Peter uses the equation y = StartFraction 13 over 4 EndFraction x to model the number of miles that he has walked in x hours. Wh
2 answers:
Answer:
C:Peter walks at a rate of 13/4 miles per hour.
Step-by-step explanation:
The equation used to model the number miles walked by Peter after x hours is
(1)
where
x is the number of hours
y is the number of miles walked
For an object moving in uniform motion (=at constant velocity), the distance covered in a time t can be written as
(2)
where
d is the distance covered
v is the velocity
t is the time
By comparing eq(1) and eq(2), we notice that the two are the same, if we put
which means that Peter's velocity is 13/4 miles per hour. Therefore, the correct option is
C:Peter walks at a rate of 13/4 miles per hour.
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<h3>Refer to the diagram below</h3>
- Draw one smaller circle inside another larger circle. Make sure the circle's edges do not touch in any way. Based on this diagram, you can see that any tangent of the smaller circle cannot possibly intersect the larger circle at exactly one location (hence that inner circle tangent cannot be a tangent to the larger circle). So that's why there are no common tangents in this situation.
- Start with the drawing made in problem 1. Move the smaller circle so that it's now touching the larger circle at exactly one point. Make sure the smaller circle is completely inside the larger one. They both share a common point of tangency and therefore share a common single tangent line.
- Start with the drawing made for problem 2. Move the smaller circle so that it's partially outside the larger circle. This will allow for two different common tangents to form.
- Start with the drawing made for problem 3. Move the smaller circle so that it's completely outside the larger circle, but have the circles touch at exactly one point. This will allow for an internal common tangent plus two extra external common tangents.
- Pull the two circles completely apart. Make sure they don't touch at all. This will allow us to have four different common tangents. Two of those tangents are internal, while the others are external. An internal tangent cuts through the line that directly connects the centers of the circles.
Refer to the diagram below for examples of what I mean.