Recent content by gaobo9109

Thanks. I didn't notice that

Homework Statement \int sin e^{-x}+e^x cos e^{-x}\,dx Find the integral above Homework Equations The Attempt at a Solution I tried substituting u=e^{-x}, but i get \int \frac{sin u}{u}+\frac{cos u}{u^2} \,du, which is non-integrable function.

Homework Statement p⇒¬q,q∨r⊢p⇒r, prove this using rule of natural deducton Homework Equations The Attempt at a Solution My approach is this. 1.Prove that qvr⊢¬q⇒r. 2.Assume p 3.By modus ponen, p⇒r But the problem I face is how to prove step 1.

When I arrange the six statistics questions, there will be 7 spaces to slot in the 5 pure maths questions. Since there is the restriction that pure math question must be followed by exactly one statistics question, there are three ways to arrange 5 questions in these 7 free spaces. If there is...

Homework Statement A test consists of 5 pure math questions A, B, C, D, E and 6 statistics question F, G, H, I, J, K. The examiners want to arrange all eleven questions in a random order such that a pure math question must be separated from another with exactly one statistics question...

Homework Statement Given that 1+2cosx+2cos2x+2cos3x + ....+2cosnx = sin(x+1/2)x cosec(x/2) Prove that 1-2cosx+2cos2x-2cos3x+....+2cos8x = cos(17/2)x sec(x/2) Homework Equations The Attempt at a Solution 1+2cosx+2cos2x+2cos3x + ....+2cos8x = sin(8+1/2)x cosec(x/2)...

The diagram provided in the question is quite similar to the one I have attached, except that the coil is substituted with a rectangular armature with wire around it. I find the solution weird because normally I would calculate change in magnetic flux by finding change in the magnetic field...

Homework Statement A simple DC motor consists of an armature placed between two poles of a magnet. The armature is rectangular and has dimensions of 90mm in breadth and 100mm in length. Magnetic flux density produced by the magnet is 0.5T. Number of turns of armature winding is 500. What is...

Homework Statement In colliding beam accelerator, two proton beams of the same energy are made to collide with each other from opposite direction. To improve the chances of collision, the protons are concentrated within the beam into bunches. In the laboratory frame of reference, each bunch is...

Homework Statement In an irregular quadrilateral ABCD, the length of all sides are AB=a BC=b CD=c DA=d and the length of the diagonal AC is x. Angle ABC + angle ADC = 180 prove that (ab+cd)x2=(ac+bd)(ad+bc)Homework Equations Cosine formula c2 = a2 + b2 - 2abcosθ The Attempt at a Solution I...

Homework Statement An electron of charge e and rest mass m0 is accelerated to relativistic speeds by a potential V. Show that the deBroglie wavelength is given by the expression lambda= h(2m0eV)-1/2 (1+eV/2m0c2)-1/2 The Attempt at a Solution eV = gamma m0c2 equation one p = gamma...

Homework Statement How do you integrate x/(1-4x-2x2)1/2 Homework Equations The Attempt at a Solution I tried to solve it using by-part method, but it turned out to be very complicated, and my answer doesn't match the answer given. Is there any other way to approach this question?

How did you get this substitution? Hyperbolic function is not in my school syllabus. Is there any other form of substitution to to solve this question?

Homework Statement How to you integrate (x2-5)1/2 Homework Equations The Attempt at a Solution I have tried substitution, integration by part, and none seems to work. I really don't know where to start.

Homework Statement A rectangular block of length L is traveling on a smooth surface at velocity u. When it encounters rough ground with coefficient of friction mu, it decelerates to a stop. What is the time taken for the rectangular block to stop?Homework Equations F= (mu)mgThe Attempt at a...