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AllQuestion and Answers: Page 331

Question Number 185776 Answers: 3 Comments: 0

Question Number 185774 Answers: 2 Comments: 0

Question Number 185770 Answers: 1 Comments: 0

Question Number 185768 Answers: 1 Comments: 0

Question Number 185764 Answers: 2 Comments: 0

If f(x)=−(x^2 /8)+x−(a/8)−1 has 2 diffrent real roots in ((√(7a)),+∞), find the range of a>0.

$$\mathrm{If}\:{f}\left({x}\right)=−\frac{{x}^{\mathrm{2}} }{\mathrm{8}}+{x}−\frac{{a}}{\mathrm{8}}−\mathrm{1}\:\mathrm{has}\:\mathrm{2}\:\mathrm{diffrent}\:\mathrm{real} \\ $$$$\mathrm{roots}\:\mathrm{in}\:\left(\sqrt{\mathrm{7}{a}},+\infty\right),\:\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{a}>\mathrm{0}. \\ $$

Question Number 185760 Answers: 1 Comments: 0

A=2×10^0 +10^(−1) +6×10^(−2) +6×10^(−3) +6×10^(−4) +.... (A/(13))=?

$${A}=\mathrm{2}×\mathrm{10}^{\mathrm{0}} +\mathrm{10}^{−\mathrm{1}} +\mathrm{6}×\mathrm{10}^{−\mathrm{2}} +\mathrm{6}×\mathrm{10}^{−\mathrm{3}} +\mathrm{6}×\mathrm{10}^{−\mathrm{4}} +.... \\ $$$$\frac{{A}}{\mathrm{13}}=? \\ $$

Question Number 185754 Answers: 0 Comments: 0

Question Number 185752 Answers: 0 Comments: 1

Question Number 185747 Answers: 0 Comments: 0

Question Number 185744 Answers: 0 Comments: 0

Question Number 185734 Answers: 4 Comments: 0

x = (√(8 + (√(40 + 8 (√5))))) y = (√(8 − (√(40 + 8 (√5))))) Find: x^6 + y^6 = ?

$$\mathrm{x}\:=\:\sqrt{\mathrm{8}\:+\:\sqrt{\mathrm{40}\:+\:\mathrm{8}\:\sqrt{\mathrm{5}}}} \\ $$$$\mathrm{y}\:=\:\sqrt{\mathrm{8}\:−\:\sqrt{\mathrm{40}\:+\:\mathrm{8}\:\sqrt{\mathrm{5}}}} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{x}^{\mathrm{6}} \:+\:\mathrm{y}^{\mathrm{6}} \:=\:? \\ $$

Question Number 185733 Answers: 0 Comments: 0

Question Number 185732 Answers: 1 Comments: 0

Question Number 185731 Answers: 0 Comments: 0

Question Number 185729 Answers: 1 Comments: 8

Question Number 185728 Answers: 1 Comments: 0

(x−2013)!=6!7! x=??

$$\left(\mathrm{x}−\mathrm{2013}\right)!=\mathrm{6}!\mathrm{7}! \\ $$$$\mathrm{x}=?? \\ $$

Question Number 185727 Answers: 0 Comments: 0

Question Number 185723 Answers: 1 Comments: 0

Question Number 185708 Answers: 2 Comments: 0

Question Number 185706 Answers: 3 Comments: 0

if x^2 + x + 1 = 0 find: x^(2011) + (1/x^(2011) ) = ?

$$\mathrm{if}\:\:\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$\mathrm{find}:\:\:\:\:\:\mathrm{x}^{\mathrm{2011}} \:+\:\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2011}} }\:=\:? \\ $$

Question Number 185705 Answers: 1 Comments: 0

Question Number 185701 Answers: 0 Comments: 2

1000!

$$\mathrm{1000}! \\ $$

Question Number 185700 Answers: 0 Comments: 1

Question Number 185695 Answers: 2 Comments: 0

If u^→ and v^→ are vectors in R^3 then prove that u^→ .v^→ =(1/4)∥u^→ +v^→ ∥^2 −(1/4)∥u^→ −v^→ ∥^2

$${If}\:\overset{\rightarrow} {{u}}\:{and}\:\overset{\rightarrow} {{v}}\:{are}\:{vectors}\:{in}\:\mathbb{R}^{\mathrm{3}} \\ $$$${then}\:{prove}\:{that}\: \\ $$$$\overset{\rightarrow} {{u}}.\overset{\rightarrow} {{v}}=\frac{\mathrm{1}}{\mathrm{4}}\parallel\overset{\rightarrow} {{u}}+\overset{\rightarrow} {{v}}\parallel^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{4}}\parallel\overset{\rightarrow} {{u}}−\overset{\rightarrow} {{v}}\parallel^{\mathrm{2}} \\ $$

Question Number 185694 Answers: 0 Comments: 0

Show that the set V=R^3 with standard vector addition and multiplication defined as c(u_1 ,u_2 ,u_3 )=(0,0,cu_3 )

$${Show}\:{that}\:{the}\:{set}\:{V}=\mathbb{R}^{\mathrm{3}} \:{with} \\ $$$${standard}\:{vector}\:{addition}\:{and} \\ $$$${multiplication}\:{defined}\:{as} \\ $$$${c}\left({u}_{\mathrm{1}} ,{u}_{\mathrm{2}} ,{u}_{\mathrm{3}} \right)=\left(\mathrm{0},\mathrm{0},{cu}_{\mathrm{3}} \right) \\ $$

Question Number 185693 Answers: 1 Comments: 1

If k > 0 and f(x) = (x/(∣x∣)) Find f(- (2/7) k) + f( - 2k) = ?

$$\mathrm{If}\:\:\:\mathrm{k}\:>\:\mathrm{0}\:\:\:\mathrm{and}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{x}}{\mid\mathrm{x}\mid} \\ $$$$\mathrm{Find}\:\:\:\mathrm{f}\left(-\:\frac{\mathrm{2}}{\mathrm{7}}\:\mathrm{k}\right)\:+\:\mathrm{f}\left(\:-\:\mathrm{2k}\right)\:=\:? \\ $$

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