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AlgebraQuestion and Answers: Page 271

Question Number 91474    Answers: 0   Comments: 0

f(x)=(√(4−x^2 )) and g(x)=3x+1 find the sum , different, and product f(x) and g(x).

$$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{4}−\mathrm{x}^{\mathrm{2}} }\:\:\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right)=\mathrm{3x}+\mathrm{1} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:,\:\mathrm{different},\:\mathrm{and}\:\mathrm{product} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right). \\ $$

Question Number 91473    Answers: 1   Comments: 0

Question Number 91471    Answers: 1   Comments: 0

∣2x−7∣>3

$$\mid\mathrm{2x}−\mathrm{7}\mid>\mathrm{3} \\ $$

Question Number 91470    Answers: 0   Comments: 2

∣x−3∣<0.1

$$\mid\mathrm{x}−\mathrm{3}\mid<\mathrm{0}.\mathrm{1} \\ $$

Question Number 91469    Answers: 0   Comments: 3

−5<((4−3x)/2)<l

$$−\mathrm{5}<\frac{\mathrm{4}−\mathrm{3x}}{\mathrm{2}}<\mathrm{l} \\ $$

Question Number 91468    Answers: 0   Comments: 0

Question Number 91464    Answers: 0   Comments: 12

Find the greatest coefficient in the expansion of (3 − 2x)^(−7)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{coefficient}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\:\:\:\:\:\:\:\left(\mathrm{3}\:\:−\:\:\mathrm{2x}\right)^{−\mathrm{7}} \\ $$

Question Number 91452    Answers: 2   Comments: 1

((−1))^(1/4) =?

$$\:\:\:\sqrt[{\mathrm{4}}]{−\mathrm{1}}\:=? \\ $$

Question Number 91671    Answers: 0   Comments: 2

show that (x)^(1/(ln(x))) =e

$${show}\:{that} \\ $$$$\sqrt[{{ln}\left({x}\right)}]{{x}}={e} \\ $$

Question Number 91399    Answers: 2   Comments: 13

Question Number 91390    Answers: 1   Comments: 3

ABCDEF is a 6 digit number, ABC and DEF are 3 digit numbers. find ABCDEF satisfying: 1) ABCDEF=1×ABC×DEF 2) ABCDEF=2×ABC×DEF 3) ABCDEF=3×ABC×DEF 4) ABCDEF=4×ABC×DEF 5) ABCDEF=5×ABC×DEF 6) ABCDEF=6×ABC×DEF 7) ABCDEF=7×ABC×DEF 8) ABCDEF=8×ABC×DEF 9) ABCDEF=9×ABC×DEF

$${ABCDEF}\:{is}\:{a}\:\mathrm{6}\:{digit}\:{number}, \\ $$$${ABC}\:{and}\:{DEF}\:{are}\:\mathrm{3}\:{digit}\:{numbers}. \\ $$$${find}\:{ABCDEF}\:\:{satisfying}: \\ $$$$\left.\mathrm{1}\right)\:\:\:{ABCDEF}=\mathrm{1}×{ABC}×{DEF} \\ $$$$\left.\mathrm{2}\right)\:\:\:{ABCDEF}=\mathrm{2}×{ABC}×{DEF} \\ $$$$\left.\mathrm{3}\right)\:\:\:{ABCDEF}=\mathrm{3}×{ABC}×{DEF} \\ $$$$\left.\mathrm{4}\right)\:\:\:{ABCDEF}=\mathrm{4}×{ABC}×{DEF} \\ $$$$\left.\mathrm{5}\right)\:\:\:{ABCDEF}=\mathrm{5}×{ABC}×{DEF} \\ $$$$\left.\mathrm{6}\right)\:\:\:{ABCDEF}=\mathrm{6}×{ABC}×{DEF} \\ $$$$\left.\mathrm{7}\right)\:\:\:{ABCDEF}=\mathrm{7}×{ABC}×{DEF} \\ $$$$\left.\mathrm{8}\right)\:\:\:{ABCDEF}=\mathrm{8}×{ABC}×{DEF} \\ $$$$\left.\mathrm{9}\right)\:\:\:{ABCDEF}=\mathrm{9}×{ABC}×{DEF} \\ $$

Question Number 91378    Answers: 1   Comments: 6

Question Number 91377    Answers: 0   Comments: 1

Question Number 91362    Answers: 1   Comments: 3

Question Number 91277    Answers: 2   Comments: 0

p=1−(1/2)+(1/3)−(1/4)+...+(1/(2003))−(1/(2004)) q=(1/(1003))+(1/(1004))+...+(1/(2004)) p^2 +q^2 =

$${p}=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{4}}+...+\frac{\mathrm{1}}{\mathrm{2003}}−\frac{\mathrm{1}}{\mathrm{2004}} \\ $$$${q}=\frac{\mathrm{1}}{\mathrm{1003}}+\frac{\mathrm{1}}{\mathrm{1004}}+...+\frac{\mathrm{1}}{\mathrm{2004}} \\ $$$${p}^{\mathrm{2}} +{q}^{\mathrm{2}} \:=\: \\ $$

Question Number 91258    Answers: 0   Comments: 0

prove that _2 F_1 (α,β,β−a+1,−1)=((Γ(β−a+1)Γ((β/2)+1))/(Γ(β+1)Γ((β/2)−α+1)))

$${prove}\:{that} \\ $$$$\:\:\:_{\mathrm{2}} {F}_{\mathrm{1}} \left(\alpha,\beta,\beta−{a}+\mathrm{1},−\mathrm{1}\right)=\frac{\Gamma\left(\beta−{a}+\mathrm{1}\right)\Gamma\left(\frac{\beta}{\mathrm{2}}+\mathrm{1}\right)}{\Gamma\left(\beta+\mathrm{1}\right)\Gamma\left(\frac{\beta}{\mathrm{2}}−\alpha+\mathrm{1}\right)} \\ $$

Question Number 91195    Answers: 1   Comments: 0

what is the duble fictorial furmolla?

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{duble}\:\mathrm{fictorial}\:\mathrm{furmolla}? \\ $$

Question Number 91178    Answers: 0   Comments: 2

Question Number 91166    Answers: 0   Comments: 7

Question Number 91047    Answers: 1   Comments: 6

Find the square root of: (√7) + (√5)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{square}\:\mathrm{root}\:\mathrm{of}:\:\:\:\:\sqrt{\mathrm{7}}\:\:+\:\:\sqrt{\mathrm{5}} \\ $$

Question Number 91038    Answers: 1   Comments: 1

if sin((α/2))=(4/5) and cos((β/2))=(3/5) prove sin(α)=cos(β)

$${if}\:{sin}\left(\frac{\alpha}{\mathrm{2}}\right)=\frac{\mathrm{4}}{\mathrm{5}} \\ $$$${and}\:{cos}\left(\frac{\beta}{\mathrm{2}}\right)=\frac{\mathrm{3}}{\mathrm{5}} \\ $$$${prove} \\ $$$${sin}\left(\alpha\right)={cos}\left(\beta\right) \\ $$

Question Number 90946    Answers: 0   Comments: 0

determine x,y,z ∈ R such that 2x^2 +y^2 +2z^2 −8x+2y−2xy+2xz−16z+35=0

$${determine}\:{x},{y},{z}\:\in\:\mathbb{R}\:{such}\:{that}\: \\ $$$$\mathrm{2}{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{2}{z}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{2}{y}−\mathrm{2}{xy}+\mathrm{2}{xz}−\mathrm{16}{z}+\mathrm{35}=\mathrm{0} \\ $$

Question Number 90916    Answers: 0   Comments: 0

Question Number 90842    Answers: 3   Comments: 4

x^2 −(y−z)^2 = 3 y^2 − (z−x)^2 = 5 z^2 − (x−y)^2 = 12

$${x}^{\mathrm{2}} −\left({y}−{z}\right)^{\mathrm{2}} \:=\:\mathrm{3} \\ $$$${y}^{\mathrm{2}} \:−\:\left({z}−{x}\right)^{\mathrm{2}} \:=\:\mathrm{5} \\ $$$${z}^{\mathrm{2}} \:−\:\left({x}−{y}\right)^{\mathrm{2}} \:=\:\mathrm{12} \\ $$

Question Number 90793    Answers: 1   Comments: 4

a+b+c+d=4 a^2 +b^2 +c^2 +d^2 =10 a^3 +b^3 +c^3 +d^3 =22 a^4 +b^4 +c^4 +d^4 = ?

$${a}+{b}+{c}+{d}=\mathrm{4} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +{d}^{\mathrm{2}} =\mathrm{10} \\ $$$${a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} +{d}^{\mathrm{3}} =\mathrm{22} \\ $$$${a}^{\mathrm{4}} +{b}^{\mathrm{4}} +{c}^{\mathrm{4}} +{d}^{\mathrm{4}} =\:? \\ $$

Question Number 90772    Answers: 0   Comments: 2

show that the roots of the equation x^2 −2x=(b−c)^2 −1 are rational if b and c are rational numbers.

$${show}\:{that}\:{the}\:{roots}\:{of}\:{the}\:{equation} \\ $$$${x}^{\mathrm{2}} −\mathrm{2}{x}=\left({b}−{c}\right)^{\mathrm{2}} −\mathrm{1}\:{are}\:{rational}\:{if} \\ $$$${b}\:{and}\:{c}\:{are}\:{rational}\:{numbers}. \\ $$

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