Numerical Analysis and Simulation

a proportion is an equation. a / b = c / d

cross multiply: ad = bc then solve

Exactly as in the question 0.548

No

90.70 is equivalent to 90.7 and 90.700 (although the former has lower and the latter has greater resolution - number of significant digits)

1 over 14 is 0.07, rounded to the nearest hundreth's place.

Yes, any number/term that does not contain a variable (x, y, t, etc.) is considered a constant.

This can be expanded to: (1 x 2³) + (1 x 2²) + (1 x 2¹) + (0 x 2º) = 8 + 4 + 2 + 0 = 14 {base 10}

Prefix 'centi' is used to denote sub multiples of meter and uses factor 0.01.

Prefix 'kilo' is used to denote multiples of meter and uses factor 1000.

Therefore to convert kilometers to centimeters, first kilometers are converted to meters and then meters to centimeters.

1. To convert kilometers to meters, value in kilometers has to be multiplied by factor used with prefix 'kilo':

78 kilometers = [kilometers] * 1000 = 78 * 1000 = 78000 meters

2. To convert meters to centimeters, value in meters has to be divided by factor used with prefix 'centi':

78000 meters = [meters] / 0.01 = 78000 / 0.01 = 7800000 centimeters

78 kilometers = 7800000 centimeters

It means to round the number to the nearest four decimal places (0.0000) for example the number 12.3476589 would be 12.3477 . The four decimal places are the amount of numbers after the decimal dot. For the fourth number after the decimal point, if the number after it is 5 or higher, than you round up to the next decimal number. If it is below five, you leave it as it is. If the fourth number is nine and the next one is eight for example, you also rise the third number as well as the fourth.

To determine how many 10 hundreds are in 180,320, you need to divide 180,320 by 1,000 (since 1,000 is equivalent to 10 hundreds). The result is 180.32, which means there are 180 10 hundreds in 180,320.

412

A nonlinear Volterra integral equation is a type of integral equation where the unknown function appears under an integral sign and the relationship involves nonlinear terms. It typically has the form ( u(t) = f(t) + \int_{a}^{t} K(t, s, u(s)) , ds ), where ( K ) is a nonlinear kernel, ( f ) is a known function, and ( u(t) ) is the unknown function to be determined. These equations are often encountered in various fields such as physics, engineering, and biology, where they model systems with memory and time-dependent interactions. Solving nonlinear Volterra integral equations can be challenging, often requiring numerical methods or iterative approaches.

The Runge-Kutta method is one of several numerical methods of solving differential equations. Some systems motion or process may be governed by differential equations which are difficult to impossible to solve with emperical methods. This is where numerical methods allow us to predict the motion, without having to solve the actual equation.

If any number falls more frequently than others in any game of chance, then

the game is a fixed, rigged, loaded, dishonest, stacked suckers' game.

The error bound is half of the last digit = ±0.0005

The relative error is ±0.000145 or ±0.0145%

14300000 or 14,300,000

11 and 15 both go into 165. 165 is the LCM (Least Common Multiple) of 11 and 15.

A hectare is a unit of area, originally used to measure land area, equivalent to 10,000 square meters, or about 2.47 acres.

The meter is a unit of length, equivalent to about 39 inches. More formally, the meter is the distance that a beam of light will travel in a vacuum in 1 / 299,792,458 of a second.

The two units are inconsistent with each other, and cannot be further described in terms of their difference.

total cost / number of units

Percentage of what during 40 hours?

During a 40 hour period you watch TV for 15 hours.

15 / 40 x 100 = 37.5% of time watching TV

The difference between 43 and 40 is 3.

There are an infinite variety of a set of five numbers with a mean of 53. One such set is [51,52,53,54,55].

200 g in the ratio 8 : 3 : 2 is approx 123 g, 46 g and 31 g.

The number for the amount you are being paid, or wish to be paid, as salary. This should not include any commission based earnings, or gratuities.