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
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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
Hey You!
The images are blurry and I cannot make out most of the questions. I'll solve as many as I can see!
27. ANSWER:
Students A and D have a combined score of 0 because 4 + -4 = 0
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28. SOLUTION/ANSWER:
STEP 1: 12.40 - 0.72 = 11.68
STEP 2: 11.68/2 = 5.84
Answer: Each souvenir cost $5.84.
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29. SOLUTION/ANSWER:
(-68) - 214 = -282
Answer: The lowest elevation in California is -282 feet.
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33. SOLUTION/ANSWER:
60/3 = 20
Answer: The diver's change in depth was -20 per min.
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34. SOLUTION/ANSWER:
-43 - (-34) = -9. The difference between the two is -9.
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35. SOLUTION/ANSWER:
-64.4 + (3.22) = -67.62
Answer: Equals -67.62
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37. SOLUTION/ANSWER:
3.375 = 3 3/8 as a mixed number and 27/8 as an improper fraction.
Answer: 3 3/8 (or 27/8).
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38. SOLUTION/ANSWER:
3 ÷ 5 = 0.6
5 + 0.6 = 5.6
Answer: 5 3/5 = 5.6
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39. SOLUTION/ANSWER:
1.5 + 2.8 = 4.3
Haley jogged 4.3 km that day.
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I cannot see the other questions. If you can perhaps message them to me I can try to help you! :)
Answer:
just search up Mathaway in your browser you will get your answer and a step by step explanation!
Step-by-step explanation:
Answer:
x₁ = 6 and x₂ = 8
Step-by-step explanation:
See the picture below