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) =
No, it does not represent a function
$ 524.288
Step-by-step explanation:
We will use the sum of a geometric series;
S = (first term)(1-r^n)/(1-r)
= 1(1 - 2^n) / (1 - 2)
= - (1 - 2^n)
= 2^n - 1
2 ^ (20 – 1)
2 ^ 19
= 524,288 cents
100 cents = 1 dollar
524,288 cents = 524,288/ 100 dollars
= $ 524.288
Answer:
x = 65° ∠1 = 65° ∠2 = 115°
Step-by-step explanation:
x + x + 50° = 180°
2x = 180° - 50°
2x = 130°|:2
x = 65°
