Question and Answers Forum

Water flows out of a tank through a hole of diameter 2cm above the hole (1) Determine the velocity of outflow (2) The rate of outflow when the level of the water in the tank is 2cm above the hole.

$$\mathrm{Water}\:\mathrm{flows}\:\mathrm{out}\:\mathrm{of}\:\mathrm{a}\:\mathrm{tank}\:\mathrm{through}\:\mathrm{a}\:\mathrm{hole}\:\mathrm{of}\:\mathrm{diameter}\:\mathrm{2cm}\:\mathrm{above}\:\mathrm{the}\:\mathrm{hole} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{outflow} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{The}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{outflow}\:\mathrm{when}\:\mathrm{the}\:\mathrm{level}\:\mathrm{of}\:\mathrm{the}\:\mathrm{water}\:\mathrm{in}\:\mathrm{the}\:\mathrm{tank}\:\mathrm{is}\:\mathrm{2cm}\:\mathrm{above} \\ $$$$\mathrm{the}\:\mathrm{hole}.\: \\ $$

Question Number 12470 Answers: 1 Comments: 0

((0.03125))^(1/5) =

$$\sqrt[{\mathrm{5}}]{\mathrm{0}.\mathrm{03125}}\:=\: \\ $$

Question Number 12464 Answers: 3 Comments: 0

∫ sin^3 (7x) dx

$$\int\:\mathrm{sin}^{\mathrm{3}} \left(\mathrm{7x}\right)\:\mathrm{dx} \\ $$

Question Number 12463 Answers: 1 Comments: 0

∫ ((x + 1)/((x^2 + 2x + 3)^(2/3) )) dx

$$\int\:\:\frac{\mathrm{x}\:+\:\mathrm{1}}{\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{2x}\:+\:\mathrm{3}\right)^{\mathrm{2}/\mathrm{3}} }\:\:\mathrm{dx} \\ $$

Question Number 12446 Answers: 2 Comments: 1

find x (√x) = 8^x

$$\mathrm{find}\:\mathrm{x} \\ $$$$\sqrt{\mathrm{x}}\:\:=\:\:\mathrm{8}^{\mathrm{x}} \\ $$

Question Number 12445 Answers: 0 Comments: 0

Question Number 12442 Answers: 2 Comments: 0

Solve: z^4 = − 16

$$\mathrm{Solve}:\:\:\:\mathrm{z}^{\mathrm{4}} \:=\:−\:\mathrm{16} \\ $$

Question Number 12436 Answers: 0 Comments: 6

∫ (dx/x^x ) dx

$$\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{x}} }\:\mathrm{dx} \\ $$

Question Number 12435 Answers: 0 Comments: 1

Solve equation X_4 −3X_2 +2=0

$$\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{equation}} \\ $$$$\:\:\boldsymbol{{X}}_{\mathrm{4}} −\mathrm{3}\boldsymbol{{X}}_{\mathrm{2}} +\mathrm{2}=\mathrm{0} \\ $$

Question Number 12432 Answers: 0 Comments: 1

To Tinku Tara: it is not possible to post long and narrow images, since the button ′Submit′ is not visible. Can you please solve this problem?

$${To}\:{Tinku}\:{Tara}: \\ $$$${it}\:{is}\:{not}\:{possible}\:{to}\:{post}\:{long}\:{and}\:{narrow} \\ $$$${images},\:{since}\:{the}\:{button}\:'{Submit}'\:{is} \\ $$$${not}\:{visible}.\:{Can}\:{you}\:{please}\:{solve}\:{this}\:{problem}? \\ $$

Question Number 12422 Answers: 2 Comments: 1

Question Number 12419 Answers: 2 Comments: 0

If a body of 2kg mass is at a distance of 7200km from the centre of the earth . What would the acceleration due to gravity be at this point in the Earths field ? (a) 9.6m/s^2 (b) 10m/s^2 (c) 11.3m/s^2 (d) 12.7m/s^2 (e) 15.6m/s^2

$$\mathrm{If}\:\mathrm{a}\:\mathrm{body}\:\mathrm{of}\:\mathrm{2kg}\:\mathrm{mass}\:\mathrm{is}\:\mathrm{at}\:\mathrm{a}\:\mathrm{distance}\:\mathrm{of}\:\mathrm{7200km}\:\mathrm{from}\:\mathrm{the}\:\mathrm{centre}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{earth}\:.\:\mathrm{What}\:\mathrm{would}\:\mathrm{the}\:\mathrm{acceleration}\:\mathrm{due}\:\mathrm{to}\:\mathrm{gravity}\:\mathrm{be}\:\mathrm{at}\:\mathrm{this}\:\mathrm{point}\:\mathrm{in} \\ $$$$\mathrm{the}\:\mathrm{Earths}\:\mathrm{field}\:? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{9}.\mathrm{6m}/\mathrm{s}^{\mathrm{2}} \:\left(\mathrm{b}\right)\:\mathrm{10m}/\mathrm{s}^{\mathrm{2}} \:\left(\mathrm{c}\right)\:\mathrm{11}.\mathrm{3m}/\mathrm{s}^{\mathrm{2}} \:\left(\mathrm{d}\right)\:\mathrm{12}.\mathrm{7m}/\mathrm{s}^{\mathrm{2}} \:\left(\mathrm{e}\right)\:\mathrm{15}.\mathrm{6m}/\mathrm{s}^{\mathrm{2}} \\ $$

Question Number 12414 Answers: 1 Comments: 0

does Σ_(i=1) ^∞ p_i converge, p_i ∈P

$$\mathrm{does}\:\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}{p}_{{i}} \:\:\:\mathrm{converge},\:\:\:\:{p}_{{i}} \in\mathbb{P} \\ $$

Question Number 12405 Answers: 0 Comments: 1

how to prove that there exist infinitely many rationals between any two irrationals?

$${how}\:{to}\:{prove}\:{that}\:{there}\:{exist}\:{infinitely}\:{many}\:{rationals}\:{between}\:{any}\:{two}\:{irrationals}? \\ $$$$ \\ $$

Question Number 12403 Answers: 1 Comments: 0

f(x)=⌊x−(3/e)⌋+⌊x+(3/e)⌋⇒f(1)=?

$${f}\left({x}\right)=\lfloor{x}−\frac{\mathrm{3}}{{e}}\rfloor+\lfloor{x}+\frac{\mathrm{3}}{{e}}\rfloor\Rightarrow{f}\left(\mathrm{1}\right)=? \\ $$

Question Number 12402 Answers: 0 Comments: 2

12sgn(x^2 −x−20)+3≥0⇒ (ss)=?