An object with weight W is dragged along a horizontal plane by a force acting along a rope attached to the object. If the rope makes an angle θ with the plane, then the magnitude of the force is

F= μW
μ sin θ + cos θ

where μ is a constant called the coefficient of friction.

(a) Find the rate of change of F with respect to θ.
(b) When is this rate of change equal to 0?

Analyze the data sets below. data set a 25,25,25,26,26,26,27,28,28,29,30,31,31,32,33,33,34,35,35,35 data set b 25,25,25,26,26,26,26,27,27,27,27,28,28,29,29,30,31,31,32,34 which of the following statement are true? select all that apply. a. data set a is relatively symmetric and data set b is skewed left. b.the means of the data sets are within 3 units from eachother. c.the data sets have the same standard deviation. d.the mean of data set a is 27.95 and the mean of data set b is 30. e. the data set b has a higher standard deviation than data set a. f. the mean and median of data set a are close in value.

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Jane’s favorite fruit punch consists of pear, pineapple, and plum juices in the ratio 5: 2: 3. how many cups of pear juice should she use to make 20 cups of punch?