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Answer:
The x coordinate is 0.047m while y coordinate is 0.081 m
Step-by-step explanation:
The coordinates of the center of the mass of the system are given as follows
So from the data
m1=0.310, x1=0.20,y1=0.320
m2=0.410,x2=0.110,y2=-0.380
m3=0.210,x3=-0.300,y3=0.630
Now by substitution of the values in the above equation
So the x coordinate is 0.047m while y coordinate is 0.081 m
First, we have
(1 + 2/x²) (2x - 3/x)⁵ = (2x - 3/x)⁵ + 2/x² (2x - 3/x)⁵
In the expansion of (2x - 3/x)⁵, there is no x² term. Each term takes the form
where c is a binomial coefficient, and i is taken from the range {0, 1, 2, 3, 4, 5}. Looking at just the power of x in the product, we have
and 5 - 2i = 1 only if i = 2. By the binomial theorem, this term is given by
In the other expansion, we have an additional factor of 1/x², so that any given them in the expansion contains a power of x of the form
and 3 - 2i = 1 only if x = 1. This term in the expansion is
Then the coefficient of the x term in the whole expansion is 720 - 480 = 240.