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AlgebraQuestion and Answers: Page 34

Question Number 207462 Answers: 0 Comments: 1

4 sin (x/2) = 1 find: x = ?

$$\mathrm{4}\:\mathrm{sin}\:\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\:=\:\mathrm{1}\:\:\:\:\:\mathrm{find}:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$

Question Number 207487 Answers: 1 Comments: 0

∣x^2 − 3x − 4∣ = ∣x − 4∣ find: min and max = ?

$$\mid\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{3x}\:−\:\mathrm{4}\mid\:=\:\mid\mathrm{x}\:−\:\mathrm{4}\mid \\ $$$$\mathrm{find}:\:\:\:\boldsymbol{\mathrm{min}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{max}}\:\:=\:\:? \\ $$

Question Number 207486 Answers: 2 Comments: 2

Question Number 207450 Answers: 1 Comments: 0

Find the relation between m and n for which the following holds ((d(y))/(d(x)))∣_(x=n) =(((d(x))/(d(y)))∣_(y=m) )^(−1)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{relation}\:\mathrm{between}\:{m}\:\mathrm{and}\:{n}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the}\:\mathrm{following}\:\:\mathrm{holds} \\ $$$$\:\frac{{d}\left({y}\right)}{{d}\left({x}\right)}\mid_{{x}={n}} =\left(\frac{{d}\left({x}\right)}{{d}\left({y}\right)}\mid_{{y}={m}} \right)^{−\mathrm{1}} \\ $$

Question Number 207442 Answers: 1 Comments: 3

If y=f(x), (d^2 x/dy^2 )=e^(y+1) , and the tangent line to the curve of the function f(x) on the point (x_1 ,−1) is paralel to the straight line g(x)=x−3, then find f′(x).

$$\mathrm{If}\:{y}={f}\left({x}\right),\:\frac{{d}^{\mathrm{2}} {x}}{{dy}^{\mathrm{2}} }={e}^{{y}+\mathrm{1}} ,\:\mathrm{and}\:\mathrm{the}\:\mathrm{tangent}\:\mathrm{line}\:\mathrm{to}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}\:{f}\left({x}\right)\:\mathrm{on}\:\mathrm{the}\:\mathrm{point} \\ $$$$\left({x}_{\mathrm{1}} ,−\mathrm{1}\right)\:\mathrm{is}\:\mathrm{paralel}\:\mathrm{to}\:\mathrm{the}\:\mathrm{straight}\:\mathrm{line}\:{g}\left({x}\right)={x}−\mathrm{3},\:\mathrm{then}\:\mathrm{find}\:{f}'\left({x}\right). \\ $$

Question Number 207395 Answers: 1 Comments: 0

Geometric series: ((b_4 ∙ b_7 ∙ b_(10) )/(b_1 ∙ b_3 ∙ b_5 )) = 2^(12) find: (b_5 /b_2 ) = ?

$$\mathrm{Geometric}\:\mathrm{series}: \\ $$$$\frac{\mathrm{b}_{\mathrm{4}} \:\centerdot\:\mathrm{b}_{\mathrm{7}} \:\centerdot\:\mathrm{b}_{\mathrm{10}} }{\mathrm{b}_{\mathrm{1}} \:\centerdot\:\mathrm{b}_{\mathrm{3}} \:\centerdot\:\mathrm{b}_{\mathrm{5}} }\:\:=\:\:\mathrm{2}^{\mathrm{12}} \:\:\:\:\:\mathrm{find}:\:\:\:\frac{\mathrm{b}_{\mathrm{5}} }{\mathrm{b}_{\mathrm{2}} }\:\:=\:\:? \\ $$

Question Number 207394 Answers: 1 Comments: 0

(a/b) = (c/d) a^3 − b^3 = 625 c^3 − d^3 = 1 Find: a,b,c,d = ?

$$\frac{\mathrm{a}}{\mathrm{b}}\:\:=\:\:\frac{\mathrm{c}}{\mathrm{d}} \\ $$$$\mathrm{a}^{\mathrm{3}} \:−\:\mathrm{b}^{\mathrm{3}} \:=\:\mathrm{625} \\ $$$$\mathrm{c}^{\mathrm{3}} \:−\:\mathrm{d}^{\mathrm{3}} \:=\:\mathrm{1} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\:=\:? \\ $$

Question Number 207385 Answers: 0 Comments: 1

Find: (√((2,5−(√5))^2 )) − (((1,5−(√5))^3 )^(1/2) ))^(1/3) − (√2) sin ((7π)/4)

$$\mathrm{Find}: \\ $$$$\sqrt{\left(\mathrm{2},\mathrm{5}−\sqrt{\mathrm{5}}\right)^{\mathrm{2}} }\:−\:\sqrt[{\mathrm{3}}]{\left.\left(\mathrm{1},\mathrm{5}−\sqrt{\mathrm{5}}\right)^{\mathrm{3}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} }\:−\:\sqrt{\mathrm{2}}\:\mathrm{sin}\:\frac{\mathrm{7}\pi}{\mathrm{4}} \\ $$

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 207408 Answers: 2 Comments: 0

z = ((√3)/2) − (1/2) i find: z^(11) = ?

$$\boldsymbol{\mathrm{z}}\:\:=\:\:\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:−\:\frac{\mathrm{1}}{\mathrm{2}}\:\boldsymbol{\mathrm{i}}\:\:\:\:\:\mathrm{find}:\:\:\boldsymbol{\mathrm{z}}^{\mathrm{11}} \:=\:? \\ $$

Question Number 207407 Answers: 0 Comments: 2

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))) = ?

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

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