Question
Y is inversely propotional to the sqaure of x. Given that y = 10 when x = 3 find y when x = ½
Answers
GPT 3.5
To solve this problem, we need to find the mathematical relationship between y and x. According to the statement, y is inversely proportional to the square of x.
Mathematically, we can express this relationship as:
y = k/x^2
where k is a constant of proportionality.
We are given that when x = 3, y = 10. Using this information, we can substitute these values into the equation to find the value of k:
10 = k/3^2
10 = k/9
Multiplying both sides by 9, we get:
k = 90
Now that we have the value of k, we can use it to find y when x = 1/2:
y = k/(1/2)^2
y = k/(1/4)
y = 90/1/4
y = 90 * 4/1
y = 360
Therefore, when x = 1/2, y = 360.
Mathematically, we can express this relationship as:
y = k/x^2
where k is a constant of proportionality.
We are given that when x = 3, y = 10. Using this information, we can substitute these values into the equation to find the value of k:
10 = k/3^2
10 = k/9
Multiplying both sides by 9, we get:
k = 90
Now that we have the value of k, we can use it to find y when x = 1/2:
y = k/(1/2)^2
y = k/(1/4)
y = 90/1/4
y = 90 * 4/1
y = 360
Therefore, when x = 1/2, y = 360.