A baseball diamond is a square with side 90 feet. A batter hits the ball and runs toward first base with a speed of 24 ft/sec. At what rate is his distance from second base decreasing when he is halfway to first base?

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  10.73 ft/s

Step-by-step explanation:

When the runner is halfway to first base, the triangle formed by his position and the first and second bases is a right triangle with legs of 45 ft and 90 ft. The angle between the runner's direction and the line from his position to 2nd base is ...

  angle = arctan(90/45) ≈ 63.43°

The "speed made good" in the direction of 2nd base is the product of the cosine of this angle and the runner's speed toward first.

  speed toward 2nd = cos(63.43°)×(24 ft/s) ≈ 10.73 ft/s

The rate the runner's distance to 2nd base is decreasing is 10.73 ft/sec.

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11