e myopenmaths3.s3.amazonaws.com 1 of 1 Assignment 7 ou must SHOW ALL WORK to rec
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e myopenmaths3.s3.amazonaws.com 1 of 1 Assignment 7 ou must SHOW ALL WORK to receive full credit. A 17-foot ladder is resting against the wall. The base of the ladder is pulled away from the wall at 2 ft/sec, while the ladder maintains contact with the wall How rapidly is the top of the ladder falling when the base is 8 feet away from the wall? An oil tank is leaking into a lake at a rate of 0.1 m/day. The oil slick forms a semicircular disk whose center is at the leak site, and it has a thickness of 10-6 meters. How rapidly is the slick expanding when 0.5 cubic meters of oil have been leaked? Suppose an object is on the ellipse 9z+16y2 288. When the object is at the point (4,-3), it is moving so that -1, where t is measured in seconds. When the object reaches the point (4,-3), is it moving towards or away from the origin? Defend your conclusion Two planes leave an airport. The first plane leaves the airport at noon, and flies north at 400 km/hr. The second plane leaves the airport at 1 PM, and fies west at 500 km/hr. How rapidly is the distance between the planes changing at 3 PM? A lighthouse is situated 1500 meters offshore. The beam from the lighthhouse completes 1 revolution every 3 seconds. How rapidly is the beam moving along the shoreline when the point where the beam meets the shoreline is 5000 meters from the lighthouse?Explanation / Answer
These are five different question, they are not connected, i am solving the first problem as per Chegg guidelines, post multiple question to get the remaining answers
Q1)
Length of ladder = 17 ft
When Base = 8ft
Using pythagoras theorem
H^2 + B^2 = 17^2
H^2 + 8^2 = 17^2, H^2 = 289 - 64, H = 15
Differentiating both sides on the first equation
2HdH/dt + 2BdB/dt = 0
2(15)(dH/dt) + 2(8)(2) = 0
15 dH/dt = -16
dH/dt = -16/15 ft/sec
Hence the height is decreasing at the rate of -16/15 ft/s
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