1) Find the component form of the vector that represents the velocity of an airplane descending at a speed of 100 miles per hour at angle of 15* below the horizontal Q=195*.

Q: Illustrate how you would find the unit vector having the same direction as vector (p.q.r).

A: Given vector is p,q,r. We have to illustrate the method to find the unit vector having same…

Q: 6. An airplane is taking off headed due north with an air speed of 173 miles per hour at an angle of…

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Q: Find the angle in degrees between vector a = and vector b =

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Q: An athlete standing west of a river flowing from north to south at 0.4 m/s and is 72 m wide swims at…

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Q: III) Now consider an object moving across a river so that it has two velocities with respect to the…

A: The unit direction vector along the positive x axis is denoted as i^. The unit direction vector…

Q: what is the magnitude of the vector

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Q: A vector starts at point ( -5, -3) and ends at point (9, 9) what is the magnitude of the vector,…

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Q: A particle moves in two dimensional space where i and į are unit vectors in the x and y directions…

A: given  r→=6t-4t2i^+2t j^ a) write down the particle's velocity vector in component form. ii) find…

Q: 8) An airplane is on a heading of 065° at 350 km/h and an 75 km/h wind is blowing from 310⁰.…

A: 0

Q: Suppose only F acts on the object and with this force only, the object experiences a displacement…

A: Introduction: When a force is acted upon an object, there is a displacement. The dot product of the…

Q: Express the following vector as the product of its magnitude and a unit vector: v=(3/5)i^ + (4/5)k^

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Q: Two forces of 43N and 56N act at angle of 78 degrees to each other. I need the resultant of these…

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Q: find the angle between vector A = and vector B = then write A as a sum of a vector parallel to B…

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Q: Find the angle between two vectors a = (3,4,0) and b = (4,4, 2). O a. cos Cos cos-() O d. cos-() Ос.

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Q: for a -1 2x +5 f (x) = If fis the function defined above, then f' (-1) is A -2 B 3. E) nonexistent…

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Q: 2. Which of the following is not a unit vector? A. (0-2) 0. √5 √5 B. (cos 1, sin 1, 0) C. (1, 1, 1)

A: A vector v whose magnitude is 1 is called a unit vector. A vector v whose magnitude is any positive…

Q: What is the angle in radians between the vectors a = (6, 8, -2) and b = (-7, 7, 0)? Angle: (radians)

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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.