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AlgebraQuestion and Answers: Page 1

Question Number 207361 Answers: 1 Comments: 0

y = ((tgx + ctgx)/8) , (0 ; (π/2)) Find: min(y) = ?

$$\mathrm{y}\:=\:\frac{\mathrm{tg}\boldsymbol{\mathrm{x}}\:\:+\:\:\mathrm{ctg}\boldsymbol{\mathrm{x}}}{\mathrm{8}}\:\:\:\:\:,\:\:\:\:\:\left(\mathrm{0}\:;\:\frac{\pi}{\mathrm{2}}\right) \\ $$$$\mathrm{Find}:\:\:\:\mathrm{min}\left(\mathrm{y}\right)\:=\:? \\ $$

Question Number 207332 Answers: 1 Comments: 1

(a^→ ×b^→ )×(a^→ )=? how is the solution

$$\left(\overset{\rightarrow} {\mathrm{a}}×\overset{\rightarrow} {\mathrm{b}}\right)×\left(\overset{\rightarrow} {\mathrm{a}}\right)=? \\ $$$$\mathrm{how}\:\mathrm{is}\:\mathrm{the}\:\mathrm{solution} \\ $$

Question Number 207330 Answers: 1 Comments: 0

Find: 4 cos 50° + (1/(sin 20°)) = ?

$$\mathrm{Find}:\:\:\:\mathrm{4}\:\mathrm{cos}\:\mathrm{50}°\:\:+\:\:\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{20}°}\:\:=\:\:? \\ $$

Question Number 207328 Answers: 1 Comments: 0

Find: 4 sin 50° − (1/(cos 20°)) = ?

$$\mathrm{Find}:\:\:\:\mathrm{4}\:\mathrm{sin}\:\mathrm{50}°\:−\:\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{20}°}\:\:=\:\:? \\ $$

Question Number 207327 Answers: 1 Comments: 1

(x−3) (√(x^2 −x−2)) = 0 Find: x = ?

$$\left(\mathrm{x}−\mathrm{3}\right)\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{x}−\mathrm{2}}\:\:=\:\:\mathrm{0} \\ $$$$\mathrm{Find}:\:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$

Question Number 207326 Answers: 0 Comments: 0

Find: 1. 4 cos^2 40° − (1/(cos 20°)) = ? 2. 4 cos^2 40° + (1/(cos 20°)) = ?

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

Question Number 207320 Answers: 1 Comments: 1

Question Number 207315 Answers: 1 Comments: 0

if ab+ac+bc=2 calculate minimum of 10a^2 +10b^2 +c^2

$${if}\:{ab}+{ac}+{bc}=\mathrm{2}\: \\ $$$${calculate}\:{minimum}\:{of}\:\mathrm{10}{a}^{\mathrm{2}} +\mathrm{10}{b}^{\mathrm{2}} +{c}^{\mathrm{2}} \\ $$

Question Number 207279 Answers: 0 Comments: 1

If z = i − 1 Find z^(−100) = ?

$$\mathrm{If}\:\:\:\mathrm{z}\:=\:\boldsymbol{\mathrm{i}}\:−\:\mathrm{1} \\ $$$$\mathrm{Find}\:\:\:\boldsymbol{\mathrm{z}}^{−\mathrm{100}} \:=\:? \\ $$

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 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 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) = ?

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

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