Answers created by Ananda Dasgupta

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• Integral(x³×ln(√x))dx ?
  
• If f''(x)= -f(x) and g(x)= f'(x) and F(x) = (f(x/2))^2 + (g(x/2))^2 and given that F(5) = 5 then F(10) equals ? (hint : answer is an integer from 0 - 9)
  
• Find # i# for #t>0 # if the circuit is in steady state at # t=0# ?
  
• A simple pendulum has length 20cm.it was displaced at an angle 15° and then released to execute simple harmonic motion. How much time is required for the pendulum to reach maximum speed?
  
• How do you find the binomial coefficient of #((100), (98))#?
  
• An object performs simple harmonic motion between points k an L with a period 40pi if the distance between k and L is 10cm what is the speed of object when it is 8cm away from equilbrium position?
  
• Determine a base and dimension of each of the subspaces below?
  
• Find the position #s# as a function of time #t# from the given velocity #v= {ds}/{dt}#. Then evaluate the constant of integration so that #s=s_0# when #t=0#. #v=8(s)^(1/2), qquad s_0=9# Help please?? and thank you!!!
  
• How do you know if the series #sum 1/(n^(1+1/n))# converges or diverges for (n=1 , ∞) ?
  
• How do you solve using elimination of #2x+y=4# and #-2x-y=4#?
  
• Find the moment generating function,mean and variance when the pdf of x is defined by #f(x)=(1/3)(2/3)^x. ; x=0,1,2,3,.... # ?
  
• Help? Series and Sequences Question!
  
• If f(x)=lim of 1/(1+nsin^2pix) as n approaches to infinity,find the value of f(x) for all real values of x?
  
• What real function is #(e^(ix)-e^(-ix))/(ie^(ix)+ie^(-ix))# to?
  
• Differentiate: tcos(t^2) ?
  
• How do you determine whether a linear system has one solution, many solutions, or no solution when given 5x+ 4y= -18 and 2x+3y=-24?
  
• Help me find the derivative of #sinx+x^2y=10#?
  
• Can someone help me find the derivative of e^2y+x=y ?
  
• In nuclear fission, a nucleus of uranium 238, which contains 92 protons, can divide into two smaller spheres, each having 46 protons and a radius of 5.90  10-15 m. Find the acceleration of each nucleus at the instant in which fission occur?
  
• 2x+3y=5 6x+9y=-15?
  
• How to check the dfifferentiability of f(x) where f(x)=|2x-3| at x=1?
  
• How to find potential from 2 charges through 4 points?
  
• What is the ratio of momentum @ M and N? (No friction)
  
• What is the angular momentum of earth?
  
• In class we are learning about work; why does the force and motion have to go in the same direction?
  
• How is radioactive decay used in carbon dating?
  
• If #a#, #b#, #c#, #d# and #e# are real numbers, prove that the roots of #x^5 + ax^4 + bx^3 + cx^2 + DX + e=0#, cannot be all real if #2a^2<5b#?
  
• When a skydiver with a mass of 100kg is falling in a prone position (spread eagle) at terminal velocity (max speed) towards the earth. What is the magnitude of the drag force action on the skydiver?
  
• The partial fraction decomposition of #(5x+1)/((x-1)(x+1)(x+2))# is given by #A/(x-1)+B/(x+1)+C/(x+2)# . What are the constants of A, B, and C?
  
• How do you differentiate #d/dx sqrt(1+sqrt(1+sqrt(1+sqrt(x)))) #?
  
• What are three examples of the Doppler effect in nature?
  
• Please explain ? Question 21.
  
• For what value of #k# is this system consistent? #3x + 5y + 5z = −2#, #−3x + −1y + 0z = 7# and #−6x + 6y + 10z = k#
  
• Which set of ordered pairs does not represent a function?
  
• Let say K and L are two different subspace real vector space #V#. If given #dim(K)=dim(L)=4#, how to determine minimal dimensions are possible for #V# ?
  
• What is the value of m?
  
• Show that #sin^7 x + cos^7 x < 1# if #0 < x < frac{\pi}{2}#. Please explain in words how to calculate this?
  
• Find the product of AB and BA. (See picture) Thanks?!!
  
• What are the extrema and saddle points of #f(x, y) = xye^(-x^2-y^2)#?
  
• Related rates: an aircraft is flying at 460 ft/s with an elevation of 100 ft from ground. how fast...?
  
• Can anyone prove the formula of volume expansion coefficient and the compressibility for van der Walls gas ?
  
• If you need 6 joules of work to expand a spring from 10 to 12 cm and another 10J to expand it from 12 to 14 cm. Wich is the natural lenght of the spring?
  
• Show #|f(b)-f(a)|<= |b-a|# ?
  
• Solve using trig sub: #\int(\sec^2\theta\tan^2\theta)/\sqrt(9-\tan^2\theta)d\theta#?
  
• What is the equation of the line tangent to #f(x)= -3x^5-8x^3+4x^2 # at #x=-1#?
  
• How do you find the integration of : ((1-1/x) cos(x-Inx))dx?
  
• Object A emits more light than Object B. Would it be fair to say that the more luminescent object (Object A) is emitting <em>more high energy photons<em> than Object B? If so, why? If not, why not?
  
• A 13.1 eV photon is emitted from a hydrogen atom. What is the Balmer formula n value corresponding to this emission? What is the Balmer formula m value corresponding to this emission?
  
• #int(x^3/(x + 2))# equals ??
  
• PLEASE HELP!!! Make a general comparison of the RC-time for a 3300uF capacitor with a 1000uF capacitor.?
  
• If #lim_(xrarr2)(f(x)-4)/(x-2)=C# for constant C. Find #lim_(xrarr2)#f(x). What theorems were used to come to conclusion?
  
• The half-life of a radioactive element is 5.0 days. A freshly-prepared sample contains 128 g of this element. After how many days will there be 16 g of this element left behind in the sample?
  
• What is the magnitude of the centripetal acceleration of an object on Earth's equator owing to the rotation of Earth?
  
• Using Euler's method, what is f(1) estimated to be?
  
• For a questions(Comprehension) of Mechanics refer a photo below.?
  
• How to solve the following ??
  
• How to solve this?
  
• Please help me out ASAP with this statement about Matrix?
  
• If f(x) is a function that is odd and even simultaneously then f(3)-f (2) is equal to ?
  
• Given #\ \ f(x)=1/2x^4-x^3+x-3\ \ #... Show the equation?
  
• How would I graph g(x)=3f(x-2)+1?
  
• A particle begins to move with a tangential acceleration of constant magnitude #0.6m/s^2# in a circular path. If it slips when it's total acceleration becomes #1m/s^2#, then the angle through which it has turned before slipping is?
  
• Physics Help?
  
• What is the limit as x approaches zero from above of (1+x)^cotx?
  
• #intint_Asqrt(xy-y^2)dxdyquadquadA={(x,y)inRR^2; 0<=y<=3, x/10<=y<=x}# Would anyone help me?
  
• Integral of the trigonometric functions:? B-) #int_0^pisin^2x*cos^4xdx#
  
• How to find out the breakdown voltage?
  
• Find the simplified expression of the following circuit using K Map?
  
• How do you show that the equation x-inverse tan(3x)=0 has a solution lying between x=1 and x=2? (Not sure if you need to use half-interval or newton's method??)
  
• What is the tension in the rope? And the horizontal and vertical forces exerted by the pivot?
  
• What is the integral of #cos^6(x)#?
  
• How can i find the probability of pulling a coin out of a jar? (details inside)
  
• How to evaluate:#intx^5/(x^4 + 1)^2dx#?
  
• A ball is thrown with an initial speed at an angle with the horizontal the horizontal range of the ball is R and the ball reaches a maximum height R/6. In terms of R and g find the time interval during which the ball is in motion?
  
• How do you find the limit in the following question?
  
• Find the exact value of the expression whenever it is defined?
  
• Help me with this question?
  
• If a monic cubic polynomial is divided by #x^2-9# leaving a remainder of x+8 and when divided by x leaves a remainder of -4, how do you find this polynomial?
  
• Let f(x) be a function satisfying |f(x)| ≤ x^2 for -1 ≤ x ≤ 1, how do you show that f is differentiable at x = 0 and find f’(0)?
  
• How I can round off it? 0.0505 If it is 0.051 then why ? If it is 0.050 then why . Please let me know reason, Thanks a lot.
  
• How do you know if an ordered pair (5,11) is a solution to y=2x+1?
  
• Find a General formula for f^(n) (x)?
  
• How to derive this relativistic Energy-Momentum relation?
  
• What are the range of initial values using the Newton-Raphson method for #(x-9)/(x^2+1)=0# for it to converge to 9?
  
• Prove that the function f(x)=tanh^-1(x) is an odd function ?
  
• Find #f# ?
  
• Find #f# ?
  
• Please solve q 61?
  
• A radioactive isotope #""_Z^XA# decay and emits one alpha particle and two beta particles consecutively. How to write the formula for the nuclides produced?
  
• Solve |#sinx + cosx#| = |#sinx#| + |#cosx#|, x#in# [0, 2#pi#] ?
  
• How do you evaluate #int tan^5(theta/2) d(theta)#?
  
• How do I find #sintheta# = #-cos^2theta# -1 in radians from #[0, 2pi]#?
  
• Trigonometric form of negative square root 3 +i ?
  
• How do action-reaction pairs keep a book sitting on a table in equilibrium?
  
• The number of solution of the equation 3^(sin2x+2cos2x)+ 3^(1-sin2x+2sin2x)=28 in [0,2π]?
  
• What is the period of #f(theta) = tan ( ( 13 theta)/4 )- cos ( ( 6 theta)/ 5 ) #?
  
• Write an expression for the work done by the spring? (Physics)
  
• 2 identical pendulums A&B are suspended from same point.The bobs A&B are given positive charges q1 and q2 (q1<q2). If A&B are making angles $1 and $2 with the vertical and T1 and T2 are tensions in the string respectively.Then prove that $1=$2 and T1=T2?
  
• What are the new values of V, Q, U, and E?
  
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