Evaluate the surface integral

Sinead Mcgee
2021-02-21
Answered

Let $F=[{x}^{2},0,{z}^{2}]$ , and S the surface of the box $\left|x\right|\le 1,\left|y\right|\le 3,0\le z\le 2$ .

Evaluate the surface integral$\int {\int}_{S}F\cdot ndA$ by the divergence theorem.

Evaluate the surface integral

You can still ask an expert for help

tafzijdeq

Answered 2021-02-22
Author has **92** answers

Step 1

The divergence of the function F is:

Step 2

By the divergence theorem convert the surface integral into a triple integral:

Step 3

asked 2021-11-15

The electrical currents flowing in the antennas, during an MR imaging scan are given by:

$3{i}_{3}+3{i}_{1}-5{i}_{2}=7.5$

${i}_{2}-7{i}_{3}+2{i}_{1}=-17.5$

$-10{i}_{1}+4{i}_{2}+5{i}_{3}=16$

1. Write the above system of equations in the form$Ax=b$ , where A is a 3 by 3 matrix and x and b are 3 by 1 vectors.

2. Find the determinant of A.

3. Determine$i}_{1},\text{}{i}_{2$ and $i}_{3$ by using Gaussian elimination.

1. Write the above system of equations in the form

2. Find the determinant of A.

3. Determine

asked 2021-09-08

Solve for G.S. / P.S. for the following differential equations using separation of variables.

$2{\mathrm{sin}}^{2}2tdx=\mathrm{cos}x(1+\mathrm{cos}2x)dt$

asked 2021-11-16

State and prove the linearity property of the Laplace transform by using the definition of Laplace transform. Give an example by selecting different types of function, from, trigonometric, polynomial, exponential that shows the application of this property while solving the Laplace transform by using direct rules.Does such property hold for the inverse Laplace transform as well? Prove by giving a suitable example.

asked 2021-11-23

The Munchies Cereal Company makes a cereal from several ingredients. Two of the ingredients, oats and rice, provide vitamins A and B. The company wants to know how many ounces of oats and rice it should include in each box of cereal to meet the minimum requirements of 48 milligrams of vitamin A and 12 milligrams of vitamin B while minimizing cost. An ounce of oats contributes 8 milligrams of vitamin A and 1 milligram of vitamin B, whereas an ounce of rice contributes 6 milligrams of A and 2 milligrams of B. An ounce of oats costs $0.05, and an ounce of rice costs $0.03.

a. Formulate a linear programming model for this problem.

b. Solve this model by using graphical analysis.

c. What would be the effect on the optimal solution if the cost of rice increased from $0.03 per ounce to $0.06 per ounce?

a. Formulate a linear programming model for this problem.

b. Solve this model by using graphical analysis.

c. What would be the effect on the optimal solution if the cost of rice increased from $0.03 per ounce to $0.06 per ounce?

asked 2022-01-07

I have the multivariable function

$\mathrm{log}({y}^{2}+4{x}^{2}-4)$

and I have found the maximal domain to be

${x}^{2}+\frac{{y}^{2}}{4}>1$

and I have found the maximal domain to be

asked 2021-09-18

Describe the procedure for finding critical points of a function in two independent variables.

asked 2021-03-11

Use the divergence theorem to evaluate $\int {\int}_{S}F\cdot NdS$ , where $F(x,y,z)={y}^{2}zi+{y}^{3}j+xzk$ and S is the boundary of the cube defined by $-5\le x,=5,-5\le y\le 5,{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}0\le z\le 10$ .