Quick easy one to do!! 15pts
2 answers:
You might be interested in
Answer:
<em>The SUV is running at 70 km/h</em>
Step-by-step explanation:
<u>Speed As Rate Of Change </u>
The speed can be understood as the rate of change of the distance in time. When the distance increases with time, the speed is positive and vice-versa. The instantaneous rate of change of the distance allows us to find the speed as a function of time.
This is the situation. A police car is 0.6 Km above the intersection and is approaching it at 60 km/h. Since the distance is decreasing, this speed is negative. On the other side, the SUV is 0.8 km east of intersection running from the police. The distance is increasing, so the speed should be positive. The distance traveled by the police car (y) and the distance traveled by the SUV (x) form a right triangle whose hypotenuse is the distance between them (d). We have:
To find the instant speeds, we need to compute the derivative of d respect to the time (t). Since d,x, and y depend on time, we apply the chain rule as follows:
Where x' is the speed of the SUV and y' is the speed of the police car (y'=-60 km/h)
We'll compute :
We know d'=20 km/h, so we can solve for x' and find the speed of the SUV
Thus we have
Solving for x'
Since y'=-60
The SUV is running at 70 km/h
The graph is a circle, centered at the origin, with radius=4.
We know that we can write the equation of a circle with radius r and center (a,b) as :
.
Thus, substituting (a, b) with (0, 0) and r with 4, we have:
.
The solutions of this equation are all the points forming the circle shown in the picture. The solutions of this equation are still the same even if we multiply both sides of the equation by 2, because rewriting the equation as:
,
we would still have the same roots.
Thus, the equation of the circle can be written as :
.
Answer: B
We know that we can write the equation of a circle with radius r and center (a,b) as :
Thus, substituting (a, b) with (0, 0) and r with 4, we have:
The solutions of this equation are all the points forming the circle shown in the picture. The solutions of this equation are still the same even if we multiply both sides of the equation by 2, because rewriting the equation as:
we would still have the same roots.
Thus, the equation of the circle can be written as :
Answer: B