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In the figure below, BL, AM, and CK are medians of △ABC. If KC = 108 and OC = 2n + 10, then n=
The picture is attached below.
The value of n is 31.
The median is the line connecting the vertex and its midpoint on the opposite side of the triangle.
The intersection of all 3 medians of the triangle is called the centroid.
As we know centroid divides the median in the ratio of 2:1.
In the given picture,
Medians of triangle △ABC are AM, BL, and CK.
So the centroid of the triangle is O.
Given that KC= 108
As the centroid O divides the line KC in 2:1.
Let OC=2x
KO= X
As KC= KO+OC
⇒ 108= x+2x
⇒ 3x=108
⇒ x=108/3
⇒ x=36
Then OC= 2x= 2*36= 72
As given in the question OC= 2n+10
putting the value of OC in above equation
⇒ 72= 2n+10
⇒ 2n= 72-10
⇒ 2n=62
⇒ n=62/2
⇒n=31
Therefore the value of n is 31.
Learn more about the median of the triangle
here: brainly.com/question/2264495
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Answer:
Saddle point:
Local minimum:
Local maxima: ,
Step-by-step explanation:
The function is:
The partial derivatives of the function are included below:
Local minima, local maxima and saddle points are determined by equalizing both partial derivatives to zero.
It is quite evident that one point is (0,0). Another point is found by solving the following system of linear equations:
The solution of the system is (3/8, -3/8).
Let assume that y = 0, the nonlinear system is reduced to a sole expression:
Another solution is (9/8,0).
Now, let consider that x = 0, the nonlinear system is now reduced to this:
Another solution is (0, -9/8).
The next step is to determine whether point is a local maximum, a local minimum or a saddle point. The second derivative test:
The second derivatives of the function are:
Then, the expression is simplified to this and each point is tested:
S1: (0,0)
(Saddle Point)
S2: (3/8,-3/8)
(Local maximum or minimum)
S3: (9/8, 0)
(Local maximum or minimum)
S4: (0, - 9/8)
(Local maximum or minimum)
Unfortunately, the second derivative test associated with the function does offer an effective method to distinguish between local maximum and local minimums. A more direct approach is used to make a fair classification:
S2: (3/8,-3/8)
(Local minimum)
S3: (9/8, 0)
(Local maximum)
S4: (0, - 9/8)
(Local maximum)
Saddle point:
Local minimum:
Local maxima: ,