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AlgebraQuestion and Answers: Page 57

Question Number 199528 Answers: 0 Comments: 0

Question Number 199509 Answers: 2 Comments: 2

Question Number 199486 Answers: 2 Comments: 0

Solve: 100^x = 200

$$\mathrm{Solve}:\:\:\:\mathrm{100}^{\boldsymbol{\mathrm{x}}} \:=\:\mathrm{200} \\ $$

Question Number 199482 Answers: 0 Comments: 3

can someone factor this (3x^3 y−7x^2 +5xy^3 −y^2 )

$$\mathrm{can}\:\mathrm{someone}\:\mathrm{factor}\:\mathrm{this}\:\left(\mathrm{3x}^{\mathrm{3}} \mathrm{y}−\mathrm{7x}^{\mathrm{2}} +\mathrm{5xy}^{\mathrm{3}} −\mathrm{y}^{\mathrm{2}} \right) \\ $$

Question Number 199466 Answers: 1 Comments: 0

Question Number 199458 Answers: 1 Comments: 0

Solve: log_3 p + log_r 8 =5 r+p=11. find r&p

$$\boldsymbol{{Solve}}:\:\boldsymbol{{log}}_{\mathrm{3}} \boldsymbol{{p}}\:+\:\boldsymbol{{log}}_{\boldsymbol{{r}}} \mathrm{8}\:=\mathrm{5} \\ $$$$\boldsymbol{{r}}+\boldsymbol{{p}}=\mathrm{11}.\:\:\boldsymbol{{find}}\:\boldsymbol{{r\&p}} \\ $$

Question Number 199451 Answers: 3 Comments: 0

Find: 1. lim_(n→∞) (((5n − 25)/(3n + 15)))^(1/(5n)) 2. lim_(x→∞) (((x^3 + 3x^2 + 1))^(1/3) − ((x^3 − 3x^2 + 1))^(1/3) ) 3. lim_(x→0) ((cos 4x^3 − 1)/(sin^6 2x))

$$\mathrm{Find}: \\ $$$$\mathrm{1}.\:\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\sqrt[{\mathrm{5}\boldsymbol{\mathrm{n}}}]{\frac{\mathrm{5n}\:−\:\mathrm{25}}{\mathrm{3n}\:+\:\mathrm{15}}} \\ $$$$\mathrm{2}.\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\infty} {\mathrm{lim}}\:\left(\sqrt[{\mathrm{3}}]{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{3x}^{\mathrm{2}} \:+\:\mathrm{1}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{x}^{\mathrm{3}} \:−\:\mathrm{3x}^{\mathrm{2}} \:+\:\mathrm{1}}\:\right) \\ $$$$\mathrm{3}.\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{4x}^{\mathrm{3}} \:−\:\mathrm{1}}{\mathrm{sin}^{\mathrm{6}} \:\mathrm{2x}} \\ $$

Question Number 199447 Answers: 1 Comments: 0

b_n =sin(a_1 +(n−1)d)⇒ S_n =?

$${b}_{{n}} ={sin}\left({a}_{\mathrm{1}} +\left({n}−\mathrm{1}\right){d}\right)\Rightarrow\:{S}_{{n}} =? \\ $$

Question Number 199432 Answers: 2 Comments: 0

without using calculator: what is larger? log_2 3 or log_3 5?

$${without}\:{using}\:{calculator}: \\ $$$${what}\:{is}\:{larger}?\:\mathrm{log}_{\mathrm{2}} \:\mathrm{3}\:{or}\:\mathrm{log}_{\mathrm{3}} \:\mathrm{5}? \\ $$

Question Number 199389 Answers: 2 Comments: 0

log_(12) 60=? log_6 30=a log_(15) 24=b

$$\mathrm{log}_{\mathrm{12}} \mathrm{60}=? \\ $$$$\mathrm{log}_{\mathrm{6}} \mathrm{30}={a} \\ $$$$\mathrm{log}_{\mathrm{15}} \mathrm{24}={b} \\ $$

Question Number 199385 Answers: 2 Comments: 0

Find: Ω = ∫_0 ^( 1) x^(15) (√(1 + 3x^8 )) dx = ?

$$\mathrm{Find}: \\ $$$$\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{x}^{\mathrm{15}} \:\sqrt{\mathrm{1}\:+\:\mathrm{3x}^{\mathrm{8}} }\:\mathrm{dx}\:=\:? \\ $$

Question Number 199381 Answers: 1 Comments: 0

Question Number 199309 Answers: 1 Comments: 0

a_(n+1 ) = a_n + (√(a_n ^2 + 1)) , a_0 = 0 find a_(n ) = ??

$$\:\:\:\:{a}_{{n}+\mathrm{1}\:} =\:{a}_{{n}} \:+\:\sqrt{{a}_{{n}} ^{\mathrm{2}} \:+\:\mathrm{1}}\:\:,\:{a}_{\mathrm{0}} \:=\:\mathrm{0} \\ $$$$\:\:\:\:\mathrm{find}\:\mathrm{a}_{\mathrm{n}\:} \:=\:\:?? \\ $$

Question Number 199308 Answers: 0 Comments: 0

Question Number 199290 Answers: 4 Comments: 1

If x=(√(p+iq))+(√(h+ik)) and (p/q)≠(k/h) then relate p,q,h,k ∈R such that x∈R.

$${If}\:{x}=\sqrt{{p}+{iq}}+\sqrt{{h}+{ik}} \\ $$$${and}\:\:\frac{{p}}{{q}}\neq\frac{{k}}{{h}}\:\:{then}\:{relate}\:{p},{q},{h},{k}\:\in\mathbb{R} \\ $$$${such}\:{that}\:{x}\in\mathbb{R}. \\ $$

Question Number 199259 Answers: 0 Comments: 1

Question Number 199620 Answers: 1 Comments: 0

Question Number 199230 Answers: 1 Comments: 0

x , y : positive real numbers If : 15^x = 9^y Find: 5^((3x)/(2y − x)) = ?

$$\mathrm{x}\:,\:\mathrm{y}\::\:\:\:\mathrm{positive}\:\mathrm{real}\:\mathrm{numbers} \\ $$$$\mathrm{If}\::\:\:\:\mathrm{15}^{\boldsymbol{\mathrm{x}}} \:=\:\mathrm{9}^{\boldsymbol{\mathrm{y}}} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{5}^{\frac{\mathrm{3}\boldsymbol{\mathrm{x}}}{\mathrm{2}\boldsymbol{\mathrm{y}}\:−\:\boldsymbol{\mathrm{x}}}} \:\:=\:\:? \\ $$

Question Number 199226 Answers: 1 Comments: 0

find ((2 sin 2°+4 sin 4°+...+180 sin 180°)/(90))=? [an unsolved old question #198900]

$${find} \\ $$$$\frac{\mathrm{2}\:\mathrm{sin}\:\mathrm{2}°+\mathrm{4}\:\mathrm{sin}\:\mathrm{4}°+...+\mathrm{180}\:\mathrm{sin}\:\mathrm{180}°}{\mathrm{90}}=? \\ $$$$ \\ $$$$\left[{an}\:{unsolved}\:{old}\:{question}\:#\mathrm{198900}\right] \\ $$

Question Number 199205 Answers: 0 Comments: 0

a_(n+1 ) = a_n + (√(a_n ^2 + 1)) , a_0 = α find a_(n ) = ??

$$\:\:\:\:{a}_{{n}+\mathrm{1}\:} =\:{a}_{{n}} \:+\:\sqrt{{a}_{{n}} ^{\mathrm{2}} \:+\:\mathrm{1}}\:\:,\:{a}_{\mathrm{0}} \:=\:\alpha \\ $$$$\:\:\:\mathrm{find}\:\mathrm{a}_{\mathrm{n}\:} \:=\:\:?? \\ $$

Question Number 199194 Answers: 1 Comments: 0

a_1 ,a_2 ,... a_1 =1 a_(2n) =n∙a_n a_2^(100) = ?

$$\mathrm{a}_{\mathrm{1}} ,\mathrm{a}_{\mathrm{2}} ,... \\ $$$$\mathrm{a}_{\mathrm{1}} =\mathrm{1} \\ $$$$\mathrm{a}_{\mathrm{2n}} =\mathrm{n}\centerdot\mathrm{a}_{\mathrm{n}} \\ $$$$\mathrm{a}_{\mathrm{2}^{\mathrm{100}} } \:=\:? \\ $$

Question Number 199184 Answers: 0 Comments: 3

Question Number 199183 Answers: 1 Comments: 0

B,O,M - Each is a distinct positive integer If B ∙ O ∙ M = 223 Find: max(B + O + M)=?

$$\mathrm{B},\mathrm{O},\mathrm{M}\:-\:\mathrm{Each}\:\mathrm{is}\:\mathrm{a}\:\mathrm{distinct}\:\mathrm{positive} \\ $$$$\mathrm{integer} \\ $$$$\mathrm{If}\:\:\:\mathrm{B}\:\centerdot\:\mathrm{O}\:\centerdot\:\mathrm{M}\:=\:\mathrm{223} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{max}\left(\mathrm{B}\:+\:\mathrm{O}\:+\:\mathrm{M}\right)=? \\ $$

Question Number 199170 Answers: 2 Comments: 9

n^4 +2n^3 +2n^2 +n+7 = a^2 (a∈N) →n=¿ (n∈N)

$${n}^{\mathrm{4}} +\mathrm{2}{n}^{\mathrm{3}} +\mathrm{2}{n}^{\mathrm{2}} +{n}+\mathrm{7}\:=\:{a}^{\mathrm{2}} \:\left({a}\in{N}\right) \\ $$$$\rightarrow{n}=¿\:\left({n}\in{N}\right) \\ $$

Question Number 199187 Answers: 0 Comments: 1

x is a negative real number: If ∣x−2∣=p Find: x−p=?

$$\mathrm{x}\:\mathrm{is}\:\mathrm{a}\:\mathrm{negative}\:\mathrm{real}\:\mathrm{number}: \\ $$$$\mathrm{If}\:\:\mid\mathrm{x}−\mathrm{2}\mid=\mathrm{p} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{x}−\mathrm{p}=? \\ $$

Question Number 199165 Answers: 1 Comments: 0

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