Explain this bold statement: No matter what function f[x, y] you go with, if {xtrajectory[t], ytrajectory[t]} parameterizes a trajectory in the gradient field of f[x, y] , then you are guaranteed that f[xtrajectory[t], ytrajectory[t]] goes up as t goes up.

the volume is the product of the area of the base, 3x(3x+4), and the height, 3x-1

step-by-step explanation:

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;

explanation:

step-by-step explanation:

168

step-by-step explanation:

first off, we know that he drove 3.5 hours at a rate of 48 mph.

knowing that, we want to see how many miles he drove all-together.

in this case, we can just multiply 48 by 3.5.

48 * 3.5 = 168