Task 2 The cells of the battery are treated using a programmable lathe machine. The machine has 15 programs that are able to control its speed. Program 1 has 11 ( N( 1) = 11) different speeds that can vary from 100 revolution per minute (rev/min) to 1100 (rev/min). Program 2 has 13 ( N (2) =13) speeds that can vary from 110 rev/min to 1430 rev/min ( X1(1) = 100, X2(1)=110, and so on). The number of speeds of the higher programs increases using geometric progression and the speeds within the same program follow the same pattern of the common difference achieved in program 1 and 2 and increase using arithmetic progression. 1. Determine the general formulas of the speeds of the programs and the number of speeds of the programs. 2. Construct a sequence using the final speed of each program. Is there any relation between these speeds? 3. Determine the number of speeds of program 10, and the value of speed number 7 within program 10. 4. Determine the total number of speeds that can be produced. 5. Determine the value of the maximum speed that can be produced by the lathe machine. 6. If a speed of 3000 rev./min is required to handle a specific manufacturing task, which (program/s) can be used to achieve it exactly. On the other hand, if the program cannot achieve the speed of 3000 rev./min; recommend the speed that can be used and the program that can provide the closest value of 3000 rev./min. 7. Repeat 1-6 if the number of speeds is incre
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
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