To find the area of a regular octagon, you can split the shape into eight congruent triangles from the center, find the area of one triangle, and then multiply it by eight.
If you use this method, you will find that the base of the triangle is the side length of the octagon (in this case, 15 units), and that the height is the apothem (in this case, 18.1 units).
From here, you can use the basic formula used to find the area of a triangle:
A = 1/2bh
A = 1/2 (15) (18.1)
A = 135.75 square units
Finally multiply the area of that triangle by eight.
8(135.75) = 1086
The area of the octagon is 1086 square units.
If x represents distance measured east of downtown, and y represents distance measured north of downtown, the circle of radius 40 centered at (-2.5, -2.8) will have an equation of the form
(x - h)² + (y - k)² = r²
where the center is (h, k) and the radius is r. The locus of points 4 miles from USC will satisfy the equation
(x +2.5)² + (y + 2.8)² = 1600
Answer:
first one on top.
Step-by-step explanation:
(tan(<em>x</em>) + cot(<em>x</em>)) / (tan(<em>x</em>) - cot(<em>x</em>)) = (tan²(<em>x</em>) + 1) / (tan²(<em>x</em>) - 1)
… = (sin²(<em>x</em>) + cos²(<em>x</em>)) / (sin²(<em>x</em>) - cos²(<em>x</em>))
… = -1/cos(2<em>x</em>)
Then as <em>x</em> approaches <em>π</em>/2, the limit is -1/cos(2•<em>π</em>/2) = -sec(<em>π</em>) = 1.
