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 m/s, how fast is the boat approaching the dock when it is 4 m from the dock

-1.031 m/s or  

Step-by-step explanation:

We take the length of the rope from the dock to the bow of the boat as y.

We take x be the horizontal  distance from the dock to the boat.

We know that the rate of change of the rope length is = -1 m/s

We need to find the rate of change of the horizontal  distance from the dock to the boat =   = ?

for x = 4

Applying Pythagorean Theorem we have

   .... equ 1

solving, where x = 4, we have

Differentiating equ 1 implicitly with respect to t, we have

substituting values of

x = 4

y =

= -1

into the equation, we get

= -1.031 m/s

hello from mrbilldoesmath!

answer:

a(n) - a(n-1) -3

discussion:

this ones a bit interesting. given a(n) = 5 - 3n consider this:

a(n-1) = 5 - 3(n-1)

          = (5 - 3n) + 3             => but a(n) = 5 - 3n, the first term

          = a(n)   + 3                 => subtract 3 from both sides

a(n-1) -3 = a(n)  

or

a(n) - a(n-1) -3

you,

mrb

find out the value of b

step-by-step explanation: