10.15-10.16 with fractions

Consider the vector field.f(x, y, z) = xy2z2i + x2yz2j + x2y2zk(a) find the curl of the vector field.

Marysya12 [62]

First introduce the following notations:
$P=yx^2z^2\\Q=x^2yz^2\\R=x^2y^2z\\\text{Then compute the partial derivative like this:}\\R_y=2x^2yz\\Q_z=2x^2yz\\P_z=2yx^2z\\R_x=2xy^2z\\Q_x=2xyz^2\\P_y=x^2z^2\\\text{Then evaluate each of the following:}\\R_y-Q_z=2x^2yz-2x^2yz=0\\P_z-R_x=2yx^2z-2xy^2z=2xyx(x-y)\\Q_x-R_y=2xyz^2-x^2z^2=z^2x(2y-x)\\\text{Our answer will be then:}\\Curl(f)=(2xyx(x-y))j+(z^2x(2y-x))k$

7 0

3 years ago

Dylan's expenditures for each of the past six months were: March $1,248.59; April, $1,365.38; May, $1,024.30; June, $1,100.40; J

ivann1987 [24]

Answer:

The average monthly expenditure is 1,155.35 $.

Step-by-step explanation:

The average of any sequency is given by the sum of it's individual parts divided by the number of parts it has. So in this case the average of monthly expenditure will be the sum of all individual expenditures divided by the number of months. The question can be solved like this:

average = (March+ April + May + June + July+ August)/6

average = (1,249.59 + 1,365.38 + 1,024.3 + 1,100.4 + 992,4 + 1,200.02)/6

average = 1,155.35 $

3 0

3 years ago

Read 2 more answers

Suppose you can somehow choose two people at random who took the SAT in 2014. A reminder that scores were Normally distributed w

Sindrei [870]

Answer:

22.29% probability that both of them scored above a 1520

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 1497, \sigma = 322$

The first step to solve the question is find the probability that a student has of scoring above 1520, which is 1 subtracted by the pvalue of Z when X = 1520.

So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1520 - 1497}{322}$