A game is played using one die. If the die is rolled and shows 4, the player wins $5. If the die shows any number other than 4,
1 answer:
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Answer:
θ is decreasing at the rate of units/sec
or (θ) =
Step-by-step explanation:
Given :
Length of side opposite to angle θ is y
Length of side adjacent to angle θ is x
θ is part of a right angle triangle
At this instant,
x = 8 , = 7
( denotes the rate of change of x with respect to time)
y = 8 , = -14
( The negative sign denotes the decreasing rate of change )
Here because it is a right angle triangle,
tanθ = -------------------------------------------------------------------1
At this instant,
tanθ = = 1
Therefore θ = π/4
We differentiate equation (1) with respect to time in order to obtain the rate of change of θ or (θ)
(tanθ) =
(y/x)
( Applying chain rule of differentiation for R.H.S as y*1/x)
θ
(θ) =
-
-----------------------2
Substituting the values of x , y , ,
, θ at that instant in equation (2)
2(θ) =
*(-14)-
*7
(θ) =
Therefore θ is decreasing at the rate of units/sec
or (θ) =