A piece of rope falls out of a hot air balloon from a height of 5,184 ft. If the
equation for height as a function of time
is h(t) = -16t2 - initial height where t is
time in seconds and h(t) is height in feet,
how many seconds will it take for the
piece of rope to hit the ground?

Explanation:

The equation should be h(t) = -16t^2 + (initial height). If you subtract off the initial height, then you'll have a negative starting height, which is not correct. Try plugging t = 0 into h(t) = -16t^2 - (initial height) and you'll see what I mean.

The initial height is 5184. We want to find the t value when h(t) = 0. So we want to find the time value when the height is 0.

h(t) = -16t^2 + (initial height)

h(t) = -16t^2 + 5184

0 = -16t^2 + 5184

16t^2 = 5184

t^2 = 5184/16

t^2 = 324

t = sqrt(324)

t = 18

It takes 18 seconds for the rope to hit the ground.

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.