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Sound Waves

Consider the wave equation when the solution s admits spherical symmetry, ie, s(t,x,y,z)=v(t,r), where ... , the wave equation becomes: (1) making the substitution for some twice differentiable function h, show that (1) becomes hence, show that the general solution reads for any twice differentiable functions f

Trigonometric Equations : Solution and Area of Triangle

1. Find all the solutions of the equation 3sin20(degrees) = cos2x(degrees) in the range 0(degrees) is less then or equal to x(degrees) which is less than or equal to 180(degrees). 2. A triangle has sides A-C =3cm A-B = 5 cm B-C = 4 cm Find the area of

Function indicated domain of definition

The problems are from complex variable class. Please specify the terms that you use if necessary and explain each step of your solution. If there is anything unclear in the problem, please tell me. Thank you very much. 4. Use the given theorem to show that each of these functions is differentiable in the indicated domain of

Trigonometry : Word Problems

Q1. A glass crystal sculpture is made in the shape of a regular octagonal prism with 10 cm sides. Each of the lateral faces is square. To avoid breakage in shipment, the piece is padded with plastic foam beads when it is packed in its square-based rectangular box. The layer of beads must be at least 1 cm thick on all sides of


A handicap ramp is 5.26 meters above the ground. What will the length of the ramp if it makes an angle of 23 degrees with the floor?

Measure Height of Mountain : Angle of Elevation

To measure the height of a mountain a surveyor takes two sightings of the peak at a distance of 900 meters apart on a direct line to the mountain (see attached picture). The first observation results in an angle of elevation of 47 degrees, whereas the second results an angle of elevation of 35 degrees. If the transit is 2 meters

Applications of Trigonometry and Vectors

Please see the attached file for the fully formatted problems. 1. Find the indicated part of each triangle ABC. C = 118°, b = 130km, a = 75km; find c The correct answer to this problem is 180 km how did they come up with that answer? 2. Height of a Balloon: The angles of elevation of a balloon from two points A and B on


Find the exact value, given that sin A = -4/5 with A in quadrant IV tan 2A Which is the correct answer? - 7/24 24/7 - 24/7 7/24


Solve the equation for solutions in the interval [0, 360). tan 4x = 0 Which is the correct answer? x = 33, 57, 147, 237, 327 x = 0, 90, 180, 270 x = 0, 45, 90, 135, 180, 225, 270 x = 0, 45, 90, 135, 180, 225, 270, 315

Trigonometric Identities

If you would please give me each step to solve these problems so I can get a better understanding how to solve these types of problems would be very helpful. Thanks. Graph each expression and use the graph to conjecture an identity. Then verify your conjecture algebraically. 1. sec x - sin x tan x Verify that each equat

Wave Equations : Comparison Between Circular and Square Vibrating Membranes

Please see the attached file for the fully formatted problems. Consider a circular membrane of radius a and a square membrane Assume the two membranes (i) have the same area. .... (ii) obey the same wave equation... (iii) Have the same boundary conditions phi = 0 at their boundaries. A) TABULATE (i) the 3 lowest frequen

Volume of a Hypersphere : n-Tuple Integral

Please do #4. Please see the attached file for full problem description. In this project, we find formulas for the enclosed by a hypersphere in n?dimensional spaces 1 Use a double integral, and trigonometric substitution, together with Formula 64 in the Table of Integrals, to find the area of a circle with radius r 2 U

Using triangle ABC, show that form is able to find side lengths.

Let ABC be a triangle. Prove that (cos(A/2))^x, (cos(B/2))^x, and (cos(C/2))^x are the lengths of a triangle for any x greater than or equal to 0. From what I have found in my books, it is impossible to solve for side lengths of a triangle using AAA b/c there is no formula to do so. It is possible to find similar triangles

Circumscribable Quadrilateral and Finding Lengths

In the attached figure, the quadrilateral ABCD has the following lengths of sides and diagonals: DC=7, CB=8, BA=13, AD=13, AC=15, and BD=13. 1. Verify that quadrilateral ABCD is circumscribable 2. Find the remaining lengths of DE, BE, AE, and CE. Although it appears there is a right angle, it is not labeled as though it

Determine the remaining sides and angles of ABC

Angle B = 18.7degrees angle C = 124.1degrees one side of the triangle AC=94.6m. use the law of sines to solve the triangle involving SAA. a/sinA=b/sinB substituting the known values given 94.6/sin18.7degrees=b/sin124.1degrees b=94.6 sin124.1/sin18.7 b=? Can you help me did I set it up right? find C from the fact that t

Pythagorean Theorem

I need to use the theorem to show that the area on the outside of A plus the outside of B = outside of C. I can't use something as easy as a square but I don't need anything too crazy. Please help with any suggestions as well as how I would find the area.

Trigonometric Function : Solve for solution in the interval [0,2pi]

The two graphical methods are intersection-of-graphs method f(x)=g(x) correspond to the x-coordinates of the points of intersection of the graphs of y=f(x) and y=g(x). or can use the X-Intercept method f(x)=0 are represented by the x-intercepts of the graph of y=f(x). tan3x=3tanx

Trigonometric Points in terms of Radians : Transformations

In terms of radians and X, what would be the specifications of the anlges for trigonometric points which result from the following transformations of the trigonometric point P(X)? (Work these out on a diagram of the unit circle) 1) A reflection y = x followed by a rotation through pi 2) A reflection in y = -x 3) A refle