vickye146
03.02.2020 •
Mathematics
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?
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Ответ:
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.
__
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).
__
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.
Ответ:
ok funny but do you play madden20
Step-by-step explanation: