The direction of the gradient of a scalar is the direction in which the scalar function changes most rapidly with distance moved. so â½(v) should be in the j direction. in spherical coordinates, y = r smo smo compute the gradient of r sine sino using the spherical representation for the gradient to find the expression for j in terms of the spherical coordinates and directions. use analogous methods to find representations for the other two cartesian coordinate directions. explain why your results were the directions sought without normalizing the gradient to unit magnitude.

Explain the difference between each pair of concepts. a. frequency and relative frequency b. percentage and relative frequency a. select the correct choice below. a. frequency is the total number of observations in a data set. relative frequency is the number of times a particular distinct value occurs. b. frequency is the number of times a particular distinct value occurs. relative frequency is the ratio of the frequency of a value to the total number of observations. c. frequency is the total number of observations in a data set. relative frequency is the ratio of the number of times a particular distinct value occurs to the frequency. d. frequency is the number of times a particular distinct value occurs. relative frequency is the ratio of the frequency of two different values.

An object moves from position +34m to the position -15m in 15 seconds. what is the total displacement? what is the total velocity?

Automobile fuel efficiency is often measured in miles that the car can be driven per gallon of fuel (mpg). heavier cars tend to have lower fuel efficiencies (lower mpg ratings). which variable (weight or fuel efficiency) is most naturally considered the explanatory (predictor) variable in this context?