Find the function whose exact differential is d f = cos (x) sin (y) sin (z)dx +sin
Question:
d f = cos (x) sin (y) sin (z)dx
+sin (x) cos (y) sin (z)dy
+sin (x) sin (y) cos (z)dz
and whose value at (0,0,0) is 0. Find the area of the circle of radius a given by Ï = a by doing the double integral
2π οα 1 dφ dρ.
Step by Step Answer:
Since the differential is exact f x 1 y 1 z 1 f000 ...View the full answer
Related Video
The area of a circle is given by the formula: A = ?r^2 Where A is the area, ? is a mathematical constant (approximately 3.14), and r is the radius of the circle. The radius is the distance from the center of the circle to the edge. So for example, if the radius of a circle is 5 units, the area would be: A = ?(5^2) = ?(25) = 78.5 square units Here three friends went out to a restaurant and decided to have pizza for lunch. While they were waiting for their order, one of them stepped out to take a call but promised to return in two minutes. The waiter came and presented them with the menu, and they decided to order two 10-inch pepperoni pizzas. The waiter took their order and left. Just then, the third friend returned and asked what they had ordered. They explained that they had ordered two small pepperoni pizzas as they were only three of them and it would be enough for them. However, the third friend suggested that for the same price, they could get a large pizza that would be much bigger than the two small ones. He asked the waiter for a pen and paper and proceeded to calculate the area of the two small pizzas and compared it to the area of one large pizza. The friends were amazed at how the circle measurements worked and decided to change their order from two small pizzas to one large pizza.
Students also viewed these Mathematics questions
-
Find the function whose differential is df = cos (x) cos (y)dx sin (x) sin (y)dy and whose value at x = 0, y = 0 is 0.
-
In problem find a homogeneous linear differential equation with constant coefficients whose general solution is given. y = c 1 cos x + c 2 sin x + c 3 cos 2x + c 4 sin 2x
-
Determine whether the given differential equation is exact. If it is exact, solve it. (sin y - y sin x) dx + (cos x - x cos y - y) dy = 0
-
Consider the case of the Cisco Fatty. Who was wrong? Advise how a firm might best handle this kind of online commentary.
-
Portland Optics, Inc., specializes in manufacturing lenses for large telescope cameras used in space exploration. Since the specifications for the lenses are determined by the customer and vary...
-
The financial statements of TSMC are presented in Appendix A at the end of this textbook. The complete annual report, including the notes to the financial statements, is available at the companys...
-
Describe the objectives of tort law.
-
Giant acquired all of Small's common stock on January 1, 2011. Over the next few years, Giant applied the equity method to the recording of this investment. At the date of the original acquisition,...
-
A company expects a 2 0 % return on equity invested entirely in new projects. The company's management plans to retain 3 0 % of its net profits. Earnings per share for the coming year are 3 and the...
-
Jackie Wengler, owner of Wengler Home Decorating Service, has requested that you prepare from the following balances (a) An income statement for June 201X, (b) A statement of owner?s equity for June,...
-
A two-phase system contains both liquid and gaseouswater, so its equilibrium pressure is determined by the temperature. Calculate the cyclic integral of dw rev for the following process: The volume...
-
The thermodynamic energy of a monatomic ideal gas is temperature-independent, so that dU = 0 in an isothermal process (one in which the temperature does not change). Evaluate w rev and q rev for the...
-
Houston Corporation has two products, Astros and Texans, with the following volume information: Volume Product Astros...............20,000 gal Product Texans...............10,000 gal...
-
Discuss the major threats to validity associated with this design and type of research (experimental). How will these threats be addressed, based on the discussion of the control techniques in the...
-
Develop the appropriate primary research question to be associated with this design. Develop a hypothetical research scenario that would necessitate the use of an A-B-A Design. The research will be...
-
Identify the assignment technique to be used. Develop a hypothetical research scenario that would necessitate the use of a 2 x 2 Factorial Design. The research will be considered non experimental.
-
Discuss the sampling strategy and technique used to access the appropriate case. Develop a hypothetical research scenario that would necessitate the use of an A-B-A Design. The research will be...
-
Discuss how the statistical procedures control technique will be used as a means to assign participants to each group. Discuss the rationale for this technique. Develop a hypothetical research...
-
Wilm Schmidt, the owner of Wilms Window Washing Services, had difficulty getting the debits to equal credits on the January 31, 2017, trial balance. The following errors were discovered: a. Schmidt...
-
Suppose a population of bacteria doubles every hour, but that 1.0 x 106 individuals are removed before reproduction to be converted into valuable biological by-products. Suppose the population begins...
-
Suppose there is no real change in the patients underlying mean blood pressure regardless of whether she is on medication. What is the probability that she will be put back on antihypertensive...
-
What is the probability that the sample mean will be within 1 unit of the population mean? Suppose we have a population with a normal distribution with mean = 50 and standard deviation = 10. We draw...
-
Suppose we want to choose a large enough sample so that the sample mean is within 1 unit of the population mean 99% of the time. What is the minimum sample size to achieve this goal? Suppose we have...
-
5. Solve the linear inequality. Graph the solution set on a number line. 7(x+4)-13 < 12 + 13(3 + x)
-
Can you delineate the role of central banks as key stakeholders in the financial ecosystem, elucidating their functions as monetary authorities responsible for price stability, lender of last resort...
-
write a presentation about a caf. -agenda -survey -presentation -staff, customer feedback add pictures
Study smarter with the SolutionInn App