4. A sum of money is divided among Khairul, Michael and Ethan in the ratio 6:4:5. After Khairul
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Answer:
As per the given statement:
The region bounded by the given curves about the y-axis, , y=0, x = 0 and x = 1
Using cylindrical shell method:
The volume of solid(V) is obtained by rotating about y-axis and the region under the curve y = f(x) from a to b is;
where
where x is the radius of the cylinder
f(x) is the height of the cylinder.
From the given figure:
radius = x
height(h) =f(x) =y=
a = 0 and b = 1
So, the volume V generated by rotating the given region:
therefore, the volume of V generated by rotating the given region is
The summation indicates the sum from n = 1 to n = 3 of the expression 2(n+5).
2 (n+5) = 2n + 10
2n + 10 denotes an Arithmetic Series, with a common difference of two and first term as 12.
For n =1, it equals 12
For n = 2, it equals 14
For n = 3, it equals 16
So the sum from n=1 to n=3 will be 12 + 14 + 16 = 42
Sum of an Arithmetic Series can also be written as:
Using the value of a₁ and d, we can simplify the expression as:
This expression is equivalent to the given expression and will yield the same result.
For n=3, we get the sum as:
S₃ = 3(11+3) = 42
2 (n+5) = 2n + 10
2n + 10 denotes an Arithmetic Series, with a common difference of two and first term as 12.
For n =1, it equals 12
For n = 2, it equals 14
For n = 3, it equals 16
So the sum from n=1 to n=3 will be 12 + 14 + 16 = 42
Sum of an Arithmetic Series can also be written as:
Using the value of a₁ and d, we can simplify the expression as:
This expression is equivalent to the given expression and will yield the same result.
For n=3, we get the sum as:
S₃ = 3(11+3) = 42