Nahee is running around the circular track with equation x2+y2=10000 at a speed of 2.9 meters per second. She starts at the point (0,100) and runs counterclockwise. What are Nahee's coordinates after she has been running for 13 minutes?

The coordinates are (58.1, - 81.4).

Step-by-step explanation:

The distance traveled by Nahee after 13 minutes at the rate of 2.9 m/sec along the arc of the circle with equation x² + y² = 100², will be (13 × 60 × 2.9) = 2262 m

Now, the perimeter of the circle is 2πr = m

Therefore, after traveling three full circles and a half-circle the remaining arc length will be [2262 - (628.57 × 3) - (628.57 ÷ 2)] = 62 m

Therefore, Nahee will finish his run in the fourth quadrant.

Now, the angle made by the arc length of  62 m at the center will be =

So, the angle made with positive x-axis will be (90° - 35.521°) = 54.488°

Now, the coordinates of the finishing point are (x,-y) = (rCos 54.488°, - rSin 54.488°) = (58.1, - 81.4) (Answer)

1. x> -5

2. x< 8

step-by-step explanation:

1. 2x> -10

divide by 2 from both sides of equation.

2x/2> -10/2

simplify, to find the answer.

-10/2=-5

x> -5 is the correct answer.

2. 3x< 24

divide by 3 from both sides of equation.

3x/3< 24/3

simplify, to find the answer.

24/3=8

x< 8 is the correct answer.

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