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Question Number 168071 Answers: 0 Comments: 0

A clean tube of diameter 2.5 mm is imersed in a liquidi wth a coefficient of surface tension 0.4 nm. The anglef o contact of the liquid with the glass can be assumed as1 35^0 . The density of liquid 13600 kgm3. What would bethe level of the liquid in the tube relative to the freeu srface of the liuid inside the tube Answer should be inm m

$$ \\ $$$$\mathrm{A}\:\mathrm{clean}\:\mathrm{tube}\:\mathrm{of}\:\mathrm{diameter}\:\mathrm{2}.\mathrm{5}\:\mathrm{mm}\:\mathrm{is}\:\mathrm{imersed}\:\mathrm{in}\:\mathrm{a}\:\mathrm{liquidi} \\ $$$$\mathrm{wth}\:\mathrm{a}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{surface}\:\mathrm{tension}\:\:\mathrm{0}.\mathrm{4}\:\mathrm{nm}.\:\mathrm{The}\:\mathrm{anglef} \\ $$$$\mathrm{o}\:\mathrm{contact}\:\mathrm{of}\:\mathrm{the}\:\mathrm{liquid}\:\mathrm{with}\:\mathrm{the}\:\mathrm{glass}\:\mathrm{can}\:\mathrm{be}\:\mathrm{assumed}\:\mathrm{as1} \\ $$$$\mathrm{35}^{\mathrm{0}} .\:\mathrm{The}\:\mathrm{density}\:\mathrm{of}\:\mathrm{liquid}\:\mathrm{13600}\:\mathrm{kgm3}.\:\mathrm{What}\:\mathrm{would}\: \\ $$$$\mathrm{bethe}\:\mathrm{level}\:\mathrm{of}\:\mathrm{the}\:\mathrm{liquid}\:\mathrm{in}\:\mathrm{the}\:\mathrm{tube}\:\mathrm{relative}\:\mathrm{to}\:\mathrm{the}\:\mathrm{freeu} \\ $$$$\mathrm{srface}\:\mathrm{of}\:\mathrm{the}\:\mathrm{liuid}\:\mathrm{inside}\:\mathrm{the}\:\mathrm{tube}\:\mathrm{Answer}\:\mathrm{should}\:\mathrm{be}\:\mathrm{inm} \\ $$$$\mathrm{m} \\ $$

Question Number 168064 Answers: 0 Comments: 5

q=(m/( (√p)))+(p^2 /m) make p the subject

$$\:{q}=\frac{{m}}{\:\sqrt{{p}}}+\frac{{p}^{\mathrm{2}} }{{m}} \\ $$$$\:{make}\:\:{p}\:\:{the}\:{subject} \\ $$

Question Number 168055 Answers: 2 Comments: 0

Calculate :: lim_(x→0) (((1+x)^(−(1/x^3 )) )/x)=?

$$\mathrm{Calculate}\:::\:\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\mathrm{1}+\mathrm{x}\right)^{−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }} }{\mathrm{x}}=? \\ $$

Question Number 168054 Answers: 1 Comments: 3

Simplify (((√(1+x))+(√x))/( (√(1−x))+(√x)))

$${Simplify}\:\:\frac{\sqrt{\mathrm{1}+{x}}+\sqrt{{x}}}{\:\sqrt{\mathrm{1}−{x}}+\sqrt{{x}}} \\ $$

Question Number 168053 Answers: 2 Comments: 0

Solve the system { ((x+2y+3z+2t=2)),((2x+5y−8z+6t=5)),((3x+4y−5z+2t=4)) :}

$${Solve}\:{the}\:{system}\: \\ $$$$\begin{cases}{{x}+\mathrm{2}{y}+\mathrm{3}{z}+\mathrm{2}{t}=\mathrm{2}}\\{\mathrm{2}{x}+\mathrm{5}{y}−\mathrm{8}{z}+\mathrm{6}{t}=\mathrm{5}}\\{\mathrm{3}{x}+\mathrm{4}{y}−\mathrm{5}{z}+\mathrm{2}{t}=\mathrm{4}}\end{cases} \\ $$

Question Number 168043 Answers: 1 Comments: 1

Solve the equation: ((7x^2 + 7)/( (√(7x^2 + 3)))) + ((y^2 + 18)/( (√(y^2 + 17)))) + ((3z^2 + 26)/( (√(3z^2 + 1)))) = 16

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\frac{\mathrm{7x}^{\mathrm{2}} \:+\:\mathrm{7}}{\:\sqrt{\mathrm{7x}^{\mathrm{2}} \:+\:\mathrm{3}}}\:+\:\frac{\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{18}}{\:\sqrt{\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{17}}}\:+\:\frac{\mathrm{3z}^{\mathrm{2}} \:+\:\mathrm{26}}{\:\sqrt{\mathrm{3z}^{\mathrm{2}} \:+\:\mathrm{1}}}\:=\:\mathrm{16} \\ $$

Question Number 168042 Answers: 1 Comments: 1

The number of natural number k such that k∣ n^7 −n for ∀n natural numbers

$$\:\:{The}\:{number}\:{of}\:{natural}\:{number}\:{k} \\ $$$$\:{such}\:{that}\:{k}\mid\:{n}^{\mathrm{7}} −{n}\:{for}\:\forall{n}\:{natural} \\ $$$$\:{numbers} \\ $$

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