Mathematical Analysis

54x67=(50+4)(60+7)=3000+350+240+28=3618

Due to the property of uniqueness of value of numbers, it is 22800.

If a 1000 metre sticks are placed end to end in a straight line then yes they do occupy a length equivelent to 1 kilometre

Madison defines a faction as "a number of citizens, whether amounting to a minority or majority of the whole, who are united and actuated by some common impulse of passion, or of interest, adverse to the rights of other citizens, or to the permanent and aggregate interests of the community".

A surface is a 2-dimensional manifold. Most surfaces are curved, in which for a small "differential" section of a surface, a plane figure is uniquely determined.

This is based on exercise 10 on p 165.4 of "Introduction to Complex Analysis" by Nevanlinna and Paatero, Chelsea Publishing, NY.

With w(z) == u(x,y) + i v(x,y), ( |w(z)| = constant ) ==>

1) uu + vv = const. Using notation ux == du/dx, uy == du/dy, etc., 1) ==>

2) 0 = u ux + v vx and 0 = u uy + v vy.

Using the Cauchy-Riemann equations, ux = vy and uy = -vx to eliminate derivatives of v, 2) becomes

3) 0 = u ux - v uy and 0 = u uy + v ux. Exercise 10 asserts that from this one can show that

4) 0 = (uu + vv)(ux ux + uy uy). I have not obtained that formula, but using 3) one can form the combination

5) 0 = (u ux - v uy)(u ux + v uy) + (u uy + v ux)(u uy - v ux) which simlifies to

6) 0 = (uu - vv)(ux ux + uy uy).

If w(z) is not a constant, then from the continuity of derivatives of analytic functions there must exist some domain throughout which ux or uy is non-zero. 6) indicates that in that domain either w(z) must vanish or its argument must be constant (45 or 225 degrees) so that in that domain w(z) must vanish or its modulus and argument must both be constant making w(z) constant. But if w(z) is constant in a domain, then by the uniqueness theorem (Nevanlinna and Paatero page 139) it is constant altogether.

It depends on what the dot product is meant to be equal to.

A fitting that makes it possible, for example, to glue a piece of 2" pipe into a 3" fitting (if you have a 3" x 2" bushing, that is).

Speed / Distance=Time

2283.6211MPH/60KM= 61.25219859267292 seconds

A PET scan would be most useful for detecting brain areas that are most active as a person performs mathematical calculations.

a machine has two parts the probability of

failure of one parts in a given period

of time is 0.06 the probability of failure

of the other part in the same period

os 0.08 what is the probability that the

machine fails in that period of time ?

It would be a dodecagon.

A nonagon is a polygon with 9 sides

five tenths < sixty five hundredths < seven tenths [0.5 < 0.65 < 0.7].

It is: -15 times -23 = 345

The meaning of having a million dollars is that the value of your assets and property equals 1 million dollars.

Inches were a unit of length used by some medeval european countries. An inch is roughly the same as 25.4 mm in modern measurements. So 8.5 of the ancient units is the same as 215.9 mm in the modern world.

1 cubic foot of iron, at room temperature would weigh approx 2190 newtons.

-773 is in its simplified form; no need to be "evaluated" any further.

Usually liters or cubic meters

Simplex is usually used to describe a single strand of Fiber Optic cable. This is sometimes used when a signal only needs to go in one direction, like a simple video feed from a security camera.

Duplex (sometimes called "zipcord") is two strands of Fiber Optic cable joined by a thin connection between the two jackets.

This is much more commonly used than simplex as with two fibers you can get synchronous communication between devices. Duplex cables are often labeled with A and B to determine which is the transmit and which is the receive.

If you meant a septagon it is another word for an heptagon which is a 7 sided shape.

t is the significance of Z-transform

the answer is yes because the number tells you what to multiply for example 2x4=8 because it is telling me to put four in 2 times its like 4+4 =8 same thing