What is the means-to-MAD ratio of the two data sets, expressed as a decimal to the nearest tenth?

1 answer:

3 0

To find the mean of a set, add up all of the data points and divide by the number of data points.
For the first set:
(14+18+21+15+17) ÷ 5 = 85 ÷ 5 = 17
For the second set:
(15+17+22+20+16) ÷ 5 = 90 ÷ 5 = 18

To find the MAD (mean absolute deviation) of a set, find the mean of the distances of each data point from the mean.
For the first set:
(3+1+4+2+0) ÷ 5 = 10 ÷ 5 = 2
For the second set:
(3+1+4+2+2) ÷ 5 = 12 ÷ 5 = 2.4

To find the means-to-MAD ratio of a set, divide its mean by its MAD.
For the first set:
17 ÷ 2 = 8.5
For the second set:
18 ÷ 2.4 = 7.5

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Use logarithmic differentiation to find dy/dx if y=(cosx)sinx. Write the derivative in terms of x only. Show all your work.

gladu [14]

Step-by-step explanation:

y = (cos x)^(sin x)

Take log both sides.

ln y = ln ((cos x)^(sin x))

ln y = (sin x) ln (cos x)

Take derivative.

1/y dy/dx = (sin x) (1/cos x) (-sin x) + (cos x) ln (cos x)

dy/dx = y [ (cos x) ln (cos x) − sin x tan x ]

dy/dx = (cos x)^(sin x) [ (cos x) ln (cos x) − sin x tan x ]