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Question 162570This question is from textbook
: im having trouble with two questios, i just dont understand them. i know i have to use the formula for distance or radius (r = xsqaured + y sqaured) but i dont know how to apply it. the questions are
A rock dropped into a pond sends out a circular ripple whose radius increases steadily at 6cm/s. A toy boat is floating on the pond 2 m east and 1 m north of the spot where the rock is dropped. How long does it take for the rippe to reach the boat
the second question is
A triangle has vertices at s (6,6), t(-6,12), and u(0,-12). SM is the median from the vertex S. Find the coordinates of the point that is two-thirds of the way frm S to M.
I dont know how to apply toe distance formuls, radius or mid point formula. I really need your help, i have a test tomorrow.
Thank you
- Neha =)
This question is from textbook
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! 2 meters east, 1 meter north.
The distance (radius) from the center of rock drop to toy boat is,
So the center of the rock drop is 2.23606 meters away from the toy boat.
The ripple is moving towards the boat at 6 cm/s.
This is now a rate x time=distance problem.
You know the rate, the speed of the ripple.
You calculated the distance.
Now calculate the time.
First, the units have to match (can't mix cm and m).
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Change the distance to cm.
2.23606 meters= 223.6cm
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It will take the ripple 37.27 seconds to reach the boat.
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M is the midpoint of the line from T to U.
The midpoint M has coordinates (-3,0).
The change in x from S to M is
The change in y from S to M is
Using only 2/3 of the change in x, you would have,
Using only 2/3 of the change in y, you would have,
My starting point is S at (6,6).
The point P is 2/3 of the way from S to M.
The coordinates of P are found by starting at S and adding the 2/3 change in x and y.
(6,6)+(-6,-4)=(0,2)
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P is located at (0,2)
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