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AllQuestion and Answers: Page 425

Question Number 176764 Answers: 0 Comments: 0

Question Number 176773 Answers: 0 Comments: 2

Let a, b, c >0. If ((a−b)/b)>7, ((b+c)/c)<8, Find min(a+b+c)

$$\mathrm{Let}\:{a},\:{b},\:{c}\:>\mathrm{0}.\:\mathrm{If}\: \\ $$$$\frac{{a}−{b}}{{b}}>\mathrm{7},\:\frac{{b}+{c}}{{c}}<\mathrm{8},\: \\ $$$$\mathrm{Find}\:\mathrm{min}\left({a}+{b}+{c}\right)\: \\ $$

Question Number 176281 Answers: 0 Comments: 3

Question Number 176279 Answers: 1 Comments: 0

Proof that : ∄n∈Z, n^2 +1≡0(mod 4)

$$\mathrm{Proof}\:\mathrm{that}\:: \\ $$$$\nexists{n}\in\mathbb{Z},\:{n}^{\mathrm{2}} +\mathrm{1}\equiv\mathrm{0}\left(\mathrm{mod}\:\mathrm{4}\right) \\ $$

Question Number 176278 Answers: 0 Comments: 0

Σ_(n=1) ^∞ (H_(4n) /(2^(4n) n))=???

$$\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\boldsymbol{{H}}_{\mathrm{4}\boldsymbol{{n}}} }{\mathrm{2}^{\mathrm{4}\boldsymbol{{n}}} \boldsymbol{{n}}}=??? \\ $$

Question Number 176276 Answers: 2 Comments: 0

coeff of x^2 from [6+8x−(3/2)x^2 ]^5

$$\mathrm{coeff}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} \:\mathrm{from}\: \\ $$$$\:\:\left[\mathrm{6}+\mathrm{8x}−\frac{\mathrm{3}}{\mathrm{2}}\mathrm{x}^{\mathrm{2}} \:\right]^{\mathrm{5}} \: \\ $$

Question Number 176274 Answers: 1 Comments: 0

Question Number 176270 Answers: 0 Comments: 3

kojo can do a piece of work in 5hours Edina can do the same work in 4hours. how long will it take the two of them to do the same work together if they work at the same rate

$$\:\mathrm{kojo}\:\mathrm{can}\:\mathrm{do}\:\mathrm{a}\:\mathrm{piece}\:\mathrm{of}\:\mathrm{work}\:\mathrm{in}\:\mathrm{5hours} \\ $$$$\:\mathrm{Edina}\:\mathrm{can}\:\mathrm{do}\:\mathrm{the}\:\mathrm{same}\:\mathrm{work}\:\mathrm{in}\: \\ $$$$\:\mathrm{4hours}.\:\mathrm{how}\:\mathrm{long}\:\mathrm{will}\:\mathrm{it}\:\mathrm{take}\:\mathrm{the}\:\mathrm{two} \\ $$$$\:\mathrm{of}\:\mathrm{them}\:\mathrm{to}\:\mathrm{do}\:\mathrm{the}\:\mathrm{same}\:\mathrm{work}\:\mathrm{together} \\ $$$$\mathrm{if}\:\mathrm{they}\:\mathrm{work}\:\mathrm{at}\:\mathrm{the}\:\mathrm{same}\:\mathrm{rate} \\ $$$$ \\ $$

Question Number 176776 Answers: 2 Comments: 0

Question Number 176809 Answers: 1 Comments: 0

{ ((x=cos^3 ∅)),((y=sin^3 ∅)) :} ⇒(d^2 y/dx^2 ) =?

$$\:\:\begin{cases}{\mathrm{x}=\mathrm{cos}\:^{\mathrm{3}} \emptyset}\\{\mathrm{y}=\mathrm{sin}\:^{\mathrm{3}} \emptyset}\end{cases}\:\Rightarrow\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:=? \\ $$

Question Number 176808 Answers: 1 Comments: 0

lim_(x→∞) ((sin x)/(1+cos^2 x))=?

$$\:\:\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{1}+\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}}=? \\ $$

Question Number 176774 Answers: 1 Comments: 0

How many distinct y exist satisfying ∣x^2 −8x+18∣+∣y−3∣=5

$$\mathrm{How}\:\mathrm{many}\:\mathrm{distinct}\:{y}\:\mathrm{exist}\:\mathrm{satisfying} \\ $$$$\mid{x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{18}\mid+\mid{y}−\mathrm{3}\mid=\mathrm{5} \\ $$

Question Number 176216 Answers: 0 Comments: 0

Question Number 176215 Answers: 2 Comments: 0

A certain amount of money is distributed among A, B and C in the ratio of 2:5:3 and another amount of money among B, D and E is also distributed in the same ratio. If the amount distributed among A, B and C is ⅖ of the amount distributed among B, D and E, what is the ratio in which the amount is distributed among A, C and E?

$$ \\ $$A certain amount of money is distributed among A, B and C in the ratio of 2:5:3 and another amount of money among B, D and E is also distributed in the same ratio. If the amount distributed among A, B and C is ⅖ of the amount distributed among B, D and E, what is the ratio in which the amount is distributed among A, C and E?

Question Number 176213 Answers: 1 Comments: 0

lim_(x→0) ((arctan x)/(arcsin x−x)) =?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{arctan}\:\mathrm{x}}{\mathrm{arcsin}\:\mathrm{x}−\mathrm{x}}\:=? \\ $$

Question Number 176212 Answers: 0 Comments: 2

A solid rigth triangular prism of length 12cm and a cross section which is an equilateral triangle of 6cm. Find the total surface area.

$$\:\:\mathrm{A}\:\mathrm{solid}\:\mathrm{rigth}\:\mathrm{triangular}\:\mathrm{prism}\:\mathrm{of}\: \\ $$$$\:\:\mathrm{length}\:\mathrm{12cm}\:\mathrm{and}\:\mathrm{a}\:\mathrm{cross}\:\mathrm{section}\: \\ $$$$\:\:\mathrm{which}\:\mathrm{is}\:\mathrm{an}\:\mathrm{equilateral}\:\mathrm{triangle}\:\mathrm{of} \\ $$$$\:\:\mathrm{6cm}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{total}\:\mathrm{surface}\:\mathrm{area}. \\ $$

Question Number 176211 Answers: 1 Comments: 0

Question Number 176206 Answers: 1 Comments: 0

Question Number 176205 Answers: 1 Comments: 0

In a school election for the positon of SRC president, one candidate obtained 87.5% of the vote cast others obtained 275 votes (a) How many votes did the winner obtain. (b) If the voter turnout was 55% find the total number of eligible voters in the school.

$$\:\mathrm{In}\:\mathrm{a}\:\mathrm{school}\:\mathrm{election}\:\mathrm{for}\:\mathrm{the}\:\mathrm{positon}\: \\ $$$$\:\:\mathrm{of}\:\mathrm{SRC}\:\mathrm{president},\:\mathrm{one}\:\mathrm{candidate} \\ $$$$\:\:\mathrm{obtained}\:\mathrm{87}.\mathrm{5\%}\:\mathrm{of}\:\mathrm{the}\:\mathrm{vote}\:\mathrm{cast}\: \\ $$$$\:\:\mathrm{others}\:\mathrm{obtained}\:\mathrm{275}\:\mathrm{votes} \\ $$$$\:\:\left(\mathrm{a}\right)\:\mathrm{How}\:\mathrm{many}\:\mathrm{votes}\:\mathrm{did}\:\mathrm{the}\:\mathrm{winner} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{obtain}. \\ $$$$\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{If}\:\mathrm{the}\:\mathrm{voter}\:\mathrm{turnout}\:\mathrm{was}\:\mathrm{55\%}\: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{total}\:\mathrm{number}\:\mathrm{of}\:\:\mathrm{eligible} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{voters}\:\mathrm{in}\:\mathrm{the}\:\mathrm{school}. \\ $$$$ \\ $$

Question Number 176199 Answers: 1 Comments: 0

Question Number 176195 Answers: 1 Comments: 0

Question Number 176192 Answers: 1 Comments: 0

Suppose ABCD is a rectangle. X and Y are points on BC and CD respectively, such that the area of ABX, CXY, and AYD are 3 cm^2 , 4 cm^2 , and 5 cm^2 respectively. Find the area of AXY.

$$\mathrm{Suppose}\:\mathrm{ABCD}\:\mathrm{is}\:\mathrm{a}\:\mathrm{rectangle}.\:\mathrm{X}\:\mathrm{and}\:\mathrm{Y}\:\mathrm{are}\:\mathrm{points}\:\mathrm{on}\:\mathrm{BC}\:\mathrm{and}\:\mathrm{CD}\:\mathrm{respectively}, \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{ABX},\:\mathrm{CXY},\:\mathrm{and}\:\mathrm{AYD}\:\mathrm{are}\:\mathrm{3}\:\mathrm{cm}^{\mathrm{2}} ,\:\mathrm{4}\:\mathrm{cm}^{\mathrm{2}} ,\:\mathrm{and}\:\mathrm{5}\:\mathrm{cm}^{\mathrm{2}} \:\mathrm{respectively}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{AXY}. \\ $$

Question Number 176189 Answers: 1 Comments: 0

solve for x (1+(1/x))^(x+1) =(1+(1/6))^6 show working

$${solve}\:{for}\:{x} \\ $$$$\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{x}+\mathrm{1}} =\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{6}}\right)^{\mathrm{6}} \\ $$$${show}\:{working} \\ $$

Question Number 176188 Answers: 1 Comments: 0

∫_( (√2)) ^2 ((sec^2 (sec^(−1) x))/(x(√(x^2 −1))))

$$ \\ $$$$\underset{\:\sqrt{\mathrm{2}}} {\overset{\mathrm{2}} {\int}}\frac{\mathrm{sec}^{\mathrm{2}} \left(\mathrm{sec}^{−\mathrm{1}} \mathrm{x}\right)}{\mathrm{x}\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}} \\ $$$$ \\ $$

Question Number 176187 Answers: 1 Comments: 0

∫(dy/(tan^(−1) y(1+y^2 )))

$$\int\frac{\mathrm{dy}}{\mathrm{tan}^{−\mathrm{1}} \mathrm{y}\left(\mathrm{1}+\mathrm{y}^{\mathrm{2}} \right)} \\ $$

Question Number 176185 Answers: 0 Comments: 1

∫(e^(sin^(−1) x) /( (√(1−x_ ^2 )))) dx

$$\int\frac{\mathrm{e}^{\mathrm{sin}^{−\mathrm{1}} \mathrm{x}} }{\:\sqrt{\mathrm{1}−\mathrm{x}_{} ^{\mathrm{2}} }}\:\mathrm{dx} \\ $$

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