Part 1) The general form of a circle is given as x²+y²
+4x - 12y + 4 = 0.
(a)What are the coordinates of the center of the circle?
(b)What is the length of the radius of the circle?
x²+y² +4x - 12y + 4 = 0
Group terms that contain the same variable, and move the
constant to the opposite side of the equation
(x²+4x)+(y²- 12y)=-4
Complete
the square twice. Remember to balance the equation by adding the same constants
to each side
(x²+4x+4)+(y²- 12y+36)=-4+4+36
Rewrite as perfect squares
(x+2)²+(y-6)²=36--------> (x+2)²+(y-6)²=6²
center (-2,6)
radius 6
the answer Part a) is the center is the point (-2,6)the answer Part b) isthe radius is 6Part 2)
A 10-foot ladder placed on level ground leans against the side of a house. The ladder reaches a point that is 9.2 feet up on the side of the house.
(a)What is the measure of the angle formed by the ladder and the level ground? Round your answer to the nearest degree.
see the picture attached N 1 to better understand the problem
we know that
sin ∅=opposite side angle ∅/hypotenuse
opposite side angle ∅=9.2 ft
hypotenuse=10 ft
so
sin ∅=9.2/10-----> 0.92
∅=arc sin (0.92)------> ∅=66.93°-----> ∅=67°
the answer Part a) is
67°
Part b) The same 10-foot long ladder is placed against the building according to OSHA’s safety standard.
What is the distance between the foot of the ladder and the foot of the building? Round your answer to the nearest tenth.
see the picture attached N 2 to better understand the problem
cos 75=adjacent side angle 75/hypotenuse
adjacent side angle 75=AC
hypotenuse=10 ft
so
cos 75=AC/10---------> AC=10*cos 75----> AC=2.59 ft----> AC=2.6 ft
the answer Part b) isDistance between the foot of the ladder and the foot of the building is 2.6 ft
