9514 1404 393
Answer:
(c) dZ/dt = 11/√544, so moving away at about 0.47 m/s
Step-by-step explanation:
The (x, y) coordinates of the car are related by the fact that they are on a circle centered at (12, 7) with a radius of 5. Then their rates of change are related by the derivative of the circle equation with respect to time.
(x -12)^2 + (y -7)^2 = 25
2(x -12)x' +2(y -7)y' = 0
y' = -(x -12)/(y -7)x'
At the time and point of interest, we have ...
y' = -(15 -12)/(11 -7)(1) = -3/4
__
The distance (z) to the observer is given by the Pythagorean theorem:
z^2 = (x -0)^2 +(y -2)^2
and its rate of change with time is ...
2z·z' = 2(x-0)x' +2(y -2)y'
The distance d at the point of interest is ...
z = √((15 -0)^2 +(11 -2)^2) = √(225 +81) = √306 = 3√34
So, the rate of change of distance to the observer at the time and point of interest is ...
z' = (x(x') +(y -2)y')/z
z' = ((15)(1) +(11-2)(-3/4))/(3√34) = (33/4)/(3√34)
z' = 11/√544 ≈ 0.47 . . . m/s
Answer:
- 7
- 7 i
- 4
- 4 i
Note:
I'm sorry! I only figured out the first 4. And I'm sorry if those are incorrect as well!!!
But I do hope it helps a little!
Hi there!
So first off, here are little definitions you need to know in order to be able to answer your question :
<u>Constant</u> means that the rates of change are the same.
<u>Variable</u> means that the rates of change are different.
But from what I can see, you don't even need those definitions because you got both answers right!
Continue your great work! If there's anything just let me know! :)
Answer:
1 and 2 are the answers i think
Step-by-step explanation:
Answer:
See description below.
Step-by-step explanation:
A distance -time graph of Maria's journey would look like a very steep line with slope 100 meters/1 minute until minute 4. At minute 4, Maria stopped to talk so it would like a horizontal flat line at that same distance for 3 minutes. This means at minute 7, Maria began walking again. From minute 7 on would be a positive line heading up with a slope of 75 meters/ 1 minute.
