Hint: The law of cosines for a triangle is -------------------------------------

Question

Hint: The law of cosines for a triangle is

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2) A baseball diamond is a square with sides of length 90 ft. A batter hits the ball and runs toward first base with a speed of 26 ft/s.

At what rate is his distance from second base changing when he is halfway to first base?
Answer = ...................... ft/s

At what rate is his distance from third base changing at the same moment?
Answer = ......................... ft/s

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3) A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat.

If the rope is pulled in at a rate of 1.3 m/s, how fast is the boat approaching the dock when it is 9 m from the dock?

Rate=..............

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Explanation / Answer

3 )

using righ t triangle

a^2 + b^2 = c^2

a = 1

b = 9

differentiate wrt t

2a*(da/dt) + 2b*(db/dt) = 2c(dc/dt)

a*(da/dt) + b*(db/dt) = c(dc/dt)

db/dt = c(dc/dt) - a*(da/dt) / b

here da/dt = 0 because it is not changing with time

db/dt = c(dc/dt) / b

c = sqrt(9^2+1^2) = sqrt(82)

dc/dt = 1.3 m/s

db/dt = 1.308

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