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
When u keep dividing and dont get it go up by each number and keep divind by every number until u get it which would be
Answer:
(4, 1)
Step-by-step explanation:
Since the first reflection is over the vertical line x=-3, the y-coordinate remains the same. The x-coordinate of A' will make the point (-3, 4) on the line of reflection be the midpoint between A and A':
(-3, 4) = (A +A')/2
2(-3, 4) -A = A' = (-6-(-7), 8 -4) = (1, 4)
The reflection over the line y=x simply interchanges the two coordinate values:
A'' = (4, 1)
Answer:
A. 2,310 sq ft
Step-by-step explanation:
<u>R</u><u>e</u><u>c</u><u>t</u><u>e</u><u>n</u><u>g</u><u>l</u><u>e</u><u> </u><u>b</u><u>e</u><u>l</u><u>o</u><u>w</u><u>:</u>
- A = l × b
- A = 74 × 15
- A = 1,110ft
<u>Rectangle Above</u><u>:</u>
- A = l × b
- A = 50 × 24
- A = 1,200ft
<u>A</u><u>r</u><u>e</u><u>a</u><u> </u><u>o</u><u>f</u><u> </u><u>t</u><u>h</u><u>e</u><u> </u><u>P</u><u>l</u><u>a</u><u>y</u><u>g</u><u>r</u><u>o</u><u>u</u><u>n</u><u>d</u><u>:</u>
- 1,110ft + 1,200ft
- 1,310 sq ft (A)
The blue one with four corners!!!