Answer:
E=-24
Step-by-step explanation:
Answer:
Assuming the area is made up of a square and a semicircle.
<u>Perimeter</u>
The side length of the square = 18 ft
We can see 3 full side lengths plus one side length from which we need to subtract 12 ft (see attached diagram).
⇒ perimeter of the square = (3 x 18) + (18 - 12)
= 54 + 6
= 60 ft
Circumference of a circle = d (where d is the diameter)
⇒ arc length of the semicircle = 1/2 circumference
= 1/2 · · 12
= 6 ft
Total perimeter = 60 + 6 = 78.8 ft (nearest tenth)
<u>Area</u>
Area of a square = s² (where s is the side length)
⇒ area of square = 18²
= 324 ft²
Diameter = 2r ⇒ r = 1/2 diameter
Area of a circle = r² (where r is the radius)
⇒ area of the semicircle = 1/2 · · 6²
= 18 ft²
Total area = 324 + 18 = 380.5 ft² (nearest tenth)
By definitions of the (co)tangent and cosecant function,
Turn everything into fractions with common denominators:
Recall that , so we can simplify both sides a bit.
On the left:
On the right:
(as long as , which happens in the interval when or )
So we have
Multiply numerator and denominator by sin(x) * cos(x), getting:
((sin(x) * cos(x)) - cos^2(x) / (((sin^2(x)) - (sin(x) * cos(x))) =
(cos(x) * (sin(x) - cos(x)))
------------------------------------
(sin(x) * (sin(x) - cos(x)))
and after you cancel the two identical terms (sin(x) - cos(x)), you have:
cos(x)
----------- = cot(x) <--------------- Answer
sin(x)
The distance they can see: d = √ ( 3 h / 2 )
d ( Addison ) = √ ( 3 · 256/3 / 2 ) = √ 124 = √ 64 · 2 = 8 √ 2d ( Kaylib ) = √ ( 3 · 48 / 2 ) = √ 72 = √ 36 · 2 = 6 √ 2d ( Addison ) - d ( Kaylib ) = 8 √ 2 - 6 √ 2 = 2 √ 2Answer: b. 2 √ 2 mi.