Juliet and mercutio are moving at constant speeds in the xy-plane. they start moving at the same time. juliet starts at the point (0, −6) and heads in a straight line toward the point (10, 5), reaching it in 10 seconds. mercutio starts at (7, −16) and moves in a straight line. mercutio passes through the same point on the x-axis as juliet, but 2 seconds after she does. how long does it take mercutio to reach the y-axis?

  574/17 ≈ 33.765 seconds

Step-by-step explanation:

This problem begs to be solved using parametric equations for the lines of travel. Such an equation for position (P) can be written in terms of a starting point (A) and direction of travel (V) as ...

  P = A + tV

Here, the direction of travel between points A and B is V = B-A, and the time value (t) is scaled by the amount of time it takes to get there.

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The position of Juliet as a function of time from point A to point B in 10 seconds can be written as ...

  J = A + (t/10)(B-A) = (0, -6) + (t/10)(10-0, 5-(-6))

  J = (t, 1.1t -6)

Juliet will reach the x-axis when her y-position is zero:

  1.1t -6 = 0

  t = 6/1.1 = 60/11

Her position at that point is J = (60/11, 0).

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Mercutio's position can be described similarly. Starting at point C(7, -16), he reaches D(60/11, 0) after 60/11+2 = 82/11 seconds.

  M = C +(11t/82)(D -C) = (7, -16) +(11t/82)(60/11 -7, 0 -(-16))

  M = (7 -17/82t, 88/41t -16)

Mercutio will reach the y-axis when his x-position is zero:

  7 -17/82t = 0

  7 = 17/82t

  82/17×7 = t = 574/17 ≈ 33.765 . . . . seconds

It takes Mercutio about 33.765 seconds to reach the y-axis.

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above

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step-by-step explanation: