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Question Number 183064 Answers: 1 Comments: 0

f(1)=1, f(n)=2Σ_(k=1) ^(n−1) f(k). find Σ_(k=1) ^(m) f(k).

$$\:{f}\left(\mathrm{1}\right)=\mathrm{1},\:\:{f}\left({n}\right)=\mathrm{2}\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\Sigma}}{f}\left({k}\right).\:\:{find}\:\underset{{k}=\mathrm{1}} {\overset{{m}} {\Sigma}}{f}\left({k}\right). \\ $$

Question Number 183059 Answers: 0 Comments: 1

10^5 ∙ 10^5 ∙ ... ∙ 10^5 _( 5 units) = a 5^(10) + 5^(10) + .... + 5^(10) _( 25 units) = b Find: (b/a) = ?

$$\underset{\:\mathrm{5}\:\boldsymbol{\mathrm{units}}} {\underbrace{\mathrm{10}^{\mathrm{5}} \:\centerdot\:\mathrm{10}^{\mathrm{5}} \:\centerdot\:...\:\centerdot\:\mathrm{10}^{\mathrm{5}} }}\:=\:\boldsymbol{\mathrm{a}} \\ $$$$\underset{\:\mathrm{25}\:\boldsymbol{\mathrm{units}}} {\underbrace{\mathrm{5}^{\mathrm{10}} \:+\:\mathrm{5}^{\mathrm{10}} \:+\:....\:+\:\mathrm{5}^{\mathrm{10}} }}\:=\:\boldsymbol{\mathrm{b}} \\ $$$$\mathrm{Find}:\:\:\:\frac{\boldsymbol{\mathrm{b}}}{\boldsymbol{\mathrm{a}}}\:=\:? \\ $$

Question Number 183058 Answers: 1 Comments: 0

How does cooking food in a copper pot transfer heat? 1) conduction 2) convection 3) radiation

$$ \\ $$$$\mathrm{How}\:\mathrm{does}\:\mathrm{cooking}\:\mathrm{food}\:\mathrm{in}\:\mathrm{a}\:\mathrm{copper}\:\mathrm{pot} \\ $$$$\mathrm{tr}{a}\mathrm{nsfer}\:\mathrm{h}{eat}? \\ $$$$\left.\mathrm{1}\right)\:{conduction} \\ $$$$\left.\mathrm{2}\right)\:{convection} \\ $$$$\left.\mathrm{3}\right)\:{radiation} \\ $$

Question Number 183053 Answers: 0 Comments: 0

Question Number 183135 Answers: 1 Comments: 0

Question Number 183112 Answers: 2 Comments: 0

Prove that (∂/∂x) ∫_0 ^x f(s)ds=f(x)

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\frac{\partial}{\partial{x}}\:\underset{\mathrm{0}} {\overset{{x}} {\int}}{f}\left({s}\right)\mathrm{d}{s}={f}\left({x}\right) \\ $$

Question Number 183044 Answers: 4 Comments: 0

Find the equation of the line which passes through the point (3, 5) and is tangent to the circle (x−1)^2 +(y−1)^2 =4

$${Find}\:{the}\:{equation}\:{of}\:{the}\:{line}\:{which} \\ $$$${passes}\:{through}\:{the}\:{point}\:\left(\mathrm{3},\:\mathrm{5}\right) \\ $$$${and}\:{is}\:{tangent}\:{to}\:{the}\:{circle} \\ $$$$\left({x}−\mathrm{1}\right)^{\mathrm{2}} +\left({y}−\mathrm{1}\right)^{\mathrm{2}} =\mathrm{4} \\ $$

Question Number 183041 Answers: 1 Comments: 0

Find: (√(12−2(√(35)))) − (√(10−2(√(21)))) = ?

$$\mathrm{Find}: \\ $$$$\sqrt{\mathrm{12}−\mathrm{2}\sqrt{\mathrm{35}}}\:\:−\:\:\sqrt{\mathrm{10}−\mathrm{2}\sqrt{\mathrm{21}}}\:\:=\:\:? \\ $$

Question Number 183039 Answers: 1 Comments: 0

A Golfer practising on a range with an accelerated tree 4.9m above the fairway is able to strike a ball so that it leaves the club with a horizontal velocity of 20m/s. (Assume the acceleration due to gravity is 9.8m/s^2 and the effect of air resistance maybe ignored unless othewise stated 1) How long after the ball leaves the club will it land on the fairway? 2) What horizontal distance will the ball travel before striking the fairway? 3) What is the acceleration of the ball 0.5s after being hit? 4) Calculate the speed of the ball 0.8s after it leaves the club? M.m

Question Number 183038 Answers: 1 Comments: 0

Solve (dy/dx)+xy=x^2 M.m

$$\mathrm{Solve} \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{xy}=\mathrm{x}^{\mathrm{2}} \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 183036 Answers: 1 Comments: 0

A bullet of mass 1kg is fired and get embedded into a block of wood of mass 1kg initially at rest the velocity of the bullet before collision is 90m/s 1) What is the velocity of the system after collision? 2) Calculate the kinetic energy before and after the collision. 3)How much energy is lost in collision?

$$\mathrm{A}\:\mathrm{bullet}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{1kg}\:\mathrm{is}\:\mathrm{fired}\:\mathrm{and}\:\mathrm{get} \\ $$$$\mathrm{embedded}\:\mathrm{into}\:\mathrm{a}\:\mathrm{block}\:\mathrm{of}\:\mathrm{wood}\:\mathrm{of} \\ $$$$\mathrm{mass}\:\mathrm{1kg}\:\mathrm{initially}\:\mathrm{at}\:\mathrm{rest}\:\mathrm{the}\:\mathrm{velocity} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{bullet}\:\mathrm{before}\:\mathrm{collision}\:\mathrm{is}\:\mathrm{90m}/\mathrm{s} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{the}\:\mathrm{system} \\ $$$$\mathrm{after}\:\mathrm{collision}? \\ $$$$\left.\mathrm{2}\right)\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{kinetic}\:\mathrm{energy}\:\mathrm{before} \\ $$$$\mathrm{and}\:\mathrm{after}\:\mathrm{the}\:\mathrm{collision}. \\ $$$$\left.\mathrm{3}\right)\mathrm{How}\:\mathrm{much}\:\mathrm{energy}\:\mathrm{is}\:\mathrm{lost}\:\mathrm{in}\:\mathrm{collision}? \\ $$

Question Number 183031 Answers: 1 Comments: 0