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Question Number 183263    Answers: 0   Comments: 2

Derive the formular that can be used to count the number of dissimilar surds obtaining after full expansion of (Σ_(x=1) ^n (√x))^4 where every x term is a prime number.

$${Derive}\:{the}\:{formular}\:{that}\:{can}\:{be}\:{used}\: \\ $$$${to}\:{count}\:{the}\:{number}\:{of}\:{dissimilar}\:{surds} \\ $$$${obtaining}\:{after}\:{full}\:{expansion}\:{of} \\ $$$$\left(\sum_{{x}=\mathrm{1}} ^{{n}} \sqrt{{x}}\right)^{\mathrm{4}} \:{where}\:{every}\:{x}\:{term}\:{is}\:{a}\:{prime}\:{number}. \\ $$

Question Number 183262    Answers: 0   Comments: 1

Simplify ^3 (√(56^3 (√(4 )) − 157^3 (√9) + 130^3 (√6) )) into a compound surd.

$${Simplify}\:\:^{\mathrm{3}} \sqrt{\mathrm{56}^{\mathrm{3}} \sqrt{\mathrm{4}\:\:}\:−\:\mathrm{157}^{\mathrm{3}} \sqrt{\mathrm{9}}\:\:+\:\mathrm{130}^{\mathrm{3}} \sqrt{\mathrm{6}}\:} \\ $$$${into}\:{a}\:{compound}\:{surd}. \\ $$

Question Number 183084    Answers: 1   Comments: 3

Question Number 183080    Answers: 0   Comments: 0

Question Number 183078    Answers: 0   Comments: 0

Question Number 183077    Answers: 0   Comments: 0

Question Number 183076    Answers: 1   Comments: 0

Question Number 183075    Answers: 2   Comments: 0

Question Number 183073    Answers: 2   Comments: 0

∫sin^2 x dx Integrate this question

$$\int\mathrm{sin}^{\mathrm{2}} \mathrm{x}\:\mathrm{dx} \\ $$$$ \\ $$$$\mathrm{Integrate}\:\mathrm{this}\:\mathrm{question} \\ $$

Question Number 183071    Answers: 2   Comments: 0

Question Number 183068    Answers: 0   Comments: 0

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

$$\mathrm{A}\:\mathrm{Golfer}\:\mathrm{practising}\:\mathrm{on}\:\mathrm{a}\:\mathrm{range} \\ $$$$\mathrm{with}\:\mathrm{an}\:\mathrm{accelerated}\:\mathrm{tree}\:\mathrm{4}.\mathrm{9m}\:\mathrm{above} \\ $$$$\mathrm{the}\:\mathrm{fairway}\:\mathrm{is}\:\mathrm{able}\:\mathrm{to}\:\mathrm{strike}\:\mathrm{a}\:\mathrm{ball} \\ $$$$\mathrm{so}\:\mathrm{that}\:\mathrm{it}\:\mathrm{leaves}\:\mathrm{the}\:\mathrm{club}\:\mathrm{with}\:\mathrm{a}\: \\ $$$$\mathrm{horizontal}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{20m}/\mathrm{s}. \\ $$$$\left(\mathrm{Assume}\:\mathrm{the}\:\mathrm{acceleration}\:\mathrm{due}\:\mathrm{to}\:\right. \\ $$$$\mathrm{gravity}\:\mathrm{is}\:\mathrm{9}.\mathrm{8m}/\mathrm{s}^{\mathrm{2}} \:\mathrm{and}\:\mathrm{the}\:\mathrm{effect}\:\mathrm{of}\:\mathrm{air} \\ $$$$\mathrm{resistance}\:\mathrm{maybe}\:\mathrm{ignored}\:\mathrm{unless} \\ $$$$\mathrm{othewise}\:\mathrm{stated}\: \\ $$$$\left.\mathrm{1}\right)\:\mathrm{How}\:\mathrm{long}\:\mathrm{after}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{leaves}\:\mathrm{the} \\ $$$$\mathrm{club}\:\mathrm{will}\:\mathrm{it}\:\mathrm{land}\:\mathrm{on}\:\mathrm{the}\:\mathrm{fairway}? \\ $$$$\left.\mathrm{2}\right)\:\mathrm{What}\:\mathrm{horizontal}\:\mathrm{distance}\:\mathrm{will}\:\mathrm{the} \\ $$$$\mathrm{ball}\:\mathrm{travel}\:\mathrm{before}\:\mathrm{striking}\:\mathrm{the}\:\mathrm{fairway}? \\ $$$$\left.\mathrm{3}\right)\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ball} \\ $$$$\mathrm{0}.\mathrm{5s}\:\mathrm{after}\:\mathrm{being}\:\mathrm{hit}? \\ $$$$\left.\mathrm{4}\right)\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ball}\: \\ $$$$\mathrm{0}.\mathrm{8s}\:\mathrm{after}\:\mathrm{it}\:\mathrm{leaves}\:\mathrm{the}\:\mathrm{club}? \\ $$$$ \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

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

Question Number 183019    Answers: 3   Comments: 2

Q f(x)=a^x +b^x g(x)=((f(x))/(f(x−2))) g(3)=?

$${Q}\:\:\:{f}\left({x}\right)={a}^{{x}} +{b}^{{x}} \:\:\:\:\:{g}\left({x}\right)=\frac{{f}\left({x}\right)}{{f}\left({x}−\mathrm{2}\right)} \\ $$$${g}\left(\mathrm{3}\right)=? \\ $$$$ \\ $$

Question Number 182999    Answers: 1   Comments: 0

(√(m^2 −4m+4)) + ((m−2n+8))^(1/4) = 0 n = ?

$$\sqrt{\mathrm{m}^{\mathrm{2}} −\mathrm{4m}+\mathrm{4}}\:+\:\sqrt[{\mathrm{4}}]{\mathrm{m}−\mathrm{2n}+\mathrm{8}}\:=\:\mathrm{0} \\ $$$$\mathrm{n}\:=\:? \\ $$

Question Number 182998    Answers: 0   Comments: 0

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