A surveyor is calculating the width of a canyon. He has taken the measurements shown below. What is the width of the canyon? Typ
e a numerical answer in the box below.
1 answer:
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Answer:
the point lies at (1.7, 3.6) in the first quadrant.
Step-by-step explanation:
The formula for a circle with centre (h,k) and radius (r) can be expressed as :
(x-h)² + (y-k)² = r²
Now for the expression of the circle with radius 3 and center (0,1), we have:
(x - 0)² + (y - 1)² = 3²
x² + (y-1)² = 9
replacing y = 1.5x + 1 in the above equation, we have:
x² + (( 1.5x + 1 ) - 1 )² = 9
x² + ( 1.5x +1 - 1)² = 9
x² + (1.5x)² = 9
x² + 2.25x² = 9
3.25x² = 9
x² = 9/3.25
x = 1.7 in the positive x - axis
Recall that:
y = 1.5x + 1
y = 1.5 (1.7) +1
y = 2.55 +1
y = 3.55
y = 3.6
Therefore, the point lies at (1.7, 3.6) in the first quadrant.