15. Keisha draws a sketch of her living room on grid paper.
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) =
Answer:
The area of the rhombus is 24 units²
Step-by-step explanation:
The area of a rhombus is half the product of the diagonals.
We can easily calculate the length of the diagonals because they are vertical and horizontal line segments.
We use the absolute value approach.
The length of diagonal BD is |7--5|=|7+5|=|12|=12
The length of diagonal AC=|0--4|=|4|=4
Therefore the area of the rhombus is