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Question Number 168040    Answers: 0   Comments: 4

Question Number 168035    Answers: 0   Comments: 3

In an examination, the probability of charles scoring the highest mark in Maths, Physics and Chemistry are 0.90, 0.75 and 0.80 respectively. Calculate the probability that he will get the highest mark in at least 3 subjects.

$$\mathrm{In}\:\mathrm{an}\:\mathrm{examination},\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of}\:\mathrm{charles} \\ $$$$\mathrm{scoring}\:\mathrm{the}\:\mathrm{highest}\:\mathrm{mark}\:\mathrm{in}\:\mathrm{Maths},\:\mathrm{Physics} \\ $$$$\mathrm{and}\:\mathrm{Chemistry}\:\mathrm{are}\:\mathrm{0}.\mathrm{90},\:\mathrm{0}.\mathrm{75}\:\mathrm{and}\:\mathrm{0}.\mathrm{80}\:\mathrm{respectively}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{he}\:\mathrm{will}\:\mathrm{get} \\ $$$$\mathrm{the}\:\mathrm{highest}\:\mathrm{mark}\:\mathrm{in}\:\mathrm{at}\:\mathrm{least}\:\mathrm{3}\:\mathrm{subjects}. \\ $$

Question Number 168166    Answers: 1   Comments: 0

lim_(x→0) ((sin (sin x)−x ((1−x))^(1/3) )/x^5 ) =?

$$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{sin}\:{x}\right)−{x}\:\sqrt[{\mathrm{3}}]{\mathrm{1}−{x}}}{{x}^{\mathrm{5}} }\:=? \\ $$

Question Number 168026    Answers: 1   Comments: 1

Math question for anyone who has a bonus code solution. Question. Find the smallest numbers that are divisible by 15 remain 9 and divide by 25 remain 19 and divide by 18 remain 12 remain and divide by 36 remain 30 remain and divide above 40 remain 34 remain Whoever solves it on the sheet, put his photo in the comment again.

$$ \\ $$Math question for anyone who has a bonus code solution. Question. Find the smallest numbers that are divisible by 15 remain 9 and divide by 25 remain 19 and divide by 18 remain 12 remain and divide by 36 remain 30 remain and divide above 40 remain 34 remain Whoever solves it on the sheet, put his photo in the comment again.

Question Number 168014    Answers: 1   Comments: 0

lim_(x→0) ((5e^x +5e^(−x) −10)/(4x^2 ))=?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{5}{e}^{{x}} +\mathrm{5}{e}^{−{x}} −\mathrm{10}}{\mathrm{4}{x}^{\mathrm{2}} }=? \\ $$

Question Number 168013    Answers: 2   Comments: 0

Question Number 168011    Answers: 2   Comments: 0

Solve (2x+5y+1)dx − (5x+2y−1)dy=0 Mastermind

$${Solve}\: \\ $$$$\left(\mathrm{2}{x}+\mathrm{5}{y}+\mathrm{1}\right){dx}\:−\:\left(\mathrm{5}{x}+\mathrm{2}{y}−\mathrm{1}\right){dy}=\mathrm{0} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 168009    Answers: 1   Comments: 0

lim_(x→∞) (((√(4x^2 −4x+1))+3x)/( (√(x^2 +x−5))+x))=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{1}}+\mathrm{3}{x}}{\:\sqrt{{x}^{\mathrm{2}} +{x}−\mathrm{5}}+{x}}=? \\ $$

Question Number 168004    Answers: 1   Comments: 0

lim_(x→∞) (√(4x^2 −16x+1))−2x+3=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{16}{x}+\mathrm{1}}−\mathrm{2}{x}+\mathrm{3}=? \\ $$

Question Number 168000    Answers: 0   Comments: 0

Divide a^(5/2) −5a^2 b^(1/3) +10a^(3/2) b^(2/3) −10ab+5a^(1/2) b^(4/3) by a^(1/2) −b^(1/3)

$${Divide}\:{a}^{\frac{\mathrm{5}}{\mathrm{2}}} −\mathrm{5}{a}^{\mathrm{2}} {b}^{\frac{\mathrm{1}}{\mathrm{3}}} +\mathrm{10}{a}^{\frac{\mathrm{3}}{\mathrm{2}}} {b}^{\frac{\mathrm{2}}{\mathrm{3}}} −\mathrm{10}{ab}+\mathrm{5}{a}^{\frac{\mathrm{1}}{\mathrm{2}}} {b}^{\frac{\mathrm{4}}{\mathrm{3}}} \:{by}\:{a}^{\frac{\mathrm{1}}{\mathrm{2}}} −{b}^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$

Question Number 167997    Answers: 0   Comments: 0

xy+3x+2y=−6 yx+y+3z=−3 zx+2z+x=2 find x and y and z

$${xy}+\mathrm{3}{x}+\mathrm{2}{y}=−\mathrm{6} \\ $$$${yx}+{y}+\mathrm{3}{z}=−\mathrm{3} \\ $$$${zx}+\mathrm{2}{z}+{x}=\mathrm{2} \\ $$$${find}\:{x}\:{and}\:{y}\:{and}\:{z} \\ $$$$ \\ $$

Question Number 167996    Answers: 0   Comments: 0

find dy/dx if y=((x+2)/( (√(x+1)))) by first principle

$${find}\:{dy}/{dx}\:{if}\:{y}=\frac{{x}+\mathrm{2}}{\:\sqrt{{x}+\mathrm{1}}}\:{by}\:{first}\:{principle} \\ $$

Question Number 167994    Answers: 0   Comments: 0

Question Number 167989    Answers: 2   Comments: 0

∫ ((3−cos x)/(3+cos x)) dx =?

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\frac{\mathrm{3}−\mathrm{cos}\:{x}}{\mathrm{3}+\mathrm{cos}\:{x}}\:{dx}\:=? \\ $$

Question Number 167986    Answers: 1   Comments: 0

cosxcos(π/6)−sin(π/6)sinx=(π/4)

$$\mathrm{cosxcos}\frac{\pi}{\mathrm{6}}−\mathrm{sin}\frac{\pi}{\mathrm{6}}\mathrm{sinx}=\frac{\pi}{\mathrm{4}} \\ $$

Question Number 167985    Answers: 2   Comments: 0

If af(x)+bf((1/x))=(1/x) where a≠b and x≠0 show that f(x)=((1/(a^2 −b^2 )))((a/x)−bx)

$$\mathrm{If}\:\:\mathrm{af}\left(\mathrm{x}\right)+\mathrm{bf}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)=\frac{\mathrm{1}}{\mathrm{x}}\:\mathrm{where}\: \\ $$$$\mathrm{a}\neq\mathrm{b}\:\mathrm{and}\:\:\mathrm{x}\neq\mathrm{0}\:\mathrm{show}\:\mathrm{that} \\ $$$$\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{a}}^{\mathrm{2}} −\boldsymbol{\mathrm{b}}^{\mathrm{2}} }\right)\left(\frac{\boldsymbol{\mathrm{a}}}{\boldsymbol{\mathrm{x}}}−\boldsymbol{\mathrm{bx}}\right) \\ $$

Question Number 167983    Answers: 0   Comments: 0

lim_(x→2^x ) (((x+2)/(2−x)))=?

$$\underset{{x}\rightarrow\mathrm{2}^{{x}} } {\mathrm{lim}}\left(\frac{{x}+\mathrm{2}}{\mathrm{2}−{x}}\right)=? \\ $$

Question Number 167982    Answers: 0   Comments: 3

lim_(x→∞) (((√(4x^2 −4x+1))+3x)/( (√(x^2 +x−5))+x))=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{1}}+\mathrm{3}{x}}{\:\sqrt{{x}^{\mathrm{2}} +{x}−\mathrm{5}}+{x}}=? \\ $$

Question Number 167981    Answers: 1   Comments: 0

lim_(x→0) ((4^x −2^x )/(8^x −4^x ))=?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{4}^{{x}} −\mathrm{2}^{{x}} }{\mathrm{8}^{{x}} −\mathrm{4}^{{x}} }=? \\ $$

Question Number 167980    Answers: 1   Comments: 3

lim_(x→∞) (√(4x^2 −16x+1))−2x+3=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{16}{x}+\mathrm{1}}−\mathrm{2}{x}+\mathrm{3}=? \\ $$

Question Number 167979    Answers: 1   Comments: 0

3 men and 4 women are to sit on a table. Calculate the number of possible sitting arrangements if (a) they sit in a row such that the men must not sit next to each other. (b) they sit in circular pattern and the clockwise and anticlockwise orders are considered the same.

$$\mathrm{3}\:\mathrm{men}\:\mathrm{and}\:\mathrm{4}\:\mathrm{women}\:\mathrm{are}\:\mathrm{to}\:\mathrm{sit}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{table}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{possible}\:\mathrm{sitting}\:\mathrm{arrangements}\:\mathrm{if} \\ $$$$\:\left({a}\right)\:\mathrm{they}\:\mathrm{sit}\:\mathrm{in}\:\mathrm{a}\:\mathrm{row}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{men}\:\mathrm{must}\:\mathrm{not}\:\mathrm{sit}\:\mathrm{next}\:\mathrm{to}\:\mathrm{each} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{other}. \\ $$$$\:\left({b}\right)\:\mathrm{they}\:\mathrm{sit}\:\mathrm{in}\:\mathrm{circular}\:\mathrm{pattern}\:\mathrm{and} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{the}\:\mathrm{clockwise}\:\mathrm{and}\:\mathrm{anticlockwise} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{orders}\:\mathrm{are}\:\mathrm{considered}\:\mathrm{the}\:\mathrm{same}. \\ $$

Question Number 167978    Answers: 0   Comments: 0

(((3 2 )),((4 5)) ) [A] = determinant (((3 2)),((4 5)))

$$\begin{pmatrix}{\mathrm{3}\:\:\:\:\:\mathrm{2}\:}\\{\mathrm{4}\:\:\:\:\:\:\mathrm{5}}\end{pmatrix}\:\:\left[{A}\right]\:=\begin{vmatrix}{\mathrm{3}\:\:\:\:\:\:\mathrm{2}}\\{\mathrm{4}\:\:\:\:\:\:\mathrm{5}}\end{vmatrix} \\ $$

Question Number 167977    Answers: 1   Comments: 0

Prove that I_n =(1/2^(n+1) )∫_π ^(4nπ) xcos (x/2)dx=((2−π)/2^(np) )

$${Prove}\:{that} \\ $$$${I}_{{n}} =\frac{\mathrm{1}}{\mathrm{2}^{{n}+\mathrm{1}} }\int_{\pi} ^{\mathrm{4}{n}\pi} {x}\mathrm{cos}\:\frac{{x}}{\mathrm{2}}{dx}=\frac{\mathrm{2}−\pi}{\mathrm{2}^{{np}} } \\ $$

Question Number 167976    Answers: 0   Comments: 0

Question Number 167974    Answers: 1   Comments: 0

Question Number 167970    Answers: 0   Comments: 0

Calculate: lim_(n→∞) Σ_(k=1) ^n (k^2 /n^3 )∙(k)^(1/k) =?

$$\mathrm{Calculate}:\:\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{k}^{\mathrm{2}} }{\mathrm{n}^{\mathrm{3}} }\centerdot\sqrt[{\mathrm{k}}]{\mathrm{k}}=? \\ $$

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