Answer:
59.16 units
Step-by-step explanation:
Given that,
The length of rectangle, L = 13
The breadth of the rectangle, B = 6
The perimeter of the shaded region = perimeter of rectangle - 2(perimeter of semicircle)
![P=13\times 6-[2\times \dfrac{2\pi r}{2}]\\\\=78-2\pi r\\\\=78-2\times 3.14\times 3\\\\=59.16](https://tex.z-dn.net/?f=P%3D13%5Ctimes%206-%5B2%5Ctimes%20%5Cdfrac%7B2%5Cpi%20r%7D%7B2%7D%5D%5C%5C%5C%5C%3D78-2%5Cpi%20r%5C%5C%5C%5C%3D78-2%5Ctimes%203.14%5Ctimes%203%5C%5C%5C%5C%3D59.16)
So, the perimeter of the shaded region is 59.16 units.
Answer:
40 inches
Step-by-step explanation:
We know that the height of water in a pool decreased 5 inches per week.
This means that we can form the equation 
, since the amount of water remaining is proportionate to the amount of weeks that have passed.
We know 
, since we need to find the change for 8 weeks.
The change will be the absolute value of -40, which just makes it positive, so 40.
Hope this helped!
Answer:
20=XY
Step-by-step explanation:
LHS ⇒ RHS:
Identities:
[1] cos(2A) = 2cos²(A) - 1 = 1 - 2sin²(A)
[2] sin(2A) = 2sin(A)cos(A)
[3] sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
[4] cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
cos(x) - cos(x + 2Θ)
= cos(x) - (cos(x)cos(2Θ) - sin(x)sin(2Θ)) [4]
= cos(x) - cos(x)(1 - 2sin²(Θ)) + sin(x)(2sin(Θ)cos(Θ)) [1] [2]
= cos(x) - cos(x) + 2sin²(Θ)cos(x) + 2sin(Θ)sin(x)cos(Θ)
= 2sin²(Θ)cos(x) + 2sin(Θ)sin(x)cos(Θ)
= 2sin(Θ)(sin(Θ)cos(x) + sin(x)cos(Θ))
= 2sin(Θ)sin(x + Θ)
