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aleksklad [387]
3 years ago
5

recall the equation for a circle with center (h,k) and radius r At what point in the first quadrant does the line with equation

y=0.5x+4 intersect the circle with radius 4 and center (0,4)
Mathematics
1 answer:
Angelina_Jolie [31]3 years ago
6 0

9514 1404 393

Answer:

  ≈ (3.578, 5.789)

Step-by-step explanation:

We can substitute for y and solve for x.

  (x -h)^2 +(y -k)^2 = r^2 . . . equation of a circle with center (h, k), radius r

  x^2 +(y -4)^2 = 4^2 . . . . . . the equation of the given circle

  x^2 +((0.5x +4) -4)^2 = 16

  (5/4)x^2 = 16

  x = 8/5√5 . . . . multiply by 4/5 and take the square root

  y = 0.5x +4

  y = 4/5√5 +4

The point of intersection is (8/5√5, 4+4/5√5), approximately (3.578, 5.789).

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