A pebble drops from a balcony that is 80 feet above the ground. The pebble lands on the top of a sign that is 16 feet high. The
1 answer:
Answer:
t =2 seconds
Step-by-step explanation:
We have, a function that represents the height y of the pebble after dropping the balcony as follows :
The pebble lands on the top of a sign that is 16 feet high.
It is required to find the time does the pebble drop before hitting the sign. The above equation becomes,
So, the pebble hits the sign after 2 seconds.
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then g(x) gives the signed area under f(x) over a given interval starting at 0.
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since the integral of any function over a single point is zero;
since the area under f(x) over the interval [0, 4] is a right triangle with length and height 4, hence area 1/2 • 4 • 4 = 8;
since the area over [4, 8] is the same as the area over [0, 4], but on the opposite side of the t-axis;
since the area over [8, 12] is the same as over [4, 8], but doesn't get canceled;
since the area over [12, 16] is the same as over [0, 4], and all together these four triangle areas cancel to zero;
since the area over [16, 20] is a trapezoid with "bases" 4 and 8, and "height" 4, hence area (4 + 8)/2 • 4 = 24;
since the area over [20, 24] is yet another trapezoid, but with bases 8 and 12, and height 4, hence area (8 + 12)/2 • 4 = 40, which we add to the previous area.