Prove that U(x,y)=e^(-x)[xsiny-ycosy] is harmonic.
If tan(A) = 1/2, find the value of tan(5A) Hint: Use De Moivre's theorem.
Find a general solution for this differential equation. Please see the attached file for the fully formatted problem. dy/dx + 2xy = xe^(-x2+2)
For this problem state the method you used and show the work required to obtain the answer. Find the general solution for this system: this is a matrix x'= 3y+z y'= x+z+2y z"= 3y+x
Find the complete solution of this equation problem y^4 - y^2 = 4x + 2xe^(-x)
A bowl is shaped like a hemisphere with radius R centimeters. An iron ball with radius R/2 centimeters is placed in the bowl and water is poured in to a depth of 2R/3 centimeters. How much water was poured in?
How do I find the surface area obtained by revolving the curve y=x-1 from x=1 to x=4 about the line x= -1?
How does the length of the curve x=t^2, y=t^3, [0,2] come out to be 3/4 + (ln2)/2?
Find the dimensions of a cylinder with a surface area of 300 cm^2 with a maximum volume.
1. 20x=y^2 2. (x-3)^2 =1/2(y+1) 3. y2+14y+4x+45=0 Find the vertex, focus, and directrix of the parabola described by the above equations.
Find the vertex, focus, and directrix of the parabola. Sketch its graph, showing the focus and the directrix.
1. 20x=y2 2. (x-3)squared =1/2(y+1) 3. y2+14y+4x+45=0 Find an equation of the parabola that satisfies the given conditions Focus F(0-4), directrix y=4 Find the vertices, the foci and the equations of the asymptotes of the hyperbola. 1.y2divided by 49 minus x2 divided by sixteen =1 2.x2-2y2=8 Find an equat
Please see the attached file for the fully formatted problems. (i) Consider the differential equation: x. = x^2 , x(0) given x(0)>0 Find the solution of x(t) of this equation in terms of x(0) and show that there is a T, which depends on x(0), such that lim x(t) = infinity t --> T- (ii) Find the solution of the
A crude-oil refinery has an underground storage tank which has a fixed volume of 'V' liters. Due to pollutants, it gets contaminated with 'P(t)' kilograms of chemical waste at time 't' which is evenly distributed throughout the tank. Oil containing a variety of pollutants with concentration of 'k' kilograms per liter enters
Find arc length of the curve defined by the following parametric system: x=cos^-1(t) (inverse cosine) y= ln t where t is less than/equal to 1, greater than/equal to (1/sqrt 2)
Find y" for x^2/a^2 - y^2/b^2 = 1
I am trying to find the interval of convergence for the attached power series (attached as a gif). I am also supposed to check the endpoints for convergence. I'm not that good with power series and the format of this power series is really throwing me off. So I am looking for the steps to find the interval of convergence (also c
Find an equation of the tangent line to the curve, Y = x^3 - 3x^2 + 5x that has the least slope. Make sure to show all of the required steps.
A billiard ball is hit and travels in a line. If s centimeters is the distance of the ball from its initial position at t seconds, then s=100t2 + 100t. If the ball hits a cushion that is 39cm from its initial position, at what velocity does it hit the cushion?
Create a proof to show that the following is true. a x (b+c) = a x b + a x c
A special window has the shape of a rectangle surrmounted by an equilateral triangle. If the perimeter is 16 feet, what dimensions will admit the most light? (hint: Area of equilateral triangle = the square root of 3/4 times x squared.)
I am stuck on how to solve the sum of the series that I have attached in a word document.
I used the product to sum identities rule since the integral involved cosines of different angles. I have attached a word document with the integral to solve and my work. I want to know if my answer is correct. If my answer is not correct, I want to know the correct answer and the steps to get it. Thanks.
Write an equation and sketch a graph of the line through the points (-4,-3) and 3,12)
We are supposed to use the definition of the Area of a Surface of Revolution to solve this problem. I have attached this formula and the answers I received in a word document. The problem: Given: y = -x^2 + 4x defined on the closed domain [0,4] Revolve the graph about the x-axis. Find the area of the surface obtained
I need to see how to find the centroid coordinates by using integrals and moments. I have attached a word document with the formulas we are supposed to use to find the centroid. Now here is the problem: Given: y = 9 - x^2, y = 2 Find the coordinates of the centroid of the above plane region. Please refer to the atta
Given: y = -x^2 + 4x defined on the closed domain [0,4] a) sketch the graph b) Revolve the graph about the x-axis. Find the area of the surface obtained.
Given: f(x)=2x, g(x)=10 a)Sketch the plane region bounded by the functions graphs and the y-axis b)Use the shell method to find the volume of the solid formed by revolving the above plane region about the y-axis. NOTE: the graph I did is attached. The answer I got was 523.599. I'm trying to check to see if I did the gr
Given: f(x)=2x, g(x)=x, x=5 a)Sketch the plane region bounded by the functions graphs b)Use the washer method to find the volume of the solid formed by revolving the above plane region about the x-axis.
Solve each of the following differential equations: ***For each problem,state the method you used and show the work required to obtain the answer.*** 1) (y-(cos^2)x)dx + cosxdy=0 2) ye^x dx= (4+e^2x)dy
The function f(x)=2x^3 - 33x^2 + 108x - 6 has two critical numbers. The smaller one equals ______ and the larger one equals______.