Answers edited by Ultrilliam

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• Evaluate the integral?
  
• If (1+i)(2+i)(3+i)....(n+i)=a+ib then show that 2.5.10....(n^2+1)=a^2+b^2 ?
  
• #int int_R e^(-(xy)/2)dA# where #R#:the region bounded by #y=1/4x,y=2x,y=1/x,y=4/x# Evaluate integrals?
  
• A particle of mass m moves under the force given by F = a(sinωt i +cosωt j). a,w are constants and t is time.It is intially at rest at the origin.What is work done on the particle up to time t and the instantaneous power given to the particle at time t?
  
• Answer question a) why does A = A (t) = 6x^2? ,
  
• PROBLEM 10 A point describes a circumference according to law s (t) = t³ + 2t² where s measured meters along the circumference and, in seconds. If a total acceleration of the point is 16 2 m / s2, when t = 2 s.calculate the radius R of the circumference?
  
• If #hat(a_1),hat(a_2)and hat(a_3)# are unit vectors and #2hat(a_1)+2hat(a_2)+hat(a_3) =0# then angle between #hat(a_1) and hat(a_2)# is ?
  
• Solve the intergral ?
  
• How to solve with integration?
  
• A point moves in #x-y# plane according to #vec r=3cos(4t)veci +3(1-sin4t) vecj#. What is the distance travelled by the particle in 0.5 sec ?
  
• Can someone help me check if this matrix is diagonalisable?
  
• Graph the parametric equation x(t)=3t and y(t)=2-2t on [0,1] ?
  
• Show that the nuclear density of 1H1(mass no-1&atomic no-1)is over 10^14 times greater than its atomic density (assume the atom to have the radius of the first Bohr orbit).In this question,what should I put for nuclear mass&atomic mass?
  
• What is diffraction a result of?
  
• FInd numeric value of #int_1^esqrt(lnx)dx-int_0^1e^(x^2)dx#?
  
• Find the value of the line integral.F · dr (Hint: If F is conservative, the integration may be easier on an alternative path.) F(x,y) = ye^xyi + xe^xyj (a) r1(t) = ti − (t − 8)j, 0 ≤ t ≤ 8 ?
  
• Solve L(sin4t) ?
  
• Find curl F for the vector field at the point (9, -9, 7). F(x,y,z) = x^2zi - 2xzj + yzk ?
  
• Consider two insulated chambers (A,B) of same volume connected by a closed knob, S. One mole of perfect gas is confined in chamber A. What is the change in entropy of gas when knob S is opened? ( R= 8.31 )
  
• I have a Work word problem I need help completing?
  
• Find the value of the line integral. F · dr C (Hint: If F is conservative, the integration may be easier on an alternative path.) F(x, y) = yi − xj?
  
• Solve it please. "?"
  
• For derivation of equation for stationary wave, y1=Asin(kx-omega t) and y2=Asin(kx+omega t) are considered. Why y1=Asin (kx-omega t) and y2=Asin(kx+omega t+pi) cannot be used to derive?
  
• Determine the Fourier series expansion for full wave rectified sine wave i. (details inside)?
  
• How do you determine the concavity of # y=2cosx+sin2x#?
  
• A meteorological balloon of mass 0.2 Kg falls vertically from rest, the total resistance at V m/s is approximately (1+0.1V)N taking g=9.8 m/s^2# . Calculate: a) The terminal velocity? b) Time taken for the balloon to reach half of the terminal velocity?
  
• A particle of mass m strikes a wall at an angle of incidence 60° with velocity V elastically. Then the change in momentum is?
  
• Find the instaneous rate of change of y=2x+3 ?
  
• D (log sin cos tan e^cosx)/dx ?
  
• Does amplitude of a spring mass system change when mass is added?
  
• The cost of fuel is running an engine is proportional to the square of the speed in km/h is ₹48 per hour when the speed is 16 kn/h.Other costs amount to ₹300 per hour.Find the most economical speed?
  
• Find the differential of the following function?: y = sin 5x^3
  
• What is the derivative of #Tan^-1 (y/x)#?
  
• A block of charge q and mass m is connected to a spring of constant k. An electric field E exists parallel to the ground. The block is released from rest from a unstreched spring. Find Maximum displacement?
  
• A ladder 5m long is standing vertically, flat against a vertical wall, while its lower end in on the horizontal floor. ... Find the speed at which the upper end is moving down the wall 4 seconds after the lower end has left the wall ?
  
• Light of wavelength 5000 Å and intensity 39.8 W/m² is incident on a metal surface. If only 1% photons of incident light emit photo electrons, then what will be the number of electrons emitted/sec/unit area from the surface?
  
• Find the complete integral of the equation (∂z/∂x_1)(∂z/∂x_2)(∂z/∂x_3)=z³x_1x_2x_3?
  
• If a particle moves with acceleration = #10x-2x^3# and v= 0 at x=1, is the motion simple harmonic? And how do you describe the motion?
  
• How to prove ?
  
• How to Find the directional derivative of?:
  
• Physics Work and Energy Question?
  
• The value of #lim_(h→0)1/hint_2^(2+h)sin(x^2)dx#is?
  
• Why isn't #dy/dx = 3x + 2y# a linear differential equation?
  
• Determine if F is a linear transformación f(x,y,z)=(x,x+y+z) ?
  
• Ordinary boron is a mixture of 10B5(mass no=10,atomic no=5)&11B5(mass no=11,atomic no=5)isotopes & has a composite atomic mass of 10.82u.What percentage of each isotope is present in ordinary boron?
  
• Find the value of the line integral F · dr C (Hint: If F is conservative, the integration may be easier on an alternative path.) (x2 + y2)dx + 2xy dy?
  
• The sum of A and B is 5i+j and their difference is 3i-j what is vector A?
  
• Is Electric potential and e.m.f are same or different terms?
  
• How do you find the lim & definite integrals ? for :{lim as x approaches 0 (1/x^3) * integrals (t^2/t^4+1)dt} intervals{0,x}
  
• How is impulse related to momentum?
  
• How can Newton's first law be derived from Newton's second law?
  
• How to calculate average pressure as volume changes via intergration?
  
• Solve this differential equation explicitly, either by using partial fractions, or with a computer algebra system. Use the initial populations 350 and 450. Can anyone please help me with this problem and explain how you got the answers?
  
• Evaluate the limit #lim_(x to pi) (e^sinx -1)/(x-pi)# without using L'Hôpital's rule?
  
• How about Answer ?
  
• Can you help me with this double integral?
  
• How do you find the antiderivative of #e^( -x)*cos2x#?
  
• How to find the curvature K of the curve?
  
• Integral of [x+3÷(5-x²-4x)½]dx?
  
• A stone is thrown into a circular pond of radius 1 meter. Suppose the stone falls uniformly at random on the area of the pond. What will be the expected distance of the stone from the center of the pond?
  
• #intint_D cosxy dxdy#, where #D: {[x>=0],[y>=0],[x>=y]}#?
  
• Rope of length 80m and mass M is connecting two rods 50 meters high. The minimum distance of the curve from the ground is 10 meters. How far are the two rods apart?
  
• Linear/Separable Differential Equations Question (Engineering First Year Calculus)?
  
• If d^(2)x/dt^(2)+g/b(x-a)=0,(a,b,g being positive constants) and x=a' and dx/dt=0 when t=0,show that x=a+(a'-a)cos{√(g)/(b)t}?
  
• How to derive this relativistic Energy-Momentum relation?
  
• The electric potential is V= 5x − 3x^2y+2yz. Find the expressions for the x, y, and z components of the electric field over this region. What is the magnitude of the field at the point P that has coordinates (1, 0, -2) m?
  
• A projectile is thrown with the speed 'u' at an angle '⍬' to the horizontal. What is the radius of curvature of it's trajectory when the velocity vector of the projectile makes an angle '⍺' with the horizontal?
  
• How do you find the area of the region bounded by the spiral #r=7theta# for #0<=theta<=pi#?
  
• Relativity problems?
  
• How do i evaluate this double integral, the integrand is y^1/2*sin y dydx? x^2 < y < 1 0<x< 1
  
• Help me please, Two particles each of mass m, are joined by a thin string of length 2L, as shown in Figure 48. A uniform force F is applied in the middle of the string (x = 0) forming a right angle with the initial position of the string. Show that th????
  
• Let #F(x)=int_0^x e^(-5t^4)dt#. Find the MacLaurin polynomial of degree 5 for F(x)?
  
• If vector P+vector Q=vector R ;and if P^2+Q^2=R^2 then find the angle between the vectorP and vectorQ?
  
• Two springs are in a series combination and are attached to a block of mass 'm' which is in equilibrium. Spring constants:k and k’ Extensions:x and x’ respectively. Find the force exerted by spring on the block?
  
• Help with the next complex variable limit?
  
• What is the Fourierseries of the following equation?
  
• A person moving on earth's surface starts from north and moves 500km towards south and then moves 1000km towards East and then again 500km towards north and stopped.find the magnitude of the displacement of the person ?(assume earth to be perfect sphere)
  
• Integrating factor question?
  
• What is the angle between A×B andB×A?
  
• Potential energy of mass m is U(x)=Eₒ,when 0≤x≤1, =0when x≻1.The total energy of the particle is 2Eₒ. The De Broglie wave length of the particle is λ₁ when 0≤x≤1 and λ₂ when x≻1. what is the ratio of λ₁ and λ₂ ?
  
• How do you find the equations for the tangent plane to the surface #f(x,y)=2-2/3x-y# through (3,-1,1)?
  
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