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a particle travels half of the distance of a straight journey with speed 6m/s .the remaining part of distance is covered with speed 2m/s for half of the time of remaining journey and with speed 4m/s for the other half of time .the average speed of the particle is ??????????
why is Canada a first world country?
Please show that the vector a is orthogonal to the hyperplane H = H(a,€); that is, if u and v are in H, then a is orthogonal to u - v.
Definition: Given any non-empty closed convex set C and an arbitrary vector x in R^j, there is a unique member Pcx of C closest, in the sense of the two norm, to x. The vector Pcx is called the orthogonal projection of x onto C and the operator Pc the orthogonal projection onto C.

Question: Given a point s in a convex set C, where are the points x for which s = Pcx?
Two points A and B are 85cm north and 60cm west of a point charge of −4510−3C respectively. Calculate the potential difference between A and B
A beam is supported on two rollers, each of radius 'r' is moved up an inclined plane making angle b'' by a force 'P' which acts parallel to the plane. Determine the magnitude of "P" necessary to maintain equilibrium if there is no slipping between either the rollers and the inclined plane or the rollers and the beam.The weight of the beam is Q and the wight of each roller is 'w'.
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Two points x1 and x2 at x = 0 and x = 1 m are observed. The transverse motion of the two points are found to be as follows:
y1(x,t)=0.2 sin 3πt
and y2(x,t)=0.2 sin (3πt + π/8)
Calculate the frequency, wavelength and speed of the wave.
Thirsty Cactus Corp. just paid a dividend of $2.20 per share. The dividends are expected to grow at 22 percent for the next eight years and then level off to a growth rate of 7 percent indefinitely. If the required return is 14 percent, what is the price of the stock today?
Assume that a firm in a perfectly competitive industry has the following total cost schedule:
Outputs: Total costs ($)
10 $110
15 150
20 180
25 225
30 300
35 385
40 480
a. Calculate a marginal cost and an average cost schedule for the firm.
b. If the prevailing market price is $17 per unit, how many units will be produced and sold? What are the profits per unit? What are total profits?
c. Is the industry in long-run equilibrium at this price?
Solve DE r^2 +4r+3=12
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