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AlgebraQuestion and Answers: Page 58

Question Number 199732 Answers: 2 Comments: 0

Question Number 199731 Answers: 2 Comments: 0

Question Number 199721 Answers: 0 Comments: 0

Question Number 199711 Answers: 3 Comments: 0

Question Number 199709 Answers: 1 Comments: 0

u_1 = 2 u_(n+1) = 3u_n + 2 u_n → n ¿

$${u}_{\mathrm{1}} \:=\:\mathrm{2}\: \\ $$$${u}_{{n}+\mathrm{1}} \:=\:\mathrm{3}{u}_{{n}} \:+\:\mathrm{2} \\ $$$${u}_{{n}} \:\rightarrow\:{n}\:¿ \\ $$

Question Number 199694 Answers: 1 Comments: 0

Question Number 199671 Answers: 1 Comments: 0

Question Number 199654 Answers: 1 Comments: 0

x^4 + 4x^3 − 8x + 1 − m = 0 has 4 real roots find m=?

$$\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{4x}^{\mathrm{3}} \:−\:\mathrm{8x}\:+\:\mathrm{1}\:−\:\mathrm{m}\:=\:\mathrm{0} \\ $$$$\mathrm{has}\:\mathrm{4}\:\mathrm{real}\:\mathrm{roots} \\ $$$$\mathrm{find}\:\:\mathrm{m}=? \\ $$

Question Number 199632 Answers: 2 Comments: 0

In a swimming pool there are four pipes that fill it with water. When pipes 1, 2, 3 work, the pool fills in 12 minutes. When pipes 2, 3, 4 work, the pool fills in 15 minutes. When pipes 1 and 4 work, the pool fills in 20 minutes. Find how many minutes the pool fills if all four pipes work simultaneously.

Question Number 199606 Answers: 1 Comments: 0

Question Number 199602 Answers: 3 Comments: 0

2 + 7 + 12 + ... + x = 270 Find: x = ?

$$\mathrm{2}\:+\:\mathrm{7}\:+\:\mathrm{12}\:+\:...\:+\:\boldsymbol{\mathrm{x}}\:=\:\mathrm{270} \\ $$$$\mathrm{Find}:\:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$

Question Number 199592 Answers: 0 Comments: 9

Question Number 199593 Answers: 0 Comments: 0

if {a_n } is geometric sequence and we know , p=((n+m)/2) ⇒ S_p = f(a_n ,a_m ,n,m)=? ■Attention: The purpose of obtaining a relationship without the need for direct calculation is the common ratio of the sequence. For example, in a geometric sequence with a negative common ratio, if the sixth and tenth terms are equal to 5 and 12, the sum of the first 7 terms of this sequence?

$${if}\:\left\{{a}_{{n}} \right\}\:{is}\:{geometric}\:{sequence}\:{and}\: \\ $$$$ \\ $$$${we}\:{know}\:,\:{p}=\frac{{n}+{m}}{\mathrm{2}}\:\:\Rightarrow \\ $$$$\:{S}_{{p}} \:=\:{f}\left({a}_{{n}} ,{a}_{{m}} ,{n},{m}\right)=? \\ $$$$\blacksquare{Attention}:\: \\ $$The purpose of obtaining a relationship without the need for direct calculation is the common ratio of the sequence. For example, in a geometric sequence with a negative common ratio, if the sixth and tenth terms are equal to 5 and 12, the sum of the first 7 terms of this sequence?

Question Number 199550 Answers: 2 Comments: 0

If x = (√(7 + 4(√3))) Find: ((x^4 − x^3 − 9x^2 − 2x + 5)/(x^2 − 4x + 3)) = ?

$$\mathrm{If} \\ $$$$\mathrm{x}\:=\:\sqrt{\mathrm{7}\:+\:\mathrm{4}\sqrt{\mathrm{3}}} \\ $$$$\mathrm{Find}: \\ $$$$\frac{\mathrm{x}^{\mathrm{4}} \:−\:\mathrm{x}^{\mathrm{3}} \:−\:\mathrm{9x}^{\mathrm{2}} \:−\:\mathrm{2x}\:+\:\mathrm{5}}{\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4x}\:+\:\mathrm{3}}\:\:=\:\:? \\ $$

Question Number 199547 Answers: 3 Comments: 0

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 = ?

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

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