\mathrm{x}} \right)+\mathrm{3}=\mathrm{0} \\ $$

Question Number 89938 Answers: 0 Comments: 1

If x(x+1) = 1 find (x+1)^3 −(1/((x+1)^3 ))

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

Question Number 89928 Answers: 1 Comments: 0

Question Number 89907 Answers: 1 Comments: 0

If the sum of 4 numbers is between 53 and 57 then the arithmetic mean of the numbers could be one of the following a)11.5 b)12 c)12.5 d)13 e)14

$${If}\:{the}\:{sum}\:{of}\:\mathrm{4}\:{numbers}\:{is}\:{between} \\ $$$$\mathrm{53}\:{and}\:\mathrm{57}\:{then}\:{the}\:{arithmetic}\:{mean}\:{of} \\ $$$${the}\:{numbers}\:{could}\:{be}\:{one}\:{of}\:{the} \\ $$$${following} \\ $$$$ \\ $$$$\left.{a}\left.\right)\left.\mathrm{1}\left.\mathrm{1}\left..\mathrm{5}\:{b}\right)\mathrm{12}\:{c}\right)\mathrm{12}.\mathrm{5}\:{d}\right)\mathrm{13}\:{e}\right)\mathrm{14} \\ $$

Question Number 89834 Answers: 1 Comments: 1

Find x e^x = x^2 −1 anyother method apart from Newton′s

$${Find}\:{x}\: \\ $$$$\boldsymbol{{e}}^{\boldsymbol{{x}}} =\:\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{1} \\ $$$$\boldsymbol{{anyother}}\:\boldsymbol{{method}}\:\boldsymbol{{apart}}\:\boldsymbol{{from}}\:\boldsymbol{{N}}{ewton}'{s} \\ $$

Question Number 89829 Answers: 0 Comments: 9

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