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AlgebraQuestion and Answers: Page 78

Question Number 190297 Answers: 1 Comments: 0

Question Number 190284 Answers: 2 Comments: 0

find the remainder if 4^(2023) divides by 7

$$\mathrm{find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{if}\:\mathrm{4}^{\mathrm{2023}} \: \\ $$$$\mathrm{divides}\:\mathrm{by}\:\mathrm{7} \\ $$

Question Number 190275 Answers: 1 Comments: 0

Find the value of i^n for every positive integer n, where i^2 = −1, i^3 = i^2 i, i^4 = i^2 i^2 , etc.

$$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{i}^{\mathrm{n}} \:\mathrm{for}\:\mathrm{every}\:\mathrm{positive} \\ $$$$\:\mathrm{integer}\:\mathrm{n},\:\mathrm{where}\:\mathrm{i}^{\mathrm{2}} \:=\:−\mathrm{1},\:\mathrm{i}^{\mathrm{3}} =\:\mathrm{i}^{\mathrm{2}} \mathrm{i},\:\mathrm{i}^{\mathrm{4}} \:=\:\mathrm{i}^{\mathrm{2}} \mathrm{i}^{\mathrm{2}} \:,\:{etc}. \\ $$

Question Number 190241 Answers: 1 Comments: 0

show that a⊛b=a+ab+b is a monoid when G=Z

$${show}\:{that}\:{a}\circledast{b}={a}+{ab}+{b}\:{is}\:{a}\:{monoid}\:{when}\:{G}={Z} \\ $$

Question Number 190239 Answers: 0 Comments: 0

Question Number 190238 Answers: 0 Comments: 0

Question Number 190237 Answers: 0 Comments: 0

Question Number 190137 Answers: 2 Comments: 0

{ ((fog^(−1) (x)=3x+2)),((gof(x)=2x−1)) :} find f(x)=? and fof(3)=?

$$\begin{cases}{\mathrm{fog}^{−\mathrm{1}} \left(\mathrm{x}\right)=\mathrm{3x}+\mathrm{2}}\\{\mathrm{gof}\left(\mathrm{x}\right)=\mathrm{2x}−\mathrm{1}}\end{cases} \\ $$$${find}\:\:\:\:\:\:\mathrm{f}\left(\mathrm{x}\right)=?\:\:\:\mathrm{and}\:\:\:\:\mathrm{fof}\left(\mathrm{3}\right)=? \\ $$

Question Number 190131 Answers: 1 Comments: 0

if: x^2 +y^2 +z^2 + 14 = 2(x + 2y + 3z) find: T=((xyz)/(x^3 +y^3 +z^3 ))

$$\:\mathrm{if}:\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} \:+\:\mathrm{14}\:=\:\mathrm{2}\left(\mathrm{x}\:+\:\mathrm{2y}\:+\:\mathrm{3z}\right) \\ $$$$\:\mathrm{find}:\:\:\mathrm{T}=\frac{\mathrm{xyz}}{\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} +\mathrm{z}^{\mathrm{3}} }\: \\ $$

Question Number 190115 Answers: 1 Comments: 0

if: (a+b)(a+1) = b find: P = (√(a^3 +b^3 −3ab))

$$\mathrm{if}:\:\:\left(\mathrm{a}+\mathrm{b}\right)\left(\mathrm{a}+\mathrm{1}\right)\:=\:\mathrm{b} \\ $$$$\:\mathrm{find}:\:\:\mathrm{P}\:=\:\:\sqrt{\mathrm{a}^{\mathrm{3}} +\mathrm{b}^{\mathrm{3}} −\mathrm{3ab}} \\ $$

Question Number 190093 Answers: 2 Comments: 3

prove that : c= ( (√5) +2)^( (1/3)) − ((√5) −2)^( (1/3)) is a rational number.

$$ \\ $$$$\:\:\:\:\:{prove}\:\:{that}\:: \\ $$$$ \\ $$$${c}=\:\left(\:\sqrt{\mathrm{5}}\:+\mathrm{2}\right)^{\:\frac{\mathrm{1}}{\mathrm{3}}} \:−\:\left(\sqrt{\mathrm{5}}\:−\mathrm{2}\right)^{\:\frac{\mathrm{1}}{\mathrm{3}}} \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\mathrm{is}\:\:\:\mathrm{a}\:\:{rational}\:\:\mathrm{number}. \\ $$$$\:\:\:\:\: \\ $$$$\:\:\:\:\:\: \\ $$

Question Number 190091 Answers: 1 Comments: 0

1. Find sin52° + sin8° − cos22° 2. If a^2 + (1/a^2 ) = 6 find a^3 + (1/a^3 ) 3. Find ((tan32° + tan13°)/(1 − tan32° ∙ tan13°))

$$\mathrm{1}.\:\mathrm{Find}\:\:\:\mathrm{sin52}°\:+\:\mathrm{sin8}°\:−\:\mathrm{cos22}° \\ $$$$\mathrm{2}.\:\mathrm{If}\:\:\:\mathrm{a}^{\mathrm{2}} \:+\:\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{2}} }\:=\:\mathrm{6}\:\:\:\mathrm{find}\:\:\:\mathrm{a}^{\mathrm{3}} \:+\:\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{3}} } \\ $$$$\mathrm{3}.\:\mathrm{Find}\:\:\:\frac{\mathrm{tan32}°\:+\:\mathrm{tan13}°}{\mathrm{1}\:−\:\mathrm{tan32}°\:\centerdot\:\mathrm{tan13}°} \\ $$

Question Number 190076 Answers: 2 Comments: 0

Question Number 190075 Answers: 1 Comments: 0

Question Number 190073 Answers: 0 Comments: 0

Question Number 190039 Answers: 1 Comments: 0

b+(√b)−3=0 b>0 find 2b^2 −14b + 28 = ?

$$\mathrm{b}+\sqrt{\mathrm{b}}−\mathrm{3}=\mathrm{0} \\ $$$$\mathrm{b}>\mathrm{0} \\ $$$$\mathrm{find}\:\:\:\mathrm{2b}^{\mathrm{2}} −\mathrm{14b}\:+\:\mathrm{28}\:=\:? \\ $$

Question Number 190038 Answers: 1 Comments: 0

Find: ((21 + (√(4a − 3)))/(4a + (√(3 − 4a))))

$$\mathrm{Find}:\:\:\:\frac{\mathrm{21}\:+\:\sqrt{\mathrm{4a}\:−\:\mathrm{3}}}{\mathrm{4a}\:+\:\sqrt{\mathrm{3}\:−\:\mathrm{4a}}} \\ $$

Question Number 190035 Answers: 1 Comments: 0

10^(93) − 93 Find the sum of the numbers

$$\mathrm{10}^{\mathrm{93}} \:−\:\mathrm{93} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{numbers} \\ $$

Question Number 190034 Answers: 3 Comments: 0

If x + (2/x) = (√(17)) Find: (((x^2 − 4)(x^2 − 1))/x^2 ) = ?

$$\mathrm{If}\:\:\:\mathrm{x}\:+\:\frac{\mathrm{2}}{\mathrm{x}}\:=\:\sqrt{\mathrm{17}} \\ $$$$\mathrm{Find}:\:\:\:\frac{\left(\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4}\right)\left(\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{1}\right)}{\mathrm{x}^{\mathrm{2}} }\:=\:? \\ $$

Question Number 190032 Answers: 4 Comments: 0

x > 0 xy − 18 = 0 (2x + y)_(min) = ?

$$\mathrm{x}\:>\:\mathrm{0} \\ $$$$\mathrm{xy}\:−\:\mathrm{18}\:=\:\mathrm{0} \\ $$$$\left(\mathrm{2x}\:+\:\mathrm{y}\right)_{\boldsymbol{\mathrm{min}}} \:=\:? \\ $$

Question Number 190027 Answers: 1 Comments: 0

a^2 + b^2 = 12 ab = 4 Fund: a^3 + b^3 = ?

$$\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:=\:\mathrm{12} \\ $$$$\mathrm{ab}\:=\:\mathrm{4} \\ $$$$\mathrm{Fund}:\:\:\:\mathrm{a}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{3}} \:=\:? \\ $$

Question Number 190025 Answers: 1 Comments: 0

If f(x) = 3x^5 + 2x^2 Find: f((√2) − 1) + f(1 − (√2)) + 3

$$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{3x}^{\mathrm{5}} \:+\:\mathrm{2x}^{\mathrm{2}} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{f}\left(\sqrt{\mathrm{2}}\:−\:\mathrm{1}\right)\:+\:\mathrm{f}\left(\mathrm{1}\:−\:\sqrt{\mathrm{2}}\right)\:+\:\mathrm{3} \\ $$

Question Number 190024 Answers: 1 Comments: 0

Find: (√(4+(√2))) ∙ (√(3+(√(5+(√2))))) ∙ (√(3−(√(5+(√2))))) + ∣(√(14))−4∣

$$\mathrm{Find}: \\ $$$$\sqrt{\mathrm{4}+\sqrt{\mathrm{2}}}\:\centerdot\:\sqrt{\mathrm{3}+\sqrt{\mathrm{5}+\sqrt{\mathrm{2}}}}\:\centerdot\:\sqrt{\mathrm{3}−\sqrt{\mathrm{5}+\sqrt{\mathrm{2}}}}\:+\:\mid\sqrt{\mathrm{14}}−\mathrm{4}\mid \\ $$

Question Number 190022 Answers: 1 Comments: 2

5x^2 − 3x + 5 = 0 Find: x + (1/x) = 0

$$\mathrm{5x}^{\mathrm{2}} \:−\:\mathrm{3x}\:+\:\mathrm{5}\:=\:\mathrm{0} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{x}\:+\:\frac{\mathrm{1}}{\mathrm{x}}\:=\:\mathrm{0} \\ $$

Question Number 189989 Answers: 1 Comments: 0

Question Number 189975 Answers: 1 Comments: 0

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