Answer:
Intercepts:
x = 0, y = 0
x = 1.77, y = 0
x = 2.51, y = 0
Critical points:
x = 1.25, y = 4
x = 2.17
, y = -4
x = 2.8, y = 4
Inflection points:
x = 0.81, y = 2.44
x = 1.81, y = -0.54
x = 2.52, y = 0.27
Step-by-step explanation:
We can find the intercept by setting f(x) = 0
where n = 0, 1, 2,3, 4, 5,...
Since we are restricting x between 0 and 3 we can stop at n = 2
So the function f(x) intercepts at y = 0 and x:
x = 0
x = 1.77
x = 2.51
The critical points occur at the first derivative = 0
or
where n = 0, 1, 2, 3
Since we are restricting x between 0 and 3 we can stop at n = 2
So our critical points are at
x = 1.25, 
x = 2.17
, 
x = 2.8, 
For the inflection point, we can take the 2nd derivative and set it to 0
We can solve this numerically to get the inflection points are at
x = 0.81, 
x = 1.81, 
x = 2.52, 
Answer:
The percent error is -2.1352% of Jocelyn's estimate.
Answer: 165 in length 20 in width
Step-by-step explanation: :)
To answer this question, you can use a factor tree, or the table thing (I forgot what it’s called.)
You divide the number by one of its PRIME factors, until there is only one left. The numbers you divided it by are written as shown.
Hope this helps. :)
<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.
