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AllQuestion and Answers: Page 1322

Question Number 75291 Answers: 1 Comments: 0

Question Number 75280 Answers: 1 Comments: 0

A car travels at a constant speed and covers 240km in 8hours . How far does it travel at the same speed in 5hours

$$\mathrm{A}\:\mathrm{car}\:\mathrm{travels}\:\mathrm{at}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{speed}\:\mathrm{and}\: \\ $$$$\mathrm{covers}\:\mathrm{240km}\:\mathrm{in}\:\mathrm{8hours}\:.\:\mathrm{How}\:\mathrm{far}\:\mathrm{does} \\ $$$$\mathrm{it}\:\mathrm{travel}\:\mathrm{at}\:\mathrm{the}\:\mathrm{same}\:\mathrm{speed}\:\mathrm{in}\:\mathrm{5hours} \\ $$$$ \\ $$

Question Number 75277 Answers: 1 Comments: 0

The scale of a map is 1:40,000 . Calculate the area in square centimeters on the map of forest reserved which covers 170km^2 . please help solve this question

$$\mathrm{The}\:\mathrm{scale}\:\mathrm{of}\:\mathrm{a}\:\mathrm{map}\:\mathrm{is}\:\mathrm{1}:\mathrm{40},\mathrm{000}\:.\:\mathrm{Calculate} \\ $$$$\mathrm{the}\:\mathrm{area}\:\mathrm{in}\:\mathrm{square}\:\mathrm{centimeters}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{map}\:\mathrm{of}\:\mathrm{forest}\:\mathrm{reserved}\:\mathrm{which}\:\mathrm{covers}\: \\ $$$$\mathrm{170km}^{\mathrm{2}} . \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{question} \\ $$

Question Number 75276 Answers: 0 Comments: 2

Write the formula of a circle if coordinates of ends of diameter of the circle are given ?

$$\mathrm{Write}\:\mathrm{the}\:\mathrm{formula}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{if}\:\mathrm{coordinates} \\ $$$$\mathrm{of}\:\mathrm{ends}\:\mathrm{of}\:\mathrm{diameter}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{are}\:\mathrm{given}\:? \\ $$

Question Number 75272 Answers: 1 Comments: 0

a) If z=1+i(√3) prove that prove that z^(14) =2^(13) (−1+i(√3) ) b)prove that in triangle ABC a^2 −(b−c)^2 cos^2 (A/2)=(b+c)^2 sin^2 (A/2)

$$\left.{a}\right)\:{If}\:{z}=\mathrm{1}+{i}\sqrt{\mathrm{3}}\:{prove}\:{that} \\ $$$${prove}\:{that} \\ $$$${z}^{\mathrm{14}} =\mathrm{2}^{\mathrm{13}} \left(−\mathrm{1}+{i}\sqrt{\mathrm{3}}\:\right) \\ $$$$ \\ $$$$\left.{b}\right){prove}\:{that}\:{in}\:{triangle}\:{ABC} \\ $$$${a}^{\mathrm{2}} −\left({b}−{c}\right)^{\mathrm{2}} \mathrm{cos}\:^{\mathrm{2}} \frac{{A}}{\mathrm{2}}=\left({b}+{c}\right)^{\mathrm{2}} \mathrm{sin}\:^{\mathrm{2}} \frac{{A}}{\mathrm{2}} \\ $$

Question Number 75268 Answers: 0 Comments: 0

Question Number 75267 Answers: 0 Comments: 5

Question Number 75260 Answers: 0 Comments: 0

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Question Number 75255 Answers: 0 Comments: 0

Question Number 75254 Answers: 1 Comments: 0

Question Number 75256 Answers: 0 Comments: 0

if B⊆A,A⋒B′={1,4,5} and A⊔B={1,2,3,4,5,6}, find B.

$${if}\:{B}\subseteq{A},{A}\Cap{B}'=\left\{\mathrm{1},\mathrm{4},\mathrm{5}\right\}\:{and}\:{A}\sqcup{B}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}\right\},\:{find}\:{B}. \\ $$

Question Number 75257 Answers: 1 Comments: 0

Let A={2,4,6,7,8,9} B={1,3,5,6,10} and C={x:3x+6=0 or 2x+6=0}.Find a. A∪B. b. is(A∪B)∪C=A∪(B∪C)?

$${Let}\:{A}=\left\{\mathrm{2},\mathrm{4},\mathrm{6},\mathrm{7},\mathrm{8},\mathrm{9}\right\} \\ $$$${B}=\left\{\mathrm{1},\mathrm{3},\mathrm{5},\mathrm{6},\mathrm{10}\right\}\:{and} \\ $$$${C}=\left\{{x}:\mathrm{3}{x}+\mathrm{6}=\mathrm{0}\:{or}\:\mathrm{2}{x}+\mathrm{6}=\mathrm{0}\right\}.{Find} \\ $$$${a}.\:{A}\cup{B}. \\ $$$${b}.\:{is}\left({A}\cup{B}\right)\cup{C}={A}\cup\left({B}\cup{C}\right)? \\ $$

Question Number 75248 Answers: 1 Comments: 1

Question Number 75242 Answers: 2 Comments: 0

Find th greatest coefficients in the expansion of (3a+5b)^(18) 2)If three consecutive coefficient of (1+x)^n are 28,56,70. find the value of n

$${Find}\:{th}\:{greatest}\:{coefficients} \\ $$$${in}\:{the}\:{expansion}\:{of} \\ $$$$\left(\mathrm{3}{a}+\mathrm{5}{b}\right)^{\mathrm{18}} \\ $$$$ \\ $$$$\left.\mathrm{2}\right){If}\:{three}\:{consecutive}\: \\ $$$${coefficient}\:{of}\:\left(\mathrm{1}+{x}\right)^{{n}} \:{are}\:\mathrm{28},\mathrm{56},\mathrm{70}. \\ $$$${find}\:{the}\:{value}\:{of}\:{n} \\ $$$$ \\ $$

Question Number 75230 Answers: 1 Comments: 1

Question Number 75262 Answers: 0 Comments: 3

Question Number 75225 Answers: 0 Comments: 0

Prove that lim_(x→∞) (xln∣x∣−(x−m)ln∣x−m∣)=+∞

$$\mathrm{Prove}\:\mathrm{that}\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{xln}\mid\mathrm{x}\mid−\left(\mathrm{x}−\mathrm{m}\right)\mathrm{ln}\mid\mathrm{x}−\mathrm{m}\mid\right)=+\infty \\ $$

Question Number 75224 Answers: 0 Comments: 0

Prove that lim_(x→∞) (xln∣x∣−(x−m)ln∣x−m∣)=+∞

Question Number 75223 Answers: 0 Comments: 0

Question Number 75222 Answers: 0 Comments: 1

Question Number 75220 Answers: 2 Comments: 0

Let us consider the function F(x)=∫_0 ^1 e^(−x) ln(x−lnt)dt 1)Prove that for all x≥1 , F(x) exist 2)Prove that lim_(t→0) tln(x−lnt)=0 3)Prove that F ∈ C^1 ([1:∞[,[1:∞[) and for all x≥1 F(x)=F′(x)+lnx 4) Find out the value lim_(x→∞) F(x) and lim_(x→1) F(x) 5)Can you prove that at least one of the both result is irrational???

$$\mathrm{Let}\:\mathrm{us}\:\mathrm{consider}\:\mathrm{the}\:\mathrm{function}\: \\ $$$$\mathrm{F}\left(\mathrm{x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{e}^{−\mathrm{x}} \mathrm{ln}\left(\mathrm{x}−\mathrm{lnt}\right)\mathrm{dt}\: \\ $$$$\left.\mathrm{1}\right)\mathrm{Prove}\:\mathrm{that}\:\mathrm{for}\:\mathrm{all}\:\mathrm{x}\geqslant\mathrm{1}\:,\:\:\mathrm{F}\left(\mathrm{x}\right)\:\mathrm{exist} \\ $$$$\left.\mathrm{2}\right)\mathrm{Prove}\:\mathrm{that}\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{tln}\left(\mathrm{x}−\mathrm{lnt}\right)=\mathrm{0} \\ $$$$\left.\mathrm{3}\right)\mathrm{Prove}\:\mathrm{that}\:\mathrm{F}\:\in\:\mathrm{C}^{\mathrm{1}} \left(\left[\mathrm{1}:\infty\left[,\left[\mathrm{1}:\infty\left[\right)\:\mathrm{and}\:\mathrm{for}\:\right.\right.\right.\right. \\ $$$$\mathrm{all}\:\mathrm{x}\geqslant\mathrm{1}\:\:\mathrm{F}\left(\mathrm{x}\right)=\mathrm{F}'\left(\mathrm{x}\right)+\mathrm{lnx} \\ $$$$\left.\mathrm{4}\right)\:\mathrm{Find}\:\mathrm{out}\:\mathrm{the}\:\mathrm{value}\: \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{F}\left(\mathrm{x}\right)\:\:\:\:\:\:\mathrm{and}\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}F}\left(\mathrm{x}\right) \\ $$$$\left.\mathrm{5}\right)\mathrm{Can}\:\mathrm{you}\:\mathrm{prove}\:\mathrm{that}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{both}\:\mathrm{result}\:\mathrm{is}\:\mathrm{irrational}??? \\ $$

Question Number 75228 Answers: 0 Comments: 1

Let consider A=lim_(x→0) (∫_0 ^1 (Γ(t))^x dt)^(1/x) Prove that A=∫_0 ^1 ln(Γ(t))dt Deduce the value of A

$$\:\mathrm{Let}\:\mathrm{consider}\: \\ $$$$\mathrm{A}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\int_{\mathrm{0}} ^{\mathrm{1}} \left(\Gamma\left(\mathrm{t}\right)\right)^{\mathrm{x}} \mathrm{dt}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\:\mathrm{A}=\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{ln}\left(\Gamma\left(\mathrm{t}\right)\right)\mathrm{dt}\:\: \\ $$$$\mathrm{Deduce}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{A} \\ $$

Question Number 75218 Answers: 1 Comments: 1

Simplify: (x^4 −3x^3 +4x^2 −12x) : (x^2 +4)

$$\mathrm{Simplify}:\:\left({x}^{\mathrm{4}} −\mathrm{3}{x}^{\mathrm{3}} +\mathrm{4}{x}^{\mathrm{2}} −\mathrm{12}{x}\right)\::\:\left({x}^{\mathrm{2}} +\mathrm{4}\right) \\ $$

Question Number 75212 Answers: 1 Comments: 0

Question Number 75208 Answers: 1 Comments: 0

Prove that : cos 18^0 −sin 18^0 = (√2) sin 2

$$\:\mathrm{Prove}\:\mathrm{that}\::\:\mathrm{cos}\:\mathrm{18}^{\mathrm{0}} −\mathrm{sin}\:\mathrm{18}^{\mathrm{0}} \:=\:\sqrt{\mathrm{2}}\:\mathrm{sin}\:\mathrm{2} \\ $$

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