For the equation $Y = \sqrt { X \cdot Z }$ the point $X = 20$ , $z = 5$ .
A) $Y = 10$ yields a value of .
B)lies below the contour line that includes the point $X = 15$ , $z = 7$ .
C)lies on the same contour line as the point $X = 12$ , .
D)Both a and b

Question

Quizplus · Accepted Answer

For choice A, plugging in the values of X and Z, we get Y = 10, which is a valid point on the function.

For choice B, we need to find the contour line that includes the point (15,7) and see if (20,5) lies below it. The contour line for any function is obtained by fixing a certain value of Y and plotting the resulting curve in the XZ-plane. Taking Y = 10 (as found in choice A), the contour line equation becomes:

10 = sqrt(X * Z)
100 = X * Z
Z = 100/X

Plotting this curve in the XZ-plane, we get a hyperbola that passes through (15,7). Evaluating this curve at X = 20, we get Z = 5, which is below the point (20,5). Thus, choice B is also correct.

For choice C, we need to find the contour line that includes the point (12,25) and see if (20,5) lies on it. Taking Y = sqrt(12 * 25) = 30, the contour line equation becomes:

30 = sqrt(X * Z)
900 = X * Z
Z = 900/X

Evaluating this equation at X = 20 gives Z = 45, which is not equal to 5. Thus, choice C is incorrect.

Therefore, the answer is D) both A and B are correct.

For the Equation Y=X⋅ZY = \sqrt { X \cdot Z }Y=X⋅Z​

For the Equation $Y = \sqrt { X \cdot Z }$