Answers edited by Ultrilliam

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• 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?
  
• Integrating factor question?
  
• Let #F(x)=int_0^x e^(-5t^4)dt#. Find the MacLaurin polynomial of degree 5 for F(x)?
  
• How to solve with integration?
  
• Find curl F for the vector field at the point (9, -9, 7). F(x,y,z) = x^2zi - 2xzj + yzk ?
  
• 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?
  
• Find the differential of the following function?: y = sin 5x^3
  
• Physics Work and Energy Question?
  
• If (1+i)(2+i)(3+i)....(n+i)=a+ib then show that 2.5.10....(n^2+1)=a^2+b^2 ?
  
• 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 ?
  
• Evaluate the limit #lim_(x to pi) (e^sinx -1)/(x-pi)# without using L'Hôpital's rule?
  
• 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?
  
• How do you determine the concavity of # y=2cosx+sin2x#?
  
• #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?
  
• Answer question a) why does A = A (t) = 6x^2? ,
  
• Is Electric potential and e.m.f are same or different terms?
  
• 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????
  
• 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?
  
• 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 i evaluate this double integral, the integrand is y^1/2*sin y dydx? x^2 < y < 1 0<x< 1
  
• 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)
  
• 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 ?
  
• FInd numeric value of #int_1^esqrt(lnx)dx-int_0^1e^(x^2)dx#?
  
• Does amplitude of a spring mass system change when mass is added?
  
• 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?
  
• How do you find the antiderivative of #e^( -x)*cos2x#?
  
• A particle of mass m strikes a wall at an angle of incidence 60° with velocity V elastically. Then the change in momentum is?
  
• How do you find the equations for the tangent plane to the surface #f(x,y)=2-2/3x-y# through (3,-1,1)?
  
• Graph the parametric equation x(t)=3t and y(t)=2-2t on [0,1] ?
  
• How to find the curvature K of the curve?
  
• Evaluate the integral?
  
• What is the angle between A×B andB×A?
  
• Help with the next complex variable limit?
  
• How to prove ?
  
• Find the instaneous rate of change of y=2x+3 ?
  
• Find the complete integral of the equation (∂z/∂x_1)(∂z/∂x_2)(∂z/∂x_3)=z³x_1x_2x_3?
  
• Linear/Separable Differential Equations Question (Engineering First Year Calculus)?
  
• Solve L(sin4t) ?
  
• Solve the intergral ?
  
• 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?
  
• How to Find the directional derivative of?:
  
• 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?
  
• 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?
  
• If vector P+vector Q=vector R ;and if P^2+Q^2=R^2 then find the angle between the vectorP and vectorQ?
  
• 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?
  
• Can you help me with this double integral?
  
• #intint_D cosxy dxdy#, where #D: {[x>=0],[y>=0],[x>=y]}#?
  
• 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 ?
  
• What is the derivative of #Tan^-1 (y/x)#?
  
• 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 )
  
• 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?
  
• How do you find the area of the region bounded by the spiral #r=7theta# for #0<=theta<=pi#?
  
• 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?
  
• Determine the Fourier series expansion for full wave rectified sine wave i. (details inside)?
  
• 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}?
  
• Integral of [x+3÷(5-x²-4x)½]dx?
  
• Solve it please. "?"
  
• What is the Fourierseries of the following equation?
  
• How to calculate average pressure as volume changes via intergration?
  
• D (log sin cos tan e^cosx)/dx ?
  
• 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?
  
• How is impulse related to momentum?
  
• 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?
  
• How about Answer ?
  
• 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?
  
• I have a Work word problem I need help completing?
  
• Why isn't #dy/dx = 3x + 2y# a linear differential equation?
  
• 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?
  
• 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 ?
  
• What is diffraction a result of?
  
• How to derive this relativistic Energy-Momentum relation?
  
• 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?
  
• The value of #lim_(h→0)1/hint_2^(2+h)sin(x^2)dx#is?
  
• Determine if F is a linear transformación f(x,y,z)=(x,x+y+z) ?
  
• 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 can Newton's first law be derived from Newton's second law?
  
• Can someone help me check if this matrix is diagonalisable?
  
• The sum of A and B is 5i+j and their difference is 3i-j what is vector A?
  
• 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?
  
• 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?
  
• Relativity problems?
  
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