Find the volume of a cube given the surface area.

A cube has a surface area of 54 square inches. If the length of each side is tripled, the what will the volume of the cube be?

Find the ratio of the lengths of two squares (one inside a circle and one outside a circle).

A square is inscribed in a circle, with each corner of the square touching the circle. A larger square is circumscribed outside the circle, with each side of the larger square touching a corner of the inscribed square. The sides of the larger square are longer than the sides of the smaller square by a factor of ….?

Converting the Sum of Binary Numbers into A Decimal Number

The sum of the binary numbers (1101001) and 0101100 results in the decimal equivalent of...?

Compressive Stress

A circular cross sectional bar with a diameter of 3.25 inches is loaded with a uniform axial compressive load of 22,750 pounds. What is the compressive stress along a cross section of the bar in PSI?

Stereographic projection on complex plane

Let V be a circle lying in S. Then there is a unique plane P in R^3 such that p / S = V ( / = intersection). Recall from analytuc geomerty that P = { (x_1,x_2,x_3) : x_1 b_1 + x_2 b_2 + x_3 b_3 = L, where L is a real number}. Where ( b_1,b_2,b_3) is a vector orthogonal to P . It can be assumed that (b_1)^2 + (b_2)^2 + (b_3) ...continues

Metric spaces and the topology of complex plane

Show that { cis k : k is a non-negative ineger} is dense in T = { z in C ( C here is complex plane) : |z| = 1 }. For which values of theta is { cis ( k*theta) : K is a non-negative integer} dense in T ? P. S. cis k = cos k + i sin k, i here is square root of -1. I want a full justification for each step or claim.

Upper Half Plane

Let . Let be real numbers with . Show that , is 1-1 and onto.

Show that transformation W (Z) = (a Z + b) / (c Z + d) of the upper half of a complex plane is 1-1 and onto the upper half plane if a, b, c, and d are real and satisfy condition a d > b c

Show that transformation W (Z) = (a Z + b) / (c Z + d) of the upper half of a complex plane is 1-1 and onto the upper half plane if a, b, c, and d are real and satisfy condition a d > b c

Continuity complex plane

Let G be an open subset of C ( complex plane) and let P be a polygon in G from a to b. Use the following 2 theorems to show that there is a polygon Q in G from a to b which is composed of line segments which are parallel to either the real or imaginary axes. The 2 theorems are: 1). Theorem: Suppose f: X --> omega is continuou ...continues

Find the radius of convergence for each of the following power series

1). Find the radius of convergence for each of the following power series. Please check my solution for this problem: a). sum ( n = 0 to infinity) a^n z^n, a is a complex number. My solution: R( radius of convergence) = lim |a_n/a_n+1) = lim | a^n/a^(n+1)| = 1/|a| b). Sum ( n=0 to infinity) = lim|a^(n^2)*z^n, a is ...continues