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AllQuestion and Answers: Page 353

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

Question Number 182997    Answers: 0   Comments: 0

Question Number 182996    Answers: 0   Comments: 0

Question Number 182995    Answers: 1   Comments: 0

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 182978    Answers: 2   Comments: 0

Question Number 183008    Answers: 0   Comments: 1

Question Number 183010    Answers: 0   Comments: 10

what is the formula between actual depth apparent depth and refraction index that an object is in a rarer medium?

$${what}\:{is}\:{the}\:{formula}\:{between}\:{actual}\:{depth} \\ $$$${apparent}\:{depth}\:{and}\:{refraction}\:{index} \\ $$$${that}\:{an}\:{object}\:{is}\:{in}\:{a}\:{rarer}\:{medium}? \\ $$

Question Number 182973    Answers: 3   Comments: 0

Question Number 182968    Answers: 0   Comments: 0

Question Number 182965    Answers: 0   Comments: 0

Question Number 182962    Answers: 2   Comments: 0

Question Number 182954    Answers: 0   Comments: 1

I=∫ (1/( (√(x (√x) −x^2 )))) dx I=∫ (1/( ∙ (√(x((√x) −x))))) dx I=∫ (1/( (√x) ∙ (√((√x) −x)) )) ×(2/2) dx I= ∫ (1/( (√(4(√x) −4x)))) ∙ (2/( (√x))) dx I=2∫ ( /( (√(1−(1−2 (√x))^2 )))) ∙ (1/( (√x))) dx I= −2∫ (1/( (√(1−(1−2(√x))^2 )))) ∙ d(1−2(√x)) I= −2sin^(−1) (1−2(√x)) +C Gamil AL mansob

$$\:\boldsymbol{{I}}=\int\:\frac{\mathrm{1}}{\:\sqrt{\boldsymbol{{x}}\:\sqrt{\boldsymbol{{x}}}\:−\boldsymbol{{x}}^{\mathrm{2}} }}\:\boldsymbol{{dx}}\: \\ $$$$\:\:\boldsymbol{{I}}=\int\:\frac{\mathrm{1}}{\:\:\centerdot\:\:\sqrt{\boldsymbol{{x}}\left(\sqrt{\boldsymbol{{x}}}\:−\boldsymbol{{x}}\right)}}\:\boldsymbol{{dx}} \\ $$$$\:\:\boldsymbol{{I}}=\int\:\frac{\mathrm{1}}{\:\sqrt{\boldsymbol{{x}}}\:\centerdot\:\sqrt{\sqrt{\boldsymbol{{x}}}\:−\boldsymbol{{x}}}\:}\:×\frac{\mathrm{2}}{\mathrm{2}}\:\boldsymbol{{dx}} \\ $$$$\:\boldsymbol{{I}}=\:\int\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{4}\sqrt{\boldsymbol{{x}}}\:−\mathrm{4}\boldsymbol{{x}}}}\:\centerdot\:\frac{\mathrm{2}}{\:\sqrt{\boldsymbol{{x}}}}\:\boldsymbol{{dx}} \\ $$$$\:\:\boldsymbol{{I}}=\mathrm{2}\int\:\frac{\:}{\:\sqrt{\mathrm{1}−\left(\mathrm{1}−\mathrm{2}\:\sqrt{\boldsymbol{{x}}}\right)^{\mathrm{2}} }}\:\centerdot\:\frac{\mathrm{1}}{\:\sqrt{\boldsymbol{{x}}}}\:\boldsymbol{{dx}}\: \\ $$$$\:\:\boldsymbol{{I}}=\:−\mathrm{2}\int\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−\left(\mathrm{1}−\mathrm{2}\sqrt{\boldsymbol{{x}}}\right)^{\mathrm{2}} }}\:\:\centerdot\:\boldsymbol{{d}}\left(\mathrm{1}−\mathrm{2}\sqrt{\boldsymbol{{x}}}\right) \\ $$$$\:\:\boldsymbol{{I}}=\:−\mathrm{2}\boldsymbol{{sin}}^{−\mathrm{1}} \left(\mathrm{1}−\mathrm{2}\sqrt{\boldsymbol{{x}}}\right)\:+\boldsymbol{{C}} \\ $$$$\: \\ $$$$\:\:\:\:\:\boldsymbol{\mathrm{Gamil}}\:\boldsymbol{\mathrm{AL}}\:\boldsymbol{\mathrm{mansob}} \\ $$

Question Number 182953    Answers: 0   Comments: 0

H_4 (x)=L_0 (x) x=?

$${H}_{\mathrm{4}} \left({x}\right)={L}_{\mathrm{0}} \left({x}\right)\:\:\:\:\:\:\:{x}=? \\ $$

Question Number 182952    Answers: 1   Comments: 0

what is the probability that at least two from 23 people have birthday at the same day? (an unsolved old question)

$${what}\:{is}\:{the}\:{probability}\:{that}\:{at}\:{least} \\ $$$${two}\:{from}\:\mathrm{23}\:{people}\:{have}\:{birthday}\:{at} \\ $$$${the}\:{same}\:{day}? \\ $$$$ \\ $$$$\left({an}\:{unsolved}\:{old}\:{question}\right) \\ $$

Question Number 182949    Answers: 0   Comments: 0

if z(z^2 +3x)+xy=0 show that (d^2 z/dx^2 )+(d^2 z/dy^2 ) = ((2x(x−1))/((z^2 +3)^3 ))

$$\mathrm{if}\:\mathrm{z}\left(\mathrm{z}^{\mathrm{2}} +\mathrm{3x}\right)+\mathrm{xy}=\mathrm{0}\:\mathrm{show}\:\mathrm{that} \\ $$$$\frac{\mathrm{d}^{\mathrm{2}} \mathrm{z}}{\mathrm{dx}^{\mathrm{2}} }+\frac{\mathrm{d}^{\mathrm{2}} \mathrm{z}}{\mathrm{dy}^{\mathrm{2}} }\:=\:\frac{\mathrm{2x}\left(\mathrm{x}−\mathrm{1}\right)}{\left(\mathrm{z}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{3}} } \\ $$

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