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Question Number 207274 Answers: 1 Comments: 0

log_(abc) a = 2 and log_(abc) b = 3 find: log_(abc) c = ?

$$\mathrm{log}_{\boldsymbol{\mathrm{abc}}} \:\mathrm{a}\:=\:\mathrm{2}\:\:\:\mathrm{and}\:\:\:\mathrm{log}_{\boldsymbol{\mathrm{abc}}} \:\mathrm{b}\:=\:\mathrm{3} \\ $$$$\mathrm{find}:\:\:\mathrm{log}_{\boldsymbol{\mathrm{abc}}} \:\mathrm{c}\:=\:? \\ $$

Question Number 207272 Answers: 0 Comments: 2

arcsin (x^2 − 3) = arcsin (x^2 + 3x + 4) x = ?

$$\mathrm{arcsin}\:\left(\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{3}\right)\:=\:\mathrm{arcsin}\:\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{3x}\:+\:\mathrm{4}\right) \\ $$$$\boldsymbol{\mathrm{x}}\:=\:? \\ $$

Question Number 207271 Answers: 1 Comments: 0

arg ( ((2 − i)/i) ) = 2 Find: Imz + Rez = ?

$$\mathrm{arg}\:\left(\:\frac{\mathrm{2}\:−\:\boldsymbol{\mathrm{i}}}{\boldsymbol{\mathrm{i}}}\:\right)\:=\:\mathrm{2} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{Imz}\:+\:\mathrm{Rez}\:=\:? \\ $$

Question Number 207270 Answers: 1 Comments: 0

{ ((∣x∣ + y − 1 = 0)),((x − y − 1 = 0)) :} find: 2x−3y = ?

$$\begin{cases}{\mid\mathrm{x}\mid\:+\:\mathrm{y}\:−\:\mathrm{1}\:=\:\mathrm{0}}\\{\mathrm{x}\:−\:\mathrm{y}\:−\:\mathrm{1}\:=\:\mathrm{0}}\end{cases}\:\:\:\mathrm{find}:\:\:\mathrm{2x}−\mathrm{3y}\:=\:? \\ $$

Question Number 207269 Answers: 0 Comments: 0

Find: 4 cos^2 40 − (1/(cos 20)) = ?

$$\mathrm{Find}:\:\:\:\mathrm{4}\:\mathrm{cos}^{\mathrm{2}} \:\mathrm{40}\:−\:\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{20}}\:=\:? \\ $$

Question Number 207250 Answers: 2 Comments: 0

If 2^a = 5 , 3^b = 9 and 25^c = 8 Find: a∙b∙c = ?

$$\mathrm{If}\:\:\:\mathrm{2}^{\boldsymbol{\mathrm{a}}} \:=\:\mathrm{5}\:\:,\:\:\mathrm{3}^{\boldsymbol{\mathrm{b}}} \:=\:\mathrm{9}\:\:\mathrm{and}\:\:\mathrm{25}^{\boldsymbol{\mathrm{c}}} \:=\:\mathrm{8} \\ $$$$\mathrm{Find}:\:\:\mathrm{a}\centerdot\mathrm{b}\centerdot\mathrm{c}\:=\:? \\ $$

Question Number 207249 Answers: 1 Comments: 0

{ ((x^2 + 2y^2 + xy = 37)),((y^2 + 2x^2 + 2xy = 26)) :} find: x^2 + y^2 = ?

$$\begin{cases}{\mathrm{x}^{\mathrm{2}} \:\:+\:\:\mathrm{2y}^{\mathrm{2}} \:\:+\:\:\mathrm{xy}\:\:=\:\:\mathrm{37}}\\{\mathrm{y}^{\mathrm{2}} \:\:+\:\:\mathrm{2x}^{\mathrm{2}} \:\:+\:\:\mathrm{2xy}\:\:=\:\:\mathrm{26}}\end{cases}\:\:\:\:\mathrm{find}:\:\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:=\:? \\ $$

Question Number 207248 Answers: 1 Comments: 0

If f(x) = 3^(x+1) Find ((f(2x + 1))/(f(x + 2))) = ?

$$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{3}^{\boldsymbol{\mathrm{x}}+\mathrm{1}} \\ $$$$\mathrm{Find}\:\:\:\frac{\mathrm{f}\left(\mathrm{2x}\:+\:\mathrm{1}\right)}{\mathrm{f}\left(\mathrm{x}\:+\:\mathrm{2}\right)}\:\:=\:\:? \\ $$

Question Number 207247 Answers: 1 Comments: 1

8 + ((18)/(2 + (7/(5 + (2/x))))) = 14 find: x = ?

$$\mathrm{8}\:\:+\:\:\frac{\mathrm{18}}{\mathrm{2}\:\:+\:\:\frac{\mathrm{7}}{\mathrm{5}\:\:+\:\:\frac{\mathrm{2}}{\boldsymbol{\mathrm{x}}}}}\:\:\:=\:\:\:\mathrm{14}\:\:\:\:\:\mathrm{find}:\:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$

Question Number 207243 Answers: 1 Comments: 0

Question Number 207233 Answers: 1 Comments: 1

1. lim_(n→∞) ( ((n − 1)/(n + 2)) )^(n + 3) = ? 2. lim_(x→∞) ( ((5x + 6)/(2x − 9)) )^x^2 = ? 3. lim_(n→∞) ( ((n + 3)/(n + 1)) )^n = ?

$$\mathrm{1}.\:\:\:\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\left(\:\frac{\mathrm{n}\:−\:\mathrm{1}}{\mathrm{n}\:+\:\mathrm{2}}\:\right)^{\boldsymbol{\mathrm{n}}\:+\:\mathrm{3}} \:=\:\:? \\ $$$$ \\ $$$$\mathrm{2}.\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\infty} {\mathrm{lim}}\:\left(\:\frac{\mathrm{5x}\:+\:\mathrm{6}}{\mathrm{2x}\:−\:\mathrm{9}}\:\right)^{\boldsymbol{\mathrm{x}}^{\mathrm{2}} } \:=\:\:? \\ $$$$ \\ $$$$\mathrm{3}.\:\:\:\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\left(\:\frac{\mathrm{n}\:+\:\mathrm{3}}{\mathrm{n}\:+\:\mathrm{1}}\:\right)^{\boldsymbol{\mathrm{n}}} \:=\:\:? \\ $$

Question Number 207232 Answers: 0 Comments: 0

Consider the relation R whose graph is giveny b R( (57)(58)(78)(97)(98)(55)(66)(56)(77)(88)99)o n the set S 56789 Find 1. the set of alla first(lest) elements of (SR) 2. the set of alla lst element of (SR) 3. the set of all minimalelements of (SR) 4. the set of alla mximal elements of (SR

$$ \\ $$$$\mathrm{Consider}\:\mathrm{the}\:\mathrm{relation}\:\mathrm{R}\:\mathrm{whose}\:\mathrm{graph}\:\mathrm{is}\:\mathrm{giveny} \\ $$$$\mathrm{b}\:\mathrm{R}\left(\right. \\ $$$$\left.\left(\mathrm{57}\right)\left(\mathrm{58}\right)\left(\mathrm{78}\right)\left(\mathrm{97}\right)\left(\mathrm{98}\right)\left(\mathrm{55}\right)\left(\mathrm{66}\right)\left(\mathrm{56}\right)\left(\mathrm{77}\right)\left(\mathrm{88}\right)\mathrm{99}\right)\mathrm{o} \\ $$$$\mathrm{n}\:\mathrm{the}\:\mathrm{set}\:\mathrm{S}\:\:\mathrm{56789}\:\mathrm{Find}\:\:\:\:\:\mathrm{1}.\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{alla} \\ $$$$\mathrm{first}\left(\mathrm{lest}\right)\:\mathrm{elements}\:\mathrm{of}\:\left(\mathrm{SR}\right)\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}.\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{alla} \\ $$$$\mathrm{lst}\:\mathrm{element}\:\mathrm{of}\:\left(\mathrm{SR}\right)\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}.\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{all}\: \\ $$$$\mathrm{minimalelements}\:\mathrm{of}\:\left(\mathrm{SR}\right)\:\:\:\:\:\:\:\:\:\:\mathrm{4}.\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{alla} \\ $$$$\mathrm{mximal}\:\mathrm{elements}\:\mathrm{of}\:\left(\mathrm{SR}\right. \\ $$

Question Number 207231 Answers: 1 Comments: 0

Question Number 207230 Answers: 1 Comments: 0

Question Number 207262 Answers: 1 Comments: 0

a_n - number series a_1 = 5 d = 3 a_2 ^2 −a_1 ^2 + a_4 ^2 −a_3 ^2 + a_6 ^2 −a_5 ^2 + ... + a_(10) ^2 −a_9 ^2 = ?

$$\mathrm{a}_{\boldsymbol{\mathrm{n}}} \:-\:\mathrm{number}\:\mathrm{series} \\ $$$$\mathrm{a}_{\mathrm{1}} \:=\:\mathrm{5} \\ $$$$\mathrm{d}\:=\:\mathrm{3} \\ $$$$\mathrm{a}_{\mathrm{2}} ^{\mathrm{2}} −\mathrm{a}_{\mathrm{1}} ^{\mathrm{2}} \:+\:\mathrm{a}_{\mathrm{4}} ^{\mathrm{2}} −\mathrm{a}_{\mathrm{3}} ^{\mathrm{2}} \:+\:\mathrm{a}_{\mathrm{6}} ^{\mathrm{2}} −\mathrm{a}_{\mathrm{5}} ^{\mathrm{2}} \:+\:...\:+\:\mathrm{a}_{\mathrm{10}} ^{\mathrm{2}} −\mathrm{a}_{\mathrm{9}} ^{\mathrm{2}} \:=\:? \\ $$

Question Number 207226 Answers: 2 Comments: 0

Find: (((2 − (√2))^8 ∙ (6 + 4 (√2))^8 )/((2 + (√2))^8 )) = ?

$$\mathrm{Find}:\:\:\:\frac{\left(\mathrm{2}\:−\:\sqrt{\mathrm{2}}\right)^{\mathrm{8}} \:\centerdot\:\left(\mathrm{6}\:+\:\mathrm{4}\:\sqrt{\mathrm{2}}\right)^{\mathrm{8}} }{\left(\mathrm{2}\:+\:\sqrt{\mathrm{2}}\right)^{\mathrm{8}} }\:=\:? \\ $$

Question Number 207225 Answers: 0 Comments: 1

6×5=30

$$\mathrm{6}×\mathrm{5}=\mathrm{30} \\ $$

Question Number 207220 Answers: 2 Comments: 0

Find: (i − 1)^(−100) = ?

$$\mathrm{Find}:\:\:\:\left(\boldsymbol{\mathrm{i}}\:−\:\mathrm{1}\right)^{−\mathrm{100}} \:\:=\:\:? \\ $$

Question Number 207219 Answers: 1 Comments: 0

Find: ((tg 20)/(1 + tg^2 20)) + ((tg 21)/(1 + tg^2 21)) +...+ ((tg 70)/(1 + tg^2 70))

$$\mathrm{Find}: \\ $$$$\frac{\mathrm{tg}\:\mathrm{20}}{\mathrm{1}\:+\:\mathrm{tg}^{\mathrm{2}} \:\mathrm{20}}\:+\:\frac{\mathrm{tg}\:\mathrm{21}}{\mathrm{1}\:+\:\mathrm{tg}^{\mathrm{2}} \:\mathrm{21}}\:+...+\:\frac{\mathrm{tg}\:\mathrm{70}}{\mathrm{1}\:+\:\mathrm{tg}^{\mathrm{2}} \:\mathrm{70}} \\ $$

Question Number 207218 Answers: 1 Comments: 0

2^x + ((6 ∙ 2^x − 10)/(2^x − 2)) = 4 ∙ 2^x + (1/(2^x − 2)) Find: x = ?

$$\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:\:+\:\:\frac{\mathrm{6}\:\centerdot\:\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:−\:\mathrm{10}}{\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:−\:\mathrm{2}}\:\:=\:\:\mathrm{4}\:\centerdot\:\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:\:+\:\:\frac{\mathrm{1}}{\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:−\:\mathrm{2}} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{x}\:=\:? \\ $$

Question Number 207212 Answers: 1 Comments: 1

arcsin (sin 6) = ?

$$\mathrm{arcsin}\:\left(\mathrm{sin}\:\mathrm{6}\right)\:=\:? \\ $$

Question Number 207207 Answers: 1 Comments: 0

100 x^(lg x) = x^3 Find: x = ?

$$\mathrm{100}\:\mathrm{x}^{\boldsymbol{\mathrm{lg}}\:\boldsymbol{\mathrm{x}}} \:\:=\:\:\mathrm{x}^{\mathrm{3}} \\ $$$$\mathrm{Find}:\:\:\mathrm{x}\:=\:? \\ $$

Question Number 207206 Answers: 2 Comments: 0

(√(x−3 + 2 (√(x−4)))) − (√(x + 5−6 (√(x−2)))) = 2 Find: x = ?

$$\sqrt{\mathrm{x}−\mathrm{3}\:+\:\mathrm{2}\:\sqrt{\mathrm{x}−\mathrm{4}}}\:−\:\sqrt{\mathrm{x}\:+\:\mathrm{5}−\mathrm{6}\:\sqrt{\mathrm{x}−\mathrm{2}}}\:=\:\mathrm{2} \\ $$$$\mathrm{Find}:\:\:\mathrm{x}\:=\:? \\ $$

Question Number 207205 Answers: 1 Comments: 0

{ ((x^2 + xy = 4x)),((y^2 + xy = 4y)) :} Find: log_(16) (x_1 + y_1 + x_2 + y_2 ) = ?

$$\begin{cases}{\mathrm{x}^{\mathrm{2}} \:\:+\:\:\mathrm{xy}\:\:=\:\:\mathrm{4x}}\\{\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{xy}\:\:=\:\:\mathrm{4y}}\end{cases} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{log}_{\mathrm{16}} \:\left(\mathrm{x}_{\mathrm{1}} \:+\:\mathrm{y}_{\mathrm{1}} \:+\:\mathrm{x}_{\mathrm{2}} \:+\:\mathrm{y}_{\mathrm{2}} \right)\:=\:? \\ $$

Question Number 207197 Answers: 2 Comments: 0

If xy = (1/3) , xz = (3/8) and yz = (1/2) For x , y and z compare.

$$\mathrm{If}\:\:\:\mathrm{xy}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\:\:\:,\:\:\:\mathrm{xz}\:=\:\frac{\mathrm{3}}{\mathrm{8}}\:\:\:\mathrm{and}\:\:\:\mathrm{yz}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{For}\:\:\:\mathrm{x}\:,\:\mathrm{y}\:\mathrm{and}\:\mathrm{z}\:\:\:\mathrm{compare}. \\ $$

Question Number 207196 Answers: 0 Comments: 0

if 2(a^2 −b^2 )^(5 ) it is a term of notable quotient of ((a+b)^n −(a−b)^n )/(ab+b^2 ) find n.

$${if}\:\mathrm{2}\left({a}^{\mathrm{2}} −{b}^{\mathrm{2}} \right)^{\mathrm{5}\:} {it}\:{is}\:{a}\:{term}\:{of}\:{notable}\:{quotient}\:{of}\:\:\left(\left({a}+{b}\right)^{{n}} −\left({a}−{b}\right)^{{n}} \right)/\left({ab}+{b}^{\mathrm{2}} \right)\:\:{find}\:\:{n}. \\ $$

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