Problem Set #3 – Unit Analysis Give all answers in three significant figures 1. How many oranges are in a crate if the price of a crate of oranges is $2-40 and the price of oranges is three cents per pound. On the average there are three oranges in one pound. 2. A snail travels at 1.00 cm/min. What is the velocity in furlongs per forthnight if a furlong is 660 feet, there are 2.54 cm/in and a forthnight is 14 days? 3. How many acres of peppers must Peter Piper pick to fill an order of 1000 cases if a case has 24 cans, each can has 8 peppers, the farm averages 12 peppers per square yard, and there 4840 square yards per acre? 4. A jet plane holds 1000 gals of fuel. Fuel weighs 6.00 lbs/gal. The engine consumes 1200 lbs/hr. The speed of the plane is 550 mph. How far can the plane go on 1000 gals of fuel? 5. The price of a ream of paper is $2.90. There are 250 sheets of paper in a ream. If a sheet of paper weighs .568 oz what is the price per pound of paper? 6. What is the cost to drive 405 miles if the cost of gasoline is $3.09 per gal and the car makes 46 miles/gal of gas? 7. How many cars are there in a long freight train if it takes the entire train two minutes to pass a station as it travels 40 miles per hour? Each car is fifty feet long and there are 5280 feet in a mile.
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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