Which term describes the point where the three angle bisectors of a triangle intersect?
2 answers:
Answer:
Hence, The term which describes the point where the three angle bisectors of a triangle intersect is incenter.
Step-by-step explanation:
For better understanding of the solution see the attached figure of the problem :
If the angles bisectors of all the three angles of triangle meet at a point inside a circle, then that point is equidistant from all the three vertices of the triangle.
Also, The incenter of a triangle is the center of the incircle or the largest circle that can be inscribed in the triangle.
The point at which all the three angle bisectors meet is also the center of the incircle.
Hence, The term which describes the point where the three angle bisectors of a triangle intersect is incenter.
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The time for the village to dig the new well is about 7 1/2 years. At this time the population doubles from its current size.
<h3>How to graph a function?</h3>For a function f(x) = y, the steps to draw a graph for the given function are as follows:
- Consider certain values of x
- Substitute x values in the given function to obtain y values
- Plot the x and y values in the graph
- Join the points to know the variation.
It is given that,
f(x) = 200 ×
Village's population growing rate = 9.8%
Creating a table for x and f(x) values:
x: 0 2 4 6 8 10
f(x = 0) = f(0) = 200 × = 200
f(x = 2) = f(2) = 200 × = 241
f(x = 4) = f(4) = 200 × = 291
f(x = 6) = f(6) = 200 × = 350
f(x = 8) = f(8) = 200 × = 423
f(x = 10) = f(10) = 200 × = 509
So,
(x, f(x)): (0, 200) (2, 241) (4, 291) (6, 350) (8, 423) (10, 509)
Plotting these points in the graph and joining the points, the graph is shown below.
Finding the time for the village to dig a new well:
It is given that the population doubled from its current size, the village will need to dig new water well.
The current size of the village = 200
If it doubles for a certain time 't' = 400
So,
400 = 200 ×
⇒ = 2
⇒ log = log 2
⇒ t log(1.098) = 0.301
⇒ t × 0.04 = 0.301
∴ t = 7.525 years
Therefore, the village's population becomes double at the time 7 and half years from now. So, after 7 1/2 years, the village needs to dig a new well.
Learn more about the function and its graph here:
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