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Question Number 13005 Answers: 1 Comments: 0

using De Moivre theorem solve the equation (x+1)^5 +(x−1)^5 =0

$${using}\:{De}\:{Moivre}\:{theorem}\:{solve}\:{the}\:{equation}\:\left({x}+\mathrm{1}\right)^{\mathrm{5}} +\left({x}−\mathrm{1}\right)^{\mathrm{5}} =\mathrm{0} \\ $$

Question Number 13004 Answers: 0 Comments: 0

If ∫f(x)dx=g(x) ,then why ∫_b ^a f(x)dx=g(a)−g(b)???

$${If}\:\int{f}\left({x}\right){dx}={g}\left({x}\right)\:,{then}\:{why} \\ $$$$\int_{{b}} ^{{a}} {f}\left({x}\right){dx}={g}\left({a}\right)−{g}\left({b}\right)??? \\ $$

Question Number 12998 Answers: 1 Comments: 0

((a +_− (√(2a.1.1)))/2)

$$\frac{{a}\:\underset{−} {+}\sqrt{\mathrm{2}{a}.\mathrm{1}.\mathrm{1}}}{\mathrm{2}} \\ $$

Question Number 12995 Answers: 0 Comments: 0

If a, b, c are in GP and a−b, c−a, b−c are in HP, then a+4b+c is equal to

$$\mathrm{If}\:{a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{in}\:\mathrm{GP}\:\mathrm{and}\:\:{a}−{b},\:{c}−{a},\:{b}−{c}\:\mathrm{are} \\ $$$$\mathrm{in}\:\mathrm{HP},\:\mathrm{then}\:{a}+\mathrm{4}{b}+{c}\:\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 12968 Answers: 1 Comments: 0

(x+3)^2 +(y−5)^2 =45 A(0;11) of the circle to the point of trying to find the angular coefficient.

Question Number 13000 Answers: 0 Comments: 3

∫ sin^4 x cos^3 x dx

$$\int\:\mathrm{sin}^{\mathrm{4}} \:{x}\:\mathrm{cos}^{\mathrm{3}} \:{x}\:{dx} \\ $$

Question Number 13002 Answers: 1 Comments: 0

3^((x − 3)(x − y − 2)) = 1 5^((x^2 − 2xy + y^2 + x − y − 3/2)) = (√5) Find the value of x and y

$$\mathrm{3}^{\left({x}\:−\:\mathrm{3}\right)\left({x}\:−\:{y}\:−\:\mathrm{2}\right)} \:=\:\mathrm{1} \\ $$$$\mathrm{5}^{\left({x}^{\mathrm{2}} \:−\:\mathrm{2}{xy}\:+\:{y}^{\mathrm{2}} \:+\:{x}\:−\:{y}\:−\:\mathrm{3}/\mathrm{2}\right)} \:=\:\sqrt{\mathrm{5}} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}\:\mathrm{and}\:{y} \\ $$

Question Number 12946 Answers: 1 Comments: 0

a_n =(√(3a_(n−1) +2)) a_1 =1 lim_(n→∞) a_n =?

$${a}_{{n}} =\sqrt{\mathrm{3}{a}_{{n}−\mathrm{1}} +\mathrm{2}}\:\:\:{a}_{\mathrm{1}} =\mathrm{1} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}{a}_{{n}} =? \\ $$

Question Number 12933 Answers: 2 Comments: 9

Question Number 12930 Answers: 1 Comments: 0

Question Number 12929 Answers: 0 Comments: 0

Question Number 12928 Answers: 1 Comments: 0

Question Number 12927 Answers: 0 Comments: 1

Σcos ((1/n))

$$\Sigma\mathrm{cos}\:\left(\frac{\mathrm{1}}{{n}}\right) \\ $$

Question Number 12926 Answers: 1 Comments: 0

∫_( 0) ^(π/2) log ∣tan x+cot x∣ dx =

$$\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\mathrm{log}\:\mid\mathrm{tan}\:{x}+\mathrm{cot}\:{x}\mid\:{dx}\:= \\ $$

Question Number 12962 Answers: 1 Comments: 0

Question Number 12919 Answers: 0 Comments: 0

The value of the integral ∫_( 0) ^1 e^x^2 dx lies in the interval

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integral}\:\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:{e}^{{x}^{\mathrm{2}} } {dx}\:\:\mathrm{lies} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{interval} \\ $$

Question Number 12909 Answers: 1 Comments: 0

Question Number 12908 Answers: 1 Comments: 0

Question Number 12905 Answers: 2 Comments: 0

sin (x)=3cos (x) ⇔tan (x)=3 True or false?

$$\mathrm{sin}\:\left({x}\right)=\mathrm{3cos}\:\left({x}\right)\:\Leftrightarrow\mathrm{tan}\:\left({x}\right)=\mathrm{3} \\ $$$${True}\:{or}\:{false}? \\ $$

Question Number 12903 Answers: 1 Comments: 0

Question Number 12902 Answers: 1 Comments: 0

Question Number 12895 Answers: 1 Comments: 2

Question Number 12894 Answers: 1 Comments: 2

Question Number 12889 Answers: 2 Comments: 1

f(x−1)=(2/3)+f(x) f(0)=36−f(21) ⇒f(0)=?

$${f}\left({x}−\mathrm{1}\right)=\frac{\mathrm{2}}{\mathrm{3}}+{f}\left({x}\right) \\ $$$${f}\left(\mathrm{0}\right)=\mathrm{36}−{f}\left(\mathrm{21}\right) \\ $$$$\Rightarrow{f}\left(\mathrm{0}\right)=? \\ $$

Question Number 12885 Answers: 1 Comments: 0

f(f(x))=f^2 (x) What is a solution?

$${f}\left({f}\left({x}\right)\right)={f}^{\mathrm{2}} \left({x}\right) \\ $$$$\: \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{a}\:\mathrm{solution}? \\ $$

Question Number 12883 Answers: 1 Comments: 0

for −128≤x≤127 and −127≤y≤128 where x,y∈Z Point P(x,y) is a point on the cartesian plane. From the origin, angle θ is made counter −clockwise with the positive x−axis. (1) How many unique angles θ exist if x,y∈P? (2) Furthermore, how many unique angles θ exist for the full range of x,y∈Z?

$$\mathrm{for}\:\:\:\:\:−\mathrm{128}\leqslant{x}\leqslant\mathrm{127} \\ $$$$\mathrm{and}\:\:\:−\mathrm{127}\leqslant{y}\leqslant\mathrm{128} \\ $$$$\mathrm{where}\:\:\:{x},{y}\in\mathbb{Z} \\ $$$$\: \\ $$$$\mathrm{Point}\:{P}\left({x},{y}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{cartesian}\:\mathrm{plane}. \\ $$$$\: \\ $$$$\mathrm{From}\:\mathrm{the}\:\mathrm{origin},\:\mathrm{angle}\:\theta\:\mathrm{is}\:\mathrm{made}\:\mathrm{counter} \\ $$$$−\mathrm{clockwise}\:\mathrm{with}\:\mathrm{the}\:\mathrm{positive}\:{x}−\mathrm{axis}. \\ $$$$\: \\ $$$$\left(\mathrm{1}\right)\:\mathrm{How}\:\mathrm{many}\:\mathrm{unique}\:\mathrm{angles}\:\theta\:\mathrm{exist} \\ $$$$\mathrm{if}\:{x},{y}\in\mathbb{P}? \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Furthermore},\:\mathrm{how}\:\mathrm{many}\:\mathrm{unique} \\ $$$$\mathrm{angles}\:\theta\:\mathrm{exist}\:\mathrm{for}\:\mathrm{the}\:\mathrm{full}\:\mathrm{range}\:\mathrm{of}\:{x},{y}\in\mathbb{Z}? \\ $$

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