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AlgebraQuestion and Answers: Page 75

Question Number 192862 Answers: 1 Comments: 0

Solve for x x^3 −115x+150=0

$$\mathrm{Solve}\:\mathrm{for}\:{x} \\ $$$${x}^{\mathrm{3}} −\mathrm{115}{x}+\mathrm{150}=\mathrm{0} \\ $$

Question Number 192856 Answers: 2 Comments: 0

if a+b+c +d = 63 and a,b,c,d ∈ N find the maximum value of ab+bc+cd = ?

$$\:{if}\:{a}+{b}+{c}\:+{d}\:\:=\:\mathrm{63}\:{and}\:{a},{b},{c},{d}\:\in\:\mathbb{N}\:{find}\: \\ $$$$\:\:\:{the}\:{maximum}\:{value}\:{of}\:{ab}+{bc}+{cd}\:=\:? \\ $$

Question Number 192855 Answers: 2 Comments: 0

Question Number 192852 Answers: 2 Comments: 2

find the domain of thefunction f(x) = (1/( (√(x^2 −{x}^2 )))) where {.} is the fractional part function.

$$ \\ $$$${find}\:{the}\:{domain}\:{of}\:{thefunction} \\ $$$${f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} −\left\{{x}\right\}^{\mathrm{2}} }}\:\:\:\:\:{where}\:\left\{.\right\}\:{is}\:{the}\:{fractional}\:{part}\:{function}. \\ $$

Question Number 192851 Answers: 0 Comments: 1

Solve: ((log_(a^2 (√x)) a)/(log_(2x) a)) + log_(ax) a . log_(1/a) 2x = 0

$$\mathrm{Solve}: \\ $$$$\frac{\mathrm{log}_{{a}^{\mathrm{2}} \sqrt{{x}}} \:{a}}{\mathrm{log}_{\mathrm{2}{x}} \:{a}}\:+\:\mathrm{log}_{{ax}} \:{a}\:.\:\mathrm{log}_{\frac{\mathrm{1}}{{a}}} \:\mathrm{2}{x}\:=\:\mathrm{0} \\ $$

Question Number 192839 Answers: 2 Comments: 0

Question Number 192811 Answers: 1 Comments: 0

Question Number 192793 Answers: 2 Comments: 0

x^4 +x^3 +x^2 +x+1=y^2 where y is positive integer number then find the positive integal values of (x) for which that holds

$$\boldsymbol{{x}}^{\mathrm{4}} +\boldsymbol{{x}}^{\mathrm{3}} +\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{x}}+\mathrm{1}=\boldsymbol{{y}}^{\mathrm{2}} \:\boldsymbol{{where}}\:\boldsymbol{{y}}\:\boldsymbol{{is}}\:\boldsymbol{{positive}}\:\boldsymbol{{integer}}\:\boldsymbol{{number}} \\ $$$$\boldsymbol{{then}}\:\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{positive}}\:\boldsymbol{{integal}}\:\boldsymbol{{values}}\:\boldsymbol{{of}}\:\left(\boldsymbol{{x}}\right) \\ $$$$\boldsymbol{{for}}\:\boldsymbol{{which}}\:\boldsymbol{{that}}\:\boldsymbol{{holds}} \\ $$

Question Number 192786 Answers: 1 Comments: 0

N=<aabb>∈N & N is perfect square find N ?

$${N}=<{aabb}>\in\mathbb{N}\:\:\&\:\:{N}\:\:{is}\:\:{perfect}\:{square} \\ $$$${find}\:\:{N}\:\:? \\ $$$$ \\ $$

Question Number 192780 Answers: 1 Comments: 1

Question Number 192777 Answers: 0 Comments: 2

(√(x^2 +ax−1))−(√(x^2 +bx−1))=(√a)−(√b) find x .

$$\sqrt{{x}^{\mathrm{2}} +{ax}−\mathrm{1}}−\sqrt{{x}^{\mathrm{2}} +{bx}−\mathrm{1}}=\sqrt{{a}}−\sqrt{{b}} \\ $$$${find}\:{x}\:. \\ $$

Question Number 192721 Answers: 1 Comments: 0

x^3 −3xy^2 =18 3x^2 y−y^3 =26 and what do you recommend to read to deal with such problems

$$ \\ $$$${x}^{\mathrm{3}} −\mathrm{3}{xy}^{\mathrm{2}} =\mathrm{18} \\ $$$$\mathrm{3}{x}^{\mathrm{2}} {y}−{y}^{\mathrm{3}} =\mathrm{26} \\ $$$${and}\:{what}\:{do}\:{you}\:{recommend}\:{to}\:{read}\:{to}\:{deal} \\ $$$${with}\:{such}\:{problems} \\ $$

Question Number 192720 Answers: 4 Comments: 0

Question Number 192697 Answers: 1 Comments: 0

Find the value of (9x−(1/(100))x)^3 (9x−(2/(100))x)^3 (9x−(3/(100))x)^3 ...(9x−((2013)/(100))x)^3 .

$$\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\:\:\left(\mathrm{9x}−\frac{\mathrm{1}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} \left(\mathrm{9x}−\frac{\mathrm{2}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} \left(\mathrm{9x}−\frac{\mathrm{3}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} ...\left(\mathrm{9x}−\frac{\mathrm{2013}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} . \\ $$

Question Number 192688 Answers: 1 Comments: 0

Prove that : C_n ^k = (1/(2π)) ∫^( π) _( −π) (2cos(θ/2))^n cos[((n/2)−k)θ]dθ

$$\mathrm{Prove}\:\mathrm{that}\:: \\ $$$$\mathrm{C}_{\mathrm{n}} ^{\mathrm{k}} \:=\:\frac{\mathrm{1}}{\mathrm{2}\pi}\:\underset{\:−\pi} {\int}^{\:\:\:\pi} \left(\mathrm{2cos}\frac{\theta}{\mathrm{2}}\right)^{\mathrm{n}} \mathrm{cos}\left[\left(\frac{\mathrm{n}}{\mathrm{2}}−\mathrm{k}\right)\theta\right]\mathrm{d}\theta \\ $$

Question Number 192676 Answers: 1 Comments: 0

Find: x = ? 1. lg(5x^2 − 6)∙lg(5x − 6) = 0 2. (2x − 5)∙log_3 (1,5 − x) = 0 3. 4^x − 14∙2^x − 32 = 0

$$\mathrm{Find}:\:\:\:\mathrm{x}\:=\:? \\ $$$$\mathrm{1}.\:\:\mathrm{lg}\left(\mathrm{5x}^{\mathrm{2}} \:−\:\mathrm{6}\right)\centerdot\mathrm{lg}\left(\mathrm{5x}\:−\:\mathrm{6}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{2}.\:\:\left(\mathrm{2x}\:−\:\mathrm{5}\right)\centerdot\mathrm{log}_{\mathrm{3}} \left(\mathrm{1},\mathrm{5}\:−\:\mathrm{x}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{3}.\:\:\mathrm{4}^{\boldsymbol{\mathrm{x}}} \:−\:\mathrm{14}\centerdot\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:−\:\mathrm{32}\:=\:\mathrm{0} \\ $$

Question Number 192675 Answers: 1 Comments: 0

Question Number 192661 Answers: 1 Comments: 2

Question Number 192630 Answers: 0 Comments: 0

z=xy−5x+2y. find (dz/dx) and (dz/dy) at(2,4)

$${z}={xy}−\mathrm{5}{x}+\mathrm{2}{y}.\:{find}\:\frac{{dz}}{{dx}}\:{and}\:\frac{{dz}}{{dy}}\:{at}\left(\mathrm{2},\mathrm{4}\right) \\ $$

Question Number 192629 Answers: 0 Comments: 0

Z=f(x_(1,) x_(2,) x_3 )=x_1 x_2 +x_1 ^5 −x_2 ^2 x_3 find f_1 ,f_(11) ,and f_(21)

$${Z}={f}\left({x}_{\mathrm{1},} {x}_{\mathrm{2},} {x}_{\mathrm{3}} \right)={x}_{\mathrm{1}} {x}_{\mathrm{2}} +{x}_{\mathrm{1}} ^{\mathrm{5}} −{x}_{\mathrm{2}} ^{\mathrm{2}} {x}_{\mathrm{3}} \:{find}\:{f}_{\mathrm{1}} ,{f}_{\mathrm{11}} ,{and}\:{f}_{\mathrm{21}} \\ $$

Question Number 192625 Answers: 3 Comments: 1

lim_(x→0) ((sin^4 (πcos(x)))/(1−cos(1−cos(1−cos(x)))))

$${lim}_{{x}\rightarrow\mathrm{0}} \frac{{sin}^{\mathrm{4}} \left(\pi{cos}\left({x}\right)\right)}{\mathrm{1}−{cos}\left(\mathrm{1}−{cos}\left(\mathrm{1}−{cos}\left({x}\right)\right)\right)} \\ $$

Question Number 192596 Answers: 2 Comments: 0

Question Number 192594 Answers: 0 Comments: 0

Question Number 192542 Answers: 2 Comments: 0

Question Number 192508 Answers: 1 Comments: 1

Question Number 192481 Answers: 1 Comments: 0

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