- #1

F.B

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The questions are:

1. A baseball diamond is a perfect square with each side measuring 90 feet

in length. A player runs from the first base to second base at a speed of

25 ft/s. How fast is she moving from home plate when she is 30 ft away from

first base.

2. A fish is being reeled in a rate of 2 m/s (i.e, the fishing line is

being shortened by 2 m/s by a man. If he is sitting 30 m above water on a

dock, how fast is the fish moving through water when the line is 50 m long.

My answers are these:

1. A drew my diamond and figured that i will be using half of the diamond.

Let the distance between home plate and first base be x

Let the distance from first base to second base by y

Given

y = 90 ft

dy/dt = 25 ft/s

x = 90 ft - 30ft

=60 ft

dx/dt = ?

x^2 + y^2 = z^2

90^2 + 90^2 = z^2

z = 127.3 ft

x^2 + y^2 = z^2

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

sine dz/dt = 0

2(60)(dx/dt) + 2(90)(25) = 0

dx/dt = -37.5 ft/s

Is this correct? and why is my answer negative shouldn't it be positive

because you increasing the distance from home plate or is my answer

negative because the distance to first base is decreasing.

2. Given

y = 30 m

z = 50 m

dz/dt = - 2m/s

x = ?

dx/dt = ?

x^2 + y^2 = z^2

x^2 = 50^2 - 30^2

x = 40 m

x^2 + y^2 = z^2

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

since dy/dt = 0

2(40)(dx/dt) = 2(50)(-2)

dx/dt = -2.5 m/s

Is this question correct because I am not sure when to make my numbers

negative, i know we have to when something is decreasing but I am not sure.

So can you please check if i did this two questions right?