 # Stokes theorem questions and answers

Recent questions in Green's, Stokes', and the divergence theorem
2022-03-24

2022-02-11

### Use the Divergence Theorem to calculate the surface integral F · dS, that is, calculate the flux of F across S.  $F\left(x,y,z\right)={x}^{3}+cosyi+{y}^{3}sinxzj+{z}^{3}+2ek$ S is the surface of the solid bounded by the cylinder ${y}^{2}+{z}^{2}=4$ and the planes $x=0$ and $x=4$. reproacht3 2022-01-19 Answered

### Randomly drawing three green skittles in a row from a bag that contains eight green skittles out of 25 skittles total. deiteresfp 2022-01-18 Answered

### Find the conditional probability of the given event when two fair dice (one red and one green) are rolled. The red one is 6, given that the green one is 6. Miguel Reynolds 2022-01-18 Answered

### The ratio of the number of blue sticks to the number of green sticks in a box was 4:1. When David took out some blue and sticks and replaced them with an equal number of green sticks, the ratio of the number of blue sticks to the number of green sticks became 3:1. If there were 185 green sticks in the box now, (a) find the total number of blue and green sticks in the box, (b) find the number of green sticks in the box at first. sunshine022uv 2022-01-18 Answered

### There are 16 shirts in your closet, 6 blue and 10 green. You randomly select one to wear on Monday, do not return it to the closet, then select one to wear on Tuesday. What is the probability of wearing a blue shirt on Monday and a green shirt on Tuesday? b2sonicxh 2022-01-17 Answered

### As Mark Ellon is getting ready for a meeting, the room goes dark. He fishes for a green shirt in his drawer. He wears only blue, green and white colors. His drawers have identical shirts in these colors: 28 blue, 25 green, and 13 white shirts. How many shirts did he throw on the floor to be a cent percent sure that he has a taken out a green shirt? William Boggs 2022-01-17 Answered

### A circular spinner is divided into 12 sectors of equal area: 5 red sectors, 4 blue, 2 yellow, and 1 green. In Problems 7–14, consider the experiment of spinning the spinner once. Find the probability that the spinner lands on: yellow or green? eliaskidszs 2022-01-16 Answered

### Brad and Lena are recording their classmates' eye color for a statistics assignment. In Brad's class, 3 out of the 25 students have green eyes. In Lena's class, 2 out of the 20 students have green eyes. Which class has the greater ratio of green-eyed students to total students? David Lewis 2021-12-17 Answered

### A camera shop stocks eight different types of batteries, one of which is type A7b.Assume there are at least 30 batteries. of each type.a. How many ways can a total inventory of 30 batteries be distributed among the eight different types? b. How many way can a total inventory of 30 batteries be distributed among the eight different types of the inventory must include at least four A76 batteries?c. How many ways can a total inventory of 30 batteries be distributed among the eight different types of the inventory includes at most three A7b batteries Zoe Oneal 2021-03-12 Answered

### Use Greens alesterp 2021-03-11 Answered

### Use the divergence theorem to evaluate $\int {\int }_{S}F\cdot NdS$, where $F\left(x,y,z\right)={y}^{2}zi+{y}^{3}j+xzk$ and S is the boundary of the cube defined by $-5\le x,=5,-5\le y\le 5,\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}0\le z\le 10$. iohanetc 2021-03-09 Answered

### Use Stokes' Theorem to evaluate $\int {\int }_{S}CURLf\cdot dS$.$F\left(x,y,z\right)={x}^{2}{y}^{3}zi+\mathrm{sin}\left(xyz\right)j+xyzk$,S is the part of the cone ${y}^{2}={x}^{2}+{z}^{2}$ that lies between the planes y = 0 and y = 2, oriented in the direction of the positive y-axis. CMIIh 2021-03-08 Answered

### z = x Let be the curve of intersection of the cylinder ${x}^{2}+{y}^{2}=1$ and the plane , oriented positively when viewed from above . Let S be the inside of this curve , oriented with upward -pointing normal . Use Stokes ' Theorem to evaluate $\int ScurlF\cdot dS\phantom{\rule{1em}{0ex}}\text{if}\phantom{\rule{1em}{0ex}}F=yi+zj+2xk$. ka1leE 2021-03-05 Answered

### Apply Green’s theorem to find the outward flux for the field $F\left(x,y\right)={\mathrm{tan}}^{-1}\left(\frac{y}{x}\right)i+\mathrm{ln}\left({x}^{2}+{y}^{2}\right)j$ Yasmin 2021-03-04 Answered

### Use Green's Theorem in the form of this equation to prove Green's first identity, where D and C satisfy the hypothesis of Green's Theorem and the appropriate partial derivatives of f and g exist and are continuous. (The quantity grad $g×n=Dng$ occurs in the line integral. This is the directional derivative in the direction of the normal vector n and is called the normal derivative of g.) ${\oint }_{c}F\cdot nds=\int {\int }_{D}÷F\left(x,y\right)dA$ fortdefruitI 2021-03-01 Answered

### Use Green's Theorem to evaluate ${\int }_{C}\stackrel{\to }{F}\cdot d\stackrel{\to }{r}$ where $\stackrel{\to }{F}\left(x,y\right)=x{y}^{2}i+\left(1-x{y}^{3}\right)j$ and C is the parallelogram with vertices (-1,2), (-1,-1),(1,1)and(1,4). The orientation of C is counterclockwise. vazelinahS 2021-02-25 Answered

### Let $F\left(x,y\right)=⟨4\mathrm{cos}\left(y\right),2\mathrm{sin}\left(y\right)⟩$. Compute the flux $\oint F\cdot nds$ of F across the boundary of the rectangle $0\le x\le 5,0\le y\le \frac{\pi }{2}$ using the vector form of Greens sagnuhh 2021-02-25 Answered

### Use Stokes' Theorem to evaluate ${\int }_{C}F\cdot dr$ where C is oriented counterclockwise as viewed from above.$F\left(x,y,z\right)=\left(x+{y}^{2}\right)i+\left(y+{z}^{2}\right)j+\left(z+{x}^{2}\right)k$,C is the triangle with vertices (3,0,0),(0,3,0), and (0,0,3). Cabiolab 2021-02-25 Answered

### Evaluate ${\int }_{C}{x}^{2}{y}^{2}dx+4x{y}^{3}dy$ where C is the triangle with vertices(0,0),(1,3), and (0,3). (a)Use the Greens

If you have studied calculus and analysis extensively, the chances are high that you have discovered problems on green's theorem that leaves more questions than answers for an average person. Keeping this fact in mind, we have provided Stokes theorem example that will help you find the most efficient solutions as you look through the list of stokes theorem questions based on equations and mathematical analysis. At the same time, you can compare various applications of Stoke's theorem problem like in control of the magnetic fields or the water flow.