Find the derivative of y with respect to x.
3y^2–6=x

write your answer as a rational expression in one or both variables (x and y).

y′=

Step-by-step explanation:

Here we have an implicit function, and so we must use implicit differentiation to find dy/dx.

(d/dx)(3y² - 6 = x) results in 6y(dy/dx) - 0 = (dx/dx), or 6y(dy/dx) = 1.

Then the desired derivative is

                   1

(dy/dx) =

                  6y

a rotation about point l

step-by-step explanation:

quizlet

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.