Pinocchio has a problem with lying. Everytime he lies, his nose grows. The size of his nose grows inversely to the square of the lying index(less truth is a statement). If his nose grows to 3 inches with a lying index of 2, what will be the lying index if his nose grows to 6 inches? (answer to one decimal place)
3=k/2^2
6=k/I^2
divide second equation by first.
2=4/I^2
I=sqrt 2
To find the lying index when Pinocchio's nose grows to 6 inches, we can use the relationship between the size of his nose and the lying index.
Let's denote the lying index as "x".
From the problem's information, we know that the size of Pinocchio's nose grows inversely to the square of the lying index. This inverse relationship can be expressed mathematically as:
size of nose = k/x^2,
where "k" is a constant.
Given that Pinocchio's nose grows to 3 inches with a lying index of 2, we can substitute these values into the relationship:
3 = k/2^2,
3 = k/4.
To find the value of "k", we multiply both sides of the equation by 4:
12 = k.
Now that we have the value of "k", we can use it in the relationship to find the lying index when Pinocchio's nose grows to 6 inches:
6 = 12/x^2.
To solve for "x", we divide both sides of the equation by 12:
6/12 = 12/x^2,
1/2 = 1/x^2.
To isolate "x^2", we reciprocally divide both sides of the equation:
2 = x^2.
To solve for "x", we take the square root of both sides:
√2 = x.
The approximate value of √2 is 1.4.
Therefore, when Pinocchio's nose grows to 6 inches, the lying index will be approximately 1.4.