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Question Number 183135    Answers: 1   Comments: 0

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 182984    Answers: 2   Comments: 0

Find the equation for the plane through the point A(6, 2, −4), B(−2, 4, 8), C(4, −2, 2). −Vector Analysis M.m

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{for}\:\mathrm{the}\:\mathrm{plane} \\ $$$$\mathrm{through}\:\mathrm{the}\:\mathrm{point}\:\mathrm{A}\left(\mathrm{6},\:\mathrm{2},\:−\mathrm{4}\right), \\ $$$$\mathrm{B}\left(−\mathrm{2},\:\mathrm{4},\:\mathrm{8}\right),\:\mathrm{C}\left(\mathrm{4},\:−\mathrm{2},\:\mathrm{2}\right).\:−\mathrm{Vector}\:\mathrm{Analysis} \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 182941    Answers: 0   Comments: 0

Solve: [x^2 +(xy^2 )^(1/3) ](dy/dx)=y M.m

$$\mathrm{Solve}: \\ $$$$\left[\mathrm{x}^{\mathrm{2}} +\left(\mathrm{xy}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} \right]\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{y} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 182934    Answers: 1   Comments: 0

Is that right ! IF : Σ_(k = 1) ^n (⌊(n/k)⌋−⌊((n−1)/k)⌋) = 2 so n is a prime number .

$$\:\:\:\:\:\:\:\:{Is}\:{that}\:{right}\:! \\ $$$$\:\:\:\:{IF}\:\::\: \\ $$$$\underset{{k}\:=\:\mathrm{1}} {\overset{{n}} {\sum}}\:\left(\lfloor\frac{{n}}{{k}}\rfloor−\lfloor\frac{{n}−\mathrm{1}}{{k}}\rfloor\right)\:=\:\mathrm{2} \\ $$$$\:\:\:{so}\:{n}\:{is}\:{a}\:{prime}\:{number}\:. \\ $$

Question Number 182810    Answers: 2   Comments: 0

What is the value of this infinite sum ((1/2)−(1/3))+((1/2^2 )−(1/3^2 ))+((1/2^3 )−(1/3^3 ))+...

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{this}\:\mathrm{infinite}\:\mathrm{sum} \\ $$$$\left(\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{3}}\right)+\left(\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }−\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }\right)+\left(\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} }−\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{3}} }\right)+... \\ $$$$ \\ $$$$ \\ $$

Question Number 182803    Answers: 0   Comments: 0

write an 8085 mp assembly language program to separate even numbers from a list of 10 numbers and store them in another list starting from (2300H). assume starting address of 10 numbers list is (2200H).

$${write}\:{an}\:\mathrm{8085}\:{mp}\:{assembly}\:{language}\:{program} \\ $$$${to}\:{separate}\:{even}\:{numbers}\:{from}\:{a}\:{list}\:{of} \\ $$$$\mathrm{10}\:{numbers}\:{and}\:{store}\:{them}\:{in}\:{another} \\ $$$${list}\:{starting}\:{from}\:\left(\mathrm{2300}{H}\right).\:{assume}\:{starting} \\ $$$${address}\:{of}\:\mathrm{10}\:{numbers}\:{list}\:{is}\:\left(\mathrm{2200}{H}\right). \\ $$

Question Number 182779    Answers: 4   Comments: 1

Question Number 182576    Answers: 0   Comments: 0

Question Number 182566    Answers: 0   Comments: 0

Solve (x^2 +( xy^2 )^(1/3) )(dy/dx) = y^2

$$\mathrm{Solve} \\ $$$$\left(\mathrm{x}^{\mathrm{2}} \:+\left(\:\mathrm{xy}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} \right)\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{y}^{\mathrm{2}} \\ $$

Question Number 182534    Answers: 1   Comments: 3

xy + (xy^2 )^(1/3) = y^2 Solve

$$\mathrm{xy}\:+\:\left(\mathrm{xy}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} \:=\:\mathrm{y}^{\mathrm{2}} \\ $$$$ \\ $$$$\mathrm{Solve} \\ $$

Question Number 182423    Answers: 4   Comments: 0

Question Number 182394    Answers: 1   Comments: 1

Question Number 182315    Answers: 0   Comments: 1

Question Number 182253    Answers: 0   Comments: 3

Question Number 182252    Answers: 0   Comments: 0

Question Number 182139    Answers: 1   Comments: 1

Find constant a, b, so that y(t)=(t+3)e^(2t) is solution of IVP y^′ =ay+e^(2t) , y(0)=b .

$$\mathrm{Find}\:\mathrm{constant}\:\mathrm{a},\:\mathrm{b},\:\mathrm{so}\:\mathrm{that} \\ $$$$\mathrm{y}\left(\mathrm{t}\right)=\left(\mathrm{t}+\mathrm{3}\right)\mathrm{e}^{\mathrm{2t}} \:\mathrm{is}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{IVP} \\ $$$$\mathrm{y}^{'} =\mathrm{ay}+\mathrm{e}^{\mathrm{2t}} ,\:\:\:\:\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{b} \\ $$$$ \\ $$$$. \\ $$

Question Number 182069    Answers: 1   Comments: 1

(1+x^2 )(dy/dx)+3xy=5x solve

$$\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)\frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{3xy}=\mathrm{5x} \\ $$$$ \\ $$$$\mathrm{solve} \\ $$

Question Number 182031    Answers: 0   Comments: 0

Question Number 181977    Answers: 0   Comments: 0

Question Number 181764    Answers: 3   Comments: 0

(dy/dx)+cos(x)y=cos(x) Solve

$$\frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{cos}\left(\mathrm{x}\right)\mathrm{y}=\mathrm{cos}\left(\mathrm{x}\right) \\ $$$$ \\ $$$$\mathrm{Solve} \\ $$$$ \\ $$

Question Number 181758    Answers: 0   Comments: 0

How likely have at least two of 23 student birthday on the same day? M.m

$$\mathrm{How}\:\mathrm{likely}\:\mathrm{have}\:\mathrm{at}\:\mathrm{least}\:\mathrm{two}\:\mathrm{of}\:\mathrm{23} \\ $$$$\mathrm{student}\:\mathrm{birthday}\:\mathrm{on}\:\mathrm{the}\:\mathrm{same}\:\mathrm{day}? \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 181757    Answers: 1   Comments: 0

What is the largest digit of 11^5 ∙17^3 ∙33^3 .

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{11}^{\mathrm{5}} \centerdot\mathrm{17}^{\mathrm{3}} \centerdot\mathrm{33}^{\mathrm{3}} \\ $$$$ \\ $$$$. \\ $$

Question Number 181756    Answers: 2   Comments: 0

Without using calculator, what is the value of Cos(((7π)/6))? .

$$\mathrm{Without}\:\mathrm{using}\:\mathrm{calculator},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{Cos}\left(\frac{\mathrm{7}\pi}{\mathrm{6}}\right)? \\ $$$$ \\ $$$$. \\ $$

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