A 200-foot cable weighing 800 pounds is hanging from a winch 200 feet above ground level. (a) How much per foot does this cable weigh? if a piece of this cable is A. x long, what is the weigh of this piece?
(b) Find the work (in ft-lb) done in winding up the cable when there is a 400- pound load attached to the end of the cable.

4 pd / ft

140000 ft/pd

Step-by-step explanation:

Total Weight of cable = 800 pounds

Length of cable = 200 feets

Weight per foot = Total weight / length = 800 / 200 = 4 pounds per foot

Weight of piece will be :

Weight of cable - weight per foot * x

800 - 4x

Workdone with 300 pound load attached :

∫f(x)

f(x) = (800+300 - 4x) = 1100 - 4x

∫1100 - 4xdx at 200 to 0

Integrating the above

1100x - 4/2x² at x = 200 to 0

1100x - 2x²

1100(200) - 2(200²) - 1100(0) + 2(0^²))

(220000-80000) - 0 + 0

140000 ft/pd

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.