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frutty [35]
3 years ago
12

latoya is going for a run. she runs at a speed of 6 miles per hour for 9.6 miles. for how many hours does she run?

Mathematics
1 answer:
LenKa [72]3 years ago
7 0
\begin{array}{ccc}6mi&-&1h\\9.6mi&-&xh\end{array}\ \ |cross\ multiply\\\\6x=1\cdot9.6\\\\6x=9.6\ \ \ |divide\ both\ sides\ by\ 6\\\\\boxed{x=1.6\ (h)}
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The center of a circle lies on the line y = 4x + 1 and is tangent to the x-axis at (−3,0) . What is the equation of the circle i
Hunter-Best [27]

Answer:

(x+3)^2+(y+11)^2=121

Step-by-step explanation:

Consider a sketch of the problem as shown in the picture, where:

  • Blue line is given by y = 4x + 1.
  • Point B is the center of the circle.
  • Point A is (-3, 0).

Since the center of the circle lies on the line y = 4x +1 and is tangent to the x-axis at point A, then its radius BA is perpendicular to the x-axis. To find the coordinates of point B, we must replace x = -3 into the blue line equation: y = 4x(-3) + 1 = -11.

So, we know that the center of the circle is at B=(-3, -11). And furthermore, the radius BA is of length r=11.

Since the <em>general equation of the circle</em> of radius lenght r centered at (h, k) is given by

(x-h)^2+(y-k)^2=r^2

then with h = -3, k = -11 and r= 11, the equation of our circle is

(x+3)^2+(y+11)^2=121

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Step-by-step explanation:

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Answer:

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