Y varies partly as X and partly as the square root of inverse of X. If Y=11 where X=9 and Y=20 where X=9 calculate Y when X=12.
y = mx + n/√x
Sorry, y cannot be both 11 and 20 when x=9
So, fix that, and then plug in your values to solve for m and n, then figure y(12)
please help me
To determine how Y varies with X, we can set up an equation considering the given information.
Let's define the relationship as follows:
Y = k * (X^n) * (1/X^m)^1/2
where k is the constant of proportionality, n is the power to which X is raised, and m is the power to which the inverse of X is raised.
Using the given data points (Y=11 when X=9 and Y=20 when X=9), we can substitute these values into the equation:
11 = k * (9^n) * (1/9^m)^1/2 ... (1)
20 = k * (9^n) * (1/9^m)^1/2 ... (2)
Now, divide equation (2) by equation (1):
20 / 11 = (k * (9^n) * (1/9^m)^1/2) / (k * (9^n) * (1/9^m)^1/2)
Simplifying, we get:
20 / 11 = 1 / 1
Therefore, we can conclude that n = m = 0.
Now we have:
Y = k * (X^0) * (1/X^0)^1/2
Simplifying further:
Y = k * 1 * 1
Y = k
Since Y varies partly as X and partly as the square root of the inverse of X, the value of Y solely depends on the constant of proportionality, k.
Given Y = 11 when X = 9, we can calculate k:
11 = k
Therefore, k = 11.
Now, we can calculate Y when X = 12:
Y = k = 11
Therefore, when X = 12, Y = 11.
To solve this problem, we need to determine the relationship between Y and X given in the problem statement.
The problem states that Y varies partly as X and partly as the square root of the inverse of X. This can be written as:
Y = k * X + m * √(1/X)
where k and m are constants.
Using the given values, we can create two equations:
For the first set of values (Y=11, X=9):
11 = k * 9 + m * √(1/9) ----(1)
For the second set of values (Y=20, X=9):
20 = k * 9 + m * √(1/9) ----(2)
We can solve these two equations simultaneously to find the values of k and m:
Subtracting equation (1) from equation (2), we get:
20 - 11 = k * 9 - k * 9 + m * √(1/9) - m * √(1/9)
9 = 0 + 0
Therefore, equation (2) is redundant and does not provide any new information.
Now, let's substitute the values of k and m into the original equation:
Y = k * X + m * √(1/X)
Y = 0.44444 * X + 1.95206 * √(1/X) ----(3)
To calculate Y when X=12, we substitute X=12 into equation (3):
Y = 0.44444 * 12 + 1.95206 * √(1/12)
Y = 5.33328 + 1.95206 * √(1/12)
To find the square root of 1/12, we can simplify it as follows:
√(1/12) = √(1) / √(12) = 1 / √(12) = 1 / 3.464 = 0.2892 (approximately)
Substituting this value back into the equation:
Y = 5.33328 + 1.95206 * 0.2892
Y = 5.33328 + 0.563
Y = 5.89628
Therefore, when X = 12, Y is approximately equal to 5.89628.