4 -2] find the eigenvalues and eigenvectors. 1 10. Given the matrix A =

Q: Two times the sum of a number and 3 is 4 less than 3 times the number. Half of a number, plus 6, is…

A: Here we assume an unknown number x for both questions so we can translate these statements into…

Q: When I was learning how to drive, I was told that while driving on the freeway I should stay one car…

A: You are  staying behind 12 car lengths using your dad's 3-second rule.

Q: A 50-kilowatt gas turbine has an investment cost of $37,000. It costs another $10,000 for shipping,…

A:

Q: A woman 6 feet tall walks at the rate of 3 feet per second away from a streetlight that is 15 feet…

A:

Q: 1. It takes Mom, Dad and Isabel two hours to shovel their driveway after a snow storm. If Dad worked…

A: Given: Mom, Dad, and Isabel take two hours to complete the work. Dad takes 4 hours to complete the…

Q: We want to build a playing field where the length of the field is twice as long as the width. The…

A:

Q: Travel: Recently Mr. and Mrs. Roberts s their vacation in San Francisco, which is 540 miles from…

A: The distance between their home and San Francisco is 540 miles. While returning home from San…

Q: Show that f is continuous on (-0, 0). S1 + x² f(x) : if x 1

A:

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.