Proofs

Iteration is a process where you use your previously obtained answers in your next equation. Consider the equation x_(n+1)=x_(n)+4. Where n is an arbitrary non negative integer.

We must be given an original x_0 say x_0=1 here. Then

x_1=x_0+4=5

x_2=x_1+4=9

x_3=x_2+4=13

and so on....

Assuming you are referring to US states, North / South could be Alaska and Florida. East / West could be California and Massachusetts.

If of triangle ABC and A'B'C' sides AB = A'B' and AC = A'C', and the included angle at A is larger than the included angle at A*, then BC > B'C'.

Proof:
A A'
/|\ /|
/ | \ / |
/ | \ / |
/ | \ B'/ |
B | X \C |C'
D

We construct AD such that AD = A'C' = AC and angle BAD = angle B'A'C'.

Triangles ABD and A'B'C' are congruent. Therefore BD = B'C'.

Let X be the point where the angle bisector of angle DAC meets BC.
From the congruent triangles AXC and AXD (SAS) we have that XD = XC.
Now, by the triangle inequality we have that BX + XD > BD, so BX + XC > BD, and consequently BC > BD = B'C'.

A rock composed of compressed layers (sometimes resembling a cake) are known as sedimentary.

YES! 1 over 1 = 100%

1/1 * 100% = 100%

True

208 (47+ 49 + 53 + 59)

37%

Diverting the argument to unrelated issues with a 'red herring'. Or, assuming the conclusion of an argument called 'begging the question'

First line support normally involves dealing with customers, clients or employees directly to resolve their issues. Normally the issues are fairly basic. Second line support should take over a support request once it has been established there is a problem with the supported 'system' and it is not to do with user training, user environment, etc. Second line support will liaise with third line support for any highly technical issues. Second line support is usually the middle-man between first line and third line Third line support is a non-customer focused base of technical staff that will investigate and resolve problems.

Double the percent alcohol. 40% alc is 80 proof. 200 proof is pure alc.

Let P = { x0, x1, x2, ..., xn} be a partition of the closed interval [a, b] and f a bounded function defined on that interval. Then: * the upper sum of fwith respect to the partition P is defined as: U(f, P) = cj (xj - xj-1) where cj is the supremum of f(x)in the interval [xj-1, xj]. * the lower sum of f with respect to the partition P is defined as L(f, P) = dj (xj - xj-1) where dj is the infimum of f(x) in the interval [xj-1, xj].

Here is a correct proof by contradiction.

Assume that the natural numbers are bounded, then there exists a least upper bound in the real numbers, call it x, such that n ≤ x for all n.

Consider x - 1. Since x is the least upper bound, then x - 1 is not an upper bound; i.e. there exists a specific n such that x - 1 < n.

But then, x - 1 < n implies x < n + 1, hence x is not an upper bound.

QED

This concludes the proof; i.e. there exists no upper bound in the real numbers for the set of natural numbers.

P.S. There exists sets in which the set of natural numbers are bounded, but these are not in the real number system.

The A stands for angle.

22/7

Are you tired of slow modem connections? Cellonics Incorporated has developed new technology that may end this and other communications problems forever. The new modulation and demodulation technology is called Cellonics. In general, this technology will allow for modem speeds that are 1,000 times faster than our present modems. The development is based on the way biological cells communicate with each other and nonlinear dynamical systems (NDS). Major telcos, which are telecommunications companies, will benefit from the incredible speed, simplicity, and robustness of this new technology, as well as individual users.

In current technology, the ASCII uses a combination of ones and zeros to display a single letter of the alphabet (Cellonics, 2001). Then the data is sent over radio frequency cycle to its destination where it is then decoded. The original technology also utilizes carrier signals as a reference which uses hundreds of wave cycles before a decoder can decide on the bit value (Legard, 2001), whether the bit is a one or a zero, in order to translate that into a single character.

The Cellonics technology came about after studying biological cell behaviour. The study showed that human cells respond to stimuli and generate waveforms that consist of a continuous line of pulses separated by periods of silence. The Cellonics technology found a way to mimic these pulse signals and apply them to the communications industry (Legard, 2001). The Cellonics element accepts slow analog waveforms as input and in return produces predictable, fast pulse output, thus encoding digital information and sending it over communication channels. Nonlinear Dynamical Systems (NDS) are the mathematical formulations required to simulate the cell responses and were used in building Cellonics. Because the technique is nonlinear, performance can exceed the norm, but at the same time, implementation is straightforward (Legard, 2001).

This technology will be most beneficial to businesses that do most of their work by remote and with the use of portable devices. The Cellonics technology will provide these devices with faster, better data for longer periods of time (Advantages, 2001). Cellonics also utilizes a few discrete components, most of which are bypassed or consume very little power. This reduces the number of off the shelf components in portable devices while dramatically decreasing the power used, leading to a lower cost for the entire device. The non-portable devices of companies will benefit from the lack of components the machines have and the company will not have to worry so much about parts breaking.

There are 3 feet in one yard. Therefore, 3.5 yards is equal to 3.5 x 3 = 10.5 feet.

Plumbers use various math skills, primarily arithmetic, to measure and calculate dimensions for pipes, fittings, and fixtures. They apply basic geometry to understand angles and shapes for pipe installations and layouts. Additionally, they may use algebra to determine water flow rates and pressure calculations to ensure efficient system designs. Accurate measurements and calculations are essential for proper installations and compliance with building codes.

Z-scores, t-scores, and percentile ranks are all statistical tools used to understand and interpret data distributions. Z-scores indicate how many standard deviations a data point is from the mean, allowing for comparison across different datasets. T-scores, similar in function to z-scores, are often used in smaller sample sizes and have a mean of 50 and a standard deviation of 10, facilitating easier interpretation. Percentile ranks, on the other hand, express the relative standing of a score within a distribution, showing the percentage of scores that fall below a particular value, thus providing a different type of comparison.

That depends on the sand. Choose one of these densities:

Sand, wet - 1920 kg/m³

Sand, wet, packed - 2080 kg/m³

Sand, dry - 1600 kg/m³

Sand, loose - 1440 kg/m³

Sand, rammed - 1680 kg/m³

Sand, water filled - 1920 kg/m³

Now put it into the following formula:

kilograms of sand / density = cubic meters of sand

To answer Part 4 of the Additional Mathematics Project for Form 5 from 2010, refer to the specific problem or concept outlined in that section, ensuring you understand the question requirements. Generally, you'll need to apply relevant mathematical principles or techniques, such as algebraic manipulation, geometry, or data analysis, depending on the topic. Make sure to present your solutions clearly, showing all necessary steps and justifications for your answers. If you have the project details, I can provide more targeted guidance.

The volume of a tetrahedron is one-sixth of the volume of a parallelepiped because a tetrahedron can be thought of as a pyramid with a triangular base. When a tetrahedron is inscribed within a parallelepiped, it occupies one-sixth of the space defined by the parallelepiped's volume. Since a parallelepiped can be divided into six such tetrahedra, this means the volume of the tetrahedron is 1/6 of the parallelepiped. However, if the parallelepiped is defined by its full height and includes the whole base area, the tetrahedron's volume is one-sixteenth of the total volume when considering the full dimensions of the parallelepiped.