From the top of a building, 40 feet above the ground, a construction worker locates a rock at a 12° angle of depression. How far
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Answer:
centre (5, 6 ) , r =
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r the radius
given
x² + y² - 10x - 12y + 24 = 0 ( collect x and y terms together and subtract 24 from both sides )
x² - 10x + y² - 12y = - 24
using the method of completing the square
add ( half the coefficient of the x / y terms)² to both sides
x² + 2(- 5)x + 25 + y² + 2(- 6)y + 36 = - 24 + 25 + 36
(x - 5)² + (y - 6)² = 37 ← in standard form
with centre (h, k ) = (5, 6 ) and r =
The given equation is
Consider the slope-intercept form.
Rewriting the given equation in the slope-intercept form.
Subtracting 3x from both sides, we get
Dividing both sides by 5, we get
Compared to the slope-intercept form, we get m=-0.6 and b=1.4.
Hence the slope m= -0.60.