Answer:
decreasing at 390 miles per hour
Step-by-step explanation:
Airplane A's distance in miles to the airport can be written as ...
a = 30 -250t . . . . . where t is in hours
Likewise, airplane B's distance to the airport can be written as ...
b = 40 -300t
The distance (d) between the airplanes can be found using the Pythagorean theorem:
d^2 = a^2 + b^2
Differentiating with respect to time, we have ...
2d·d' = 2a·a' +2b·b'
d' = (a·a' +b·b')/d
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To find a numerical value of this, we need to find the values of its variables at t=0.
a = 30 -250·0 = 30
a' = -250
b = 40 -300·0 = 40
b' = -300
d = √(a²+b²) = √(900+1600) = 50
Then ...
d' = (30(-250) +40(-300))/50 = -19500/50 = -390
The distance between the airplanes is decreasing at 390 miles per hour.
When it hits the ground the height would be 0.
Set h to 0 and solve for t ( time)
0 = -16t^2 + 112t + 144 divide both sides by -16:
T^2 -7t -9
Factor the polynomial :
( t- 8.1) (t+1.1
Solve for t setting each equation to 0:
T = 8.1 or t = -1.1
Time has to be positive, so the answer is
8.1 seconds
Depending on how everything gets rounded it could also be 8 seconds.
I hope this is the answer you want
The area of the side walk would be 5.5ft^2. Hope this helps
