A quantity P equals the sum of three other quantity, the first of which is a constant, the second varies directly as x and the third varies directly as x square.when x=1;P=13,when x=2,p=36 and when x=3,p=79. Find the constant.

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A quantity P equals the sum of three other quantity, the first of which is a constant, the second varies directly as x and the third varies directly as x square.when x=1;P=13,when x=2,p=36 and when x=3,p=79. Find the constant.

rishabh jain 12th Dec, 2019

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Answer (1)

Avishek Dutta 12th Dec, 2019

Let p=a+b+c
Now a is constant
b is proportional to x
let b=Kx
And c is proportional to x^2
Hence c=mx^2
13=a+k+m ..i
as p=13 when x=1
36=a+2k+4m ..ii
as p=36 when x=2
79=a+3k+9m...iii
as p=79 when x=3
2*i-ii
-10=a-2m..iv
3*i-iii
-40=2a-6m or -20=a-3m..v
3*iv-2*v
10=a
Hence constant term is 10

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