Other Math Answers

(a) A particle P moves along the x-axis with constant acceleration a in the positive x-direction. Initially
P is at the origin and is moving with velocity u in the positive x-direction. Show that the velocity v
and displacement x of P at time t are given by
v = u + at, x = ut +
1
2
at2
,
and deduce that
v
2 = u
2 + 2ax.
(b) The trajectory of a charged particle moving in a magnetic field is given by
r = b cos (Ωt)i + b sin (Ωt)j + ctk,
where b, Ω and c are positive constants. Show that the particle moves with constant speed and find the
magnitude of its acceleration.

1. If a1 = λ1i + µ1j + ν1k, a2 = λ2i + µ2j + ν2k, a3 = λ3i + µ3j + ν3k, where {i,j, k} is a standard basis, show
that
(a)
a1 · (a2 × a3) =






λ1 µ1 ν1
λ2 µ2 ν2
λ3 µ3 ν3






.
(b) Deduce that a2 · (a3 × a1), due to cyclic rotation of the vectors in a triple scalar product leaves the
value of the product unchanged.
(c) If r(t) = (3t
2 − 4)i + t
3
j + (t + 3)k, where {i,j, k} is a constant standard basis, find r˙ and ¨r. Deduce
the time derivative of r × r˙.

The sales of a company from 1993-1998 are given below:

Year 1993 1994 1995 1996 1997 1998
Sales (in lakhs of rupees) 40 45 50 55 60 65
Fit a linear curve using the least squares method. Hence find out the company’s sales in 1999.

A skateboarder rolls horizontally off the top of a staircase at a speed of 18 ms-1 and at the bottom of the stairs which has a horizontal length of 9 m as
.
Calculate the skater's vertical displacement during the jump

Find the working application with Derivation and upload the same here. With the same application answer the bellowed mentioned question.

1) How does the above application is working with derivation.

2) Which derivative method is used in the same

3) Can we used any other method in the same application. If yes which and if no why?

I was curious about how this will work if something many feet like let's say 100ft tall how will you do the weight of it? Like if you 100ft tall or 300ft it doesn't matter how can weight be determined of the height.

compute the value of 410-78 using 8-bit sign magnitude in binary

Find the Laplace transform of f(t)=e^-t,where f(t+1)=f(t)

Explain how addition and subtraction were used to derive the roman numerals below
1.IV
2.VI
3.XIX
4.LXIV
5.XCIX

show that in the motion of a heavy particle in a medium the resistance of which varies as the velocity, the greatest height abov the level of the point of projection is reached in less than half the total time of flight above that level.