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converse of the Pythagorean theorem

Please give an example of a mathematical statement whose converse is not true. Prop. 48: If in a triangle the square on one of the sides be equal to the squares on the remaining two sides of the triangle, the angle contained by the remaining two sides of the triangle is right.

Pythagoras theorem for airplane flights

An airplane flies over an observer with a velocity of 400 mph and at an altitude of 2640 ft. If the plane flies horizontally in a straight line, find the rate at which the distance x from the observer to the plane is changing 0.6 min after the plane passes over the observer.

Determine the magnitude and direction of the resultant vector.

1. Use trigonometric ratio and Pythagorean theorem to add the vectors given. Determine the magnitude and direction of the resultant vector. B=42.1 A=101.1 x θ =17.5 degrees y θ =12.9 degrees 2. Determine the resultant of the vectors with the given magnitude and directions. Positive angles are measured counte

Maclaurin series to provide proof

Please help me with step by step solutions to the following problems. 1a. Prove tan^-1 x + tan^-1 y = tan^-1 ((x+y)/(1-xy)) where -PI/2 < tan^-1 x + tan^-1 y < PI/2 . Hint: Use an identity for tan(x+y). 1b. Use part (a) to show that tan^-1 (1/2) + tan^-1 (1/3) = PI/4 . 1c. Use the first

Important information about Conversion Problems

Find the value of the trig function of the angle ( standard position) who terminal position pass through the given points (8,4) Sin thea= Cos theo= tan thea = cot thea= sec thea= csc thea= ------------------------------ Conversion Given tan thea = 1.404 what is csc= what is cot= ---------

3 questions of conversion are presented.

Find the value of the indicated function: Do not round until final evaluation Given tan(theta) = 1.067 Find: csc(theta) Find Sin(theta) -------------------------- Sin(a) = 0.7754 Find Sec(a) ???

Solutions For Five Problems of Mixed Type

Trigonometry/Algebra 1) An open-top box with a square base is to be constructed from 150 square centimeters of material. What dimensions will produce a box with largest possible volume? A) B) C) D) E) 2) Assume h 0. Compute and simplify the difference quotient for f(x) = 1 / x. 3) Solve

Trigonometric Identities and Pythagorean Theorem

1) Simplify the given expression. Compute the exact answer as a fraction, it should not contain sin, cos, or tan. cos((PI/4)-x), if cos(x)=-1/6 and PI/2 < x < PI 2) Use factoring, the quadratic formula, or identities to solve the given equation. Find the solution in the interval [0, 2*PI). 5 sin^2(x) + 3 sin (x) = 8

the trigonometric identity

Could you show me how to plot the graph and find the area of the region for r = 2cos(theta) for -pi/2 <= (theta) <= pi/2

Trigonometry - Find sin (t), cos (t), tan (t).

Please give step-by-step answers to the following trigonometry problems. 1) Assume that the terminal side of an angle of t radians passes through the point (.9, -.4) . Find sin (t), cos (t), tan (t). 2) Assume that the terminal side of an angle of t radians in standard position lies in the given quadrant on the given strai

Problems with Quadratic Reciprocity & Pythagorean Triangles

2. If p>3, show that p divides the sum of its quadratic residues that are also least residues. (see attached file for diagram) 4. Here is a quadrilateral, not a parallelogram, with integer sides and integer area: (a) What is its area? (b) Such quadrilaterals are not common; can you find another? (c) Could you find 1

Word problems for basic Trig

An airplane travels 100 km/hr for 2 hrs in a direction of 210degrees. At the end of this time how far south of the airport is the airplane? Directions are given in degrees clockwise from north The airplane is -------------kilometers south of the airport after 2 hrs -----------------------------------------------------

Applying the Pythagorean Theorem to Problems

Please help with the following problems involving applications of the Pythagorean Theorem. Provide step by step calculations. 1. The sides of a square are lengthened by 6 cm, the area become 121 cm^2. Find the length of a side of the original square. 2.Television sets. What does it mean to refer to a 20in TV set or a 25in

Pythagorean Theorem Review

The Pythagorean Theorem can also be proved directly, by choosing 0 at the right angle of a right-angled triangle whose other two vertices are u and v. Show that |v - u|^2 = |u|^2 + |v|^2 under these conditions, and explain why this is the Pythagorean theorem.

Vectors, Magnitude, & Direction of a Dart Shot from a Blow Gun

See attached file. Blow gun Using only a meter stick, brains and a calculator, find 1. Vi (coming out of the gun) muzzle velocity, (Hint:first find time) 2. Vfy (a vector) 3. Vf (a vector) When it hit the cardboard, magnitude and direction (Hint: use vfy and

Exemplifying plotting points

Please help with the following problem. Technicians at Buzz Electronics use this equation to determine the amount of current (i) traveling through a circuit at any given time (t): i = 2t^2 â?" 8t + 10 a) Graph the equation to show the relationship between time and current. b) Is this function linear, quadratic, expon

Limits of Trig Functions

** Please see the attached file for the complete solution response ** 2) The limit of f(x) = (sin x)/x as X approaches 0 is 1 a) Let (x, sin x) be a point on the graph of g near (0,0), and write a formula for the slope of the secant line joining (x, sin x) and (0,0). Evaluate this formula at x = 0.1 and x = 0.01. Then


Trigonometry has many applications in the real world. One particular area in which it can be used is in architecture. If you were an architect, describe a specific situation in which you could use right triangle trigonometry to help you design a new hospital. Give a specific example and explain how right triangle trigonometry co

Pythagorean Triples

The numbers 3, 4, and 5 are called Pythagorean triples since 3² + 4² = 5². The numbers 5, 12, and a13 are also Pythagorean triples since 5² + 12² = 13². Can you find any other Pythagorean triples? Actually, there is a set of formulas that will generate an infinite number of Pythagorean triples. Research the topic of Pyt

questions on trigonometric functions

1. The top of a 30-ft ladder is leaning against the edge of the roof of a house. If the angle of inclination of the ladder from the horizontal is 60 degree, what is the height of the house? How far is the bottom of the ladder from the base of the house? Please see the attachment for more questions on trigonometric functions.

Compactness of the Interval - Uniformly Continuous

A function f:reals->reals is said to be periodic on the reals if there exists a number p greater than zero such that f(x+p)=f(x) for all x in the reals. Prove that a continuous function on the reals is uniformly continuous on the reals. Secondary question: Is there a way to do this with just epsilon and deltas and no need f

Consider two buildings A and B facing each other across a city park

Consider two buildings A and B facing each other across a city park. The base of the lower windows of Building A are 4 metres above the ground while the base of its upper windows are 23 metres above the ground. From the base of Building A lower windows, the angle of elevation to the top of Building B is observed to be 26°. From

Law of Cosines and Law of Sines

In the triangle with sides a= 21 cm, b=45cm, and c = 60 cm, where the angle gamma is between the sides a and b, the angle beta between the sides a and c, and the angle alpha between sides b and c. a) Calculate the angle gamma in degrees by using the Law of cosines. b) Calculate the angles alpha and beta (in degrees) using

Unit Vectors in Trigonometry

1.) Perform the following operation: a. v + w = ? Where, v = 2i - 6j and w = 3i + 4j b. v - w = ? Where, v = 8i - 6j and w = - 2i + 4j 2.) Find the dot product of vector v and vector w if: a. v = 2i - 3j w = i - j 3.) Find the unit vector that has the same direction as the vector below: a.

Trigonometry Absolute Values for Complex Numbers

1. Find the absolute value of the following complex number: 2. Choose the rectangular coordinates for the following polar coordinate: 3. Determine the rectangular form of the complex number: 4. Find the polar form of the following complex number: 5. When plotted on the rectangular coordinate system in which quadrant

point of intersection.

Figure in attachment shows a cuboid OABCDEFG, where O is the origin. A has position vector 5i, C has position vector 10j and D has position vector 20k. (a) Find the cosine of angle CAF. Given that the point X lies on AC and that FX is perpendicular to AC, (b) find the position vector of point X and the distance FX. The