text stringlengths 6 976k | token_count float64 677 677 | cluster_id int64 1 1 |
|---|---|---|
On orthogonality, that is implicit in the definition usually adopted - but you will note that the formula for the cosine then involves dividing by zero. It would be possible to adopt the idea that orthogonal vectors were non-zero, but that would mean that every time you used the concept it would be necessary to conside... | 677.169 | 1 |
Remember that a^2 +b^2 = c^2. That should read ( a squared) plus (b squared) equals (c squared)the hypotenuse is c.So to answer your question, a right traingle could have many different length sides as long as it satifies this equation. However, in order to get the exact length for a particular triangle, you need more ... | 677.169 | 1 |
Proving Segment Relationship
In this lesson our instructor talks about proving segment relationship. She talks about five essential parts to a good proof. She also discusses reasons used in proof such as undefined, definitions, postulates, and previously proven theorems. She talks about congruence of segments and the t... | 677.169 | 1 |
Thanks! that formula worked like a charm for automating my radius calculations along a railroad track. It gave pretty much the same results as least squares circel fitting.
Anyone know what the name of the formula is and/or a scientific paper i can refer to it?
I have never seen a name given to it. It is included in mo... | 677.169 | 1 |
Identify the 3D Shapes PowerPoint is a great introduction to learning the names of 3D shapes. Students are asked to look at a shape and decide whether it is a cube, cylinder, cone, rectangular prism, pyramid, or sphere. Each shape is shown twice. This would also go well with my Super Shapes 2D and 3D packet!
Be sure th... | 677.169 | 1 |
CBSE Board Class 10 Math Sample Papers 2010
CBSE Board Sample Papers 2010 for Class 10 Math
Sample Paper – 2010
Class – X
Subject –Mathematics
General Instructions:
1.All questions are compulsory.
2.The question paper consists of 30 questions divided into four sections – A, B, C and D. Section A contains 10 questions o... | 677.169 | 1 |
Angles/15274: two angles are complementary.The mesure of one angle is twice the mesure of the other angle. what is the smaller of the two angles? 1 solutions Answer 7573 by rapaljer(4667) on 2005-10-13 20:45:04 (Show Source):
Linear_Algebra/15263: Sarah is visting a friend about two miles away from her house. she sees ... | 677.169 | 1 |
Parts of a Cone
Date: 04/18/2001 at 12:59:14
From: Brian McCormick
Subject: Parts of a solid cone
Hello,
I am a second grade teacher and we are currently teaching a unit on
shapes. The question came up as to whether or not a solid cone has any
edges. My contention is that the definition of an edge is where two
planes i... | 677.169 | 1 |
Lines
Perspective
can cause you to see lines differently depending on how they are presented.
If you drew three equal lines, but drew slanting lines on the end of each
as in the figure below, the added lines would change the way you see them.
The top line looks bigger and the bottom line looks the smallest.
But
this il... | 677.169 | 1 |
"You are a professional, after all", Greyskin added.
"Allright," Smith surrendered, "never mind the color. But there's also something about the straight lines being perpendicular?"
Mrs. Redroot shook her head, trying to get rid of the old ghost of her middle school education.
Lehare slammed his fist on the table: "Smit... | 677.169 | 1 |
April 19, 2011
This is the second of an occasional series of posts about perspective. Many people believe that geometrical perspective, single point, two point and three point are actually an accurate representation of what we see. Cameras see in this way after all so it must be right mustn't it? Well actually no, it i... | 677.169 | 1 |
Homework 10/5/99
Chapter 3:
Q6. When two vectors are added, the magnitude of the sum will be the greatest
when the vectors point in the same direction. In this case the magnitude will be 7.5
km. When the vectors point in different directions the sum will be smaller.
The sum will be the smallest when the vectors point i... | 677.169 | 1 |
Question 188646: This is a triganometry problem using Vectors length and direcion. In a regatta, a sailboat sailed 33 km west and 73 km south from the port, and then took the shortest route back. Find the distance and southern most angle in the triangle.
I did find the distance which is 80.1 km. Click here to see answe... | 677.169 | 1 |
1 line = no intersection
2 lines =1 intersection
3line - 3 intersections
4 line = 6 intersection,then how many intersections will 10 lines have? please any one solve it as soon as possible. i have exam on it please urgent!!!!!!!!!!! stanbon(57361) Theo(3464)
Question 206927: I donot know whether to put this question on... | 677.169 | 1 |
An identity is an equation that is true for all of the possible values of its variables. Trig identities are important, they involve the sums or differences of angles.
What are the Trigonometric Identities?
The above identities can be used to determine that other trigonometric equations are also identities. To do so, y... | 677.169 | 1 |
college cornerstone what time and financial constraints have you face since starting college? How did you deal with them
math The measure of the supplement of an angle is 20 degrees more than three times the measure of the original angle. Find the measures of the angles.
trig Two men on the same side of a tall building... | 677.169 | 1 |
Microsoft Excel
regular polygon, all of the sides are equal, and all of the
interior angles ? are equal. The
perimeter P of a regular polygon is given by the following
formula:
P=a*n
and the sum S of the interior angles (in degrees) is given by
the following formula:
S=(n-2)*180
where n is the number of sides in the re... | 677.169 | 1 |
Search community
turns
This unit uses one of the digital learning objects, Angles, to support students as they investigate measuring and drawing angles using other angles as units of measurement. It is suitable for students working at level 2 of the curriculum because they estimate and measure the size of other angles ... | 677.169 | 1 |
Vivian Kerr is a regular contributor to the Veritas Prep blog, providing tips and tricks to help students better prepare for the GMAT and the SAT.
]]> of Geometry - Part II
20 May 2013 15:59:46 +0000Karishma week, we discussed how drawing extreme diagrams can help solve Geometry questions. Today we will see how to solv... | 677.169 | 1 |
.......and to convert the tangent of the angle to a percentage, simply multiply by 100.
Example: 1 in 3 hill = 1/3 = 0.3333 = (0.3333 x 100) = 33.33%.
Or take the same slope downwards, dropping 1 foot in height for every
3 feet traversed horizontally = 1 / -3 = -0.3333 = (-0.3333 x 100) =
-33.33%.
Thus any gradient exp... | 677.169 | 1 |
Using
colored electrical tape, draw a set of coordinate axes (on the floor) down
the center of your classroom, dividing the students' desks into four
quadrants. (Avoid using masking tape as it is difficult to remove
from the floor once students have walked on it.) Establish where the
positive x-axis and the positive y-... | 677.169 | 1 |
You can put this solution on YOUR website! Since you must pick a blue from both bags to be "successful," you must multiply the individual probabilities...so
1/3 * 1/4 = 1/12, your answer.
You can put this solution on YOUR website! It is a bit difficult to explain the entire procedure, but in essence what you do is to e... | 677.169 | 1 |
Ellipse
The semi-minor axis of an ellipse is one half of the minor axis, running from the center, halfway between and perpendicular to the line running between the foci, and to the edge of the ellipse. The minor axis is the longest line segment that runs perpendicular to the major axis.
The semi-minor axis of an ellips... | 677.169 | 1 |
Now, the very last thing I want to tell you about these functions is - well, the values at certain famous points. A lot of times you want to find the values at some big point - let me tell you the values that you should know for certain. You should know - I'll write them first in degrees. You should the trig functions ... | 677.169 | 1 |
I don't know if you do the sorts of proofs where students make errors like saying that triangles are congruent by SAS when really they meant to say ASA, but if you do, I may have a trick for you. When my students get sloppy I have them start writing 3 column proofs. The first two columns are the ones you're used to, bu... | 677.169 | 1 |
Several curves are related to the Cycloid. When we relax the requirement that the fixed point be on the edge of the circle, we get the curtate cycloid and the prolate cycloid. In the former case, the point tracing out the curve is inside the circle, and, in the latter case, it is outside. A trochoid refers to any of th... | 677.169 | 1 |
In this book I have attempted to follow a middle course between the treatise which fully proves the propositions of elementary geometry and the syllabus which contains no proofs whalever. The early propositions are proved at length in order to make clear the form of geometrical demonstration and the details of proof ar... | 677.169 | 1 |
One of the main purposes in writing this book has been to try to present the subject of Geometry so that the pupil shall understand it not merely as a series of correct deductions, but shall realize the value and meaning of its principles as well. This aspect of the subject has ben directly presented in some places, an... | 677.169 | 1 |
(Such a transformation indeed exists. It belongs to the class of
inversions and its existence is established in Inversive
Geometry after just a few definitions.)
For concentric circles, i.e., circles with the same center, the
statement is quite obvious. The radii of the given circles and n must stand
in a certain relat... | 677.169 | 1 |
Is the point over my ray? Confusing...
This is a discussion on Is the point over my ray? Confusing... within the C++ Programming forums, part of the General Programming Boards category; I am trying to detect if my point (x & y) are over my ray (rayrot).
This is the best ...
I don't see why you're multiplying the cos an... | 677.169 | 1 |
egthomas asked
I understand the rules of horizontal, reflection, stretch and vertical translations however not seeing a graph and just given this information in the practice problem is very confusing. I understand to show this problem you will have to do on paper and I thank you for effort. Plz show steps so I can full... | 677.169 | 1 |
If on the coordinate plane (6,2) and (0,6) are the endpoints of the diagonal of a square, what is the distance between point (0,0) and the closest vertex of the square?
a) 1/sqrt(2) b) 1 c) sqrt(2) d) sqrt(3) e) 2*sqrt(3)
if (0,6) and (6,2) are end points of a diagonal of a square - shouldnt they be two of the vertices... | 677.169 | 1 |
a = xi + yj + zk
The coefficients of the i, j, and k parts of the equation are the vectors components. These are how long each vector is in each of the 3 axis.
For example, the vector equation pointing to the point ( 3, 2, 5 ) from the origin ( 0, 0, 0 ) in 3D space would be:
a = 2i + 3j + 5k
The second way I will repr... | 677.169 | 1 |
This lesson explains the basics and concepts about the quadrilaterals. You'll learn it
starting from your earlier learning about polygons. All this you'll learn in the
contents presented by the instructor in own handwriting, using video and with the
help of several examples with solution.
Quadrilateral: in geometry, a ... | 677.169 | 1 |
Applications of Trigonometry Lesson 3: Dot Product of Vectors lesson includes dot products of vectors, projection of vectors, work, and various applications in real-world situations. There is an eight-page "Bound-Book" style foldable to accompany the lesson, along with a *.pdf file of the completed set of notes.
Compre... | 677.169 | 1 |
Ptolemy's Ptools
Taking the Ptools into Cyberspace!
Using the properties of triangles,
we can investigate 3D games in some very interesting ways. In these games
the objects get larger as your view gets closer and smaller as your view
gets farther away. In order to look realistic game programmers must follow
the same ru... | 677.169 | 1 |
Tilted Squares
Activity time:35 minutes Level / prior knowledge: area of a square and triangle,KS3/KS4 Subject / curriculum links / skills: problem solving, generalising a solution, Pythagoras' Theorem, Preparation time: none (unless you want to make sure you can solve the problem yourself) Extra resources: projector/I... | 677.169 | 1 |
When two lines in a plane meet one another, we call Angle the inclination of the lines to one another.
We denote angles either by Greek letters (α, β, γ, and so on)or by the three point indicating the lines meeting (writing the point where they meet in the middle). For example, in the picture on the right, the angle wo... | 677.169 | 1 |
Proposition 45
To construct a parallelogram equal to a given rectilinear figure in a given rectilinear angle.
Let ABCD be the given rectilinear figure and E the given rectilinear angle.
It is required to construct a parallelogram equal to the rectilinear figure ABCD in the given angle E.
Join DB. Construct the parallel... | 677.169 | 1 |
Fire hydrant : what shape is at the very top of a fire hydrant?
This activity begins an exploration of geometric shapes by asking students why the five-sided (pentagonal) water control valve of a fire hydrant cannot be opened by a common household wrench. The activity explains how geometric shape contributes to the use... | 677.169 | 1 |
In mathematics, a spiral is a curve which emanates from a central point, getting progressively farther away as it revolves around the point.-Spiral or helix:...
using polar coordinates, an extra full turn gives rise to a quite different point on the curve.
Theta is the eighth letter of the Greek alphabet, derived from ... | 677.169 | 1 |
A reference angle is the acute version of any angle determined by repeatedly subtracting or adding 180 degrees, and subtracting the result from 180 degrees if necessary, until a value between 0 degrees and 90 degrees is obtained. For example, an angle of 30 degrees has a reference angle of 30 degrees, and an angle of 1... | 677.169 | 1 |
Welcome back! I think that we are on the verge of snow! Although it has been fairly warm lately, we are getting very close to Thanksgiving, which means snow is around the corner!
On a sadder note, my favorite spot, baseball, is done for the year. The Rangers lost, and the Mets didn't even make the Playoffs, but I guess... | 677.169 | 1 |
Have students write in their own words why they think perpendicular bisectors and circumcenters are helpful in finding the delivery regions for the pizzerias.
Extensions
Instead of points A, B, C, D, and E being pizzerias, let them represent rain gauges holding different amounts of rain measured in inches. Tell student... | 677.169 | 1 |
All squares are special cases of rhombuses and rectangles (and trapezoids), and all rhombuses and rectangles are special cases of paralleograms which are in turn special cases of trapezoids which are in turn special cases of quadrilaterals.
_________________
1) AC(imagine: diagonal of a quadrilateral) bisect BD (imagin... | 677.169 | 1 |
Triangles/456884: The sides of a length of a triangle are x, x+4, and 20, where 20 is the longest side. For which range of values is x an acute triangle 1 solutions Answer 313550 by robertb(4012) on 2011-06-02 22:12:03 (Show Source):
You can put this solution on YOUR website! For the triangle to be acute, , where c is ... | 677.169 | 1 |
Re: A few questions
Hi;
Not necessary Agnishom found the link belowHello Bobbym, Would you mind if I go to bed nowOf course you can get some sleepOh you found it, thanks. I could not remember where I copied it from. I cleaned it up a little in my notes Agnishom!
There are other triangles other than right triangles that... | 677.169 | 1 |
Trigonometry and Advanced Math
People sometimes describe trigonometry as the science of circles
and angles. It's trigonometry that helps you calculate the hypotenuse
of a triangle or the diameter of a circle. However, when you use
trigonometry in Excel, you probably won't be worrying about shapes;
instead, you'll be us... | 677.169 | 1 |
Therefore if a straight line falling on two straight lines makes the alternate angles equal to one another, then the straight lines are parallel to one another.
Q.E.D.
There is implicitly assumed an ambient plane. The term "alternate angles" doesn't have a meaning unless the lines all lie in a plane.
Note that Euclid d... | 677.169 | 1 |
Thanks
I had 4 as answer. Can someone please elaborate on the answer explanation.
KhurramEach side of the square must have a length of 10. If each side were to be 6, 7, 8, or most other numbers, there could only be four possible squares drawn, because each side, in order to have integer coordinates, would have to be dr... | 677.169 | 1 |
(designed for MSIE, requires JavaScript, best view 1024 x 768, auxiliary window needed) Let Sbe the ground plane (desert, floor tiles)
and B an image plane (the computer screen) perpendicular to S.
The observer's eye A is at height h above S and distance d in front of B.
The observer is looking straight at B, so we hav... | 677.169 | 1 |
From Higher Dimensions Database
The pyrochoron, also known as the pentachoron and the 5-cell, is the four-dimensional simplex, and has the lowest possible element count of any flat, non-degenerate four-dimensional shape. It consists of 5 regular tetrahedra joined at their faces, folded into 4D to form a 4D volume. It i... | 677.169 | 1 |
Geometry ABC is a triangle with area equal to 20 . The incircle of triangle ABC has radius equal to 2 and the circumcircle of triangle ABC has radius equal to 6 . If sinA+sinB+sinC=a/b , where a and b are coprime positive integers, what is the value of a+b ?
Geometry ƒ¡ is a circle with center O . A and B are points on... | 677.169 | 1 |
Angles are often measured in a common unit of degrees. One full
circle equals 360 degrees. But, angles can also be measured in a
scientific unit called radians. One full circle equals 2π
radians, which equals 360 degrees. Since 360 degrees = 2π
radians, π in radians equals 180 degrees and π/
2 equals 90 degrees.
It is
... | 677.169 | 1 |
In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set. In a topological space, a closed set can be defined as a set which contains all its limit pointsleft|150px|thumb|A [[spheroid]].A great ellipse is an ellipse passing through two points on a spheroid and ha... | 677.169 | 1 |
QuoteAgain, pretty much lost on me. Looking at that web page, it doesn't say anything about absolute angle, it just shows one solution. Does absolute angle mean it's always the smaller of the two possible angles?Actually, I'm not sure whether you should bother explaining any of that. I'm willing to take your word for i... | 677.169 | 1 |
1st 2 sides are 16 each and they form angle = 60 degrees
So If u draw a diagonal the triangle that contains diagonal and these 2 sides will be equilateral, with sides 16.
Therefore area of Triangle = (sqrt3/4)*16*16 =64*sqrt3
For the other triangles sides are=16,14,10
Hence its area = 40sqrt3
Area of quad = sum of 2 tr... | 677.169 | 1 |
In graphical perspective, a vanishing point is a point in the picture plane Π that is determined by a line in space. Given the oculus or eye point O and a line L not parallel to Π, let M be the line through O and parallel to L. Then the vanishing point of L is the intersection of M and Π. Traditional linear drawings us... | 677.169 | 1 |
Hello: These are my boxes in one point perspective, and various boxes. Please comment on them. Question: I was looking at a small rectangular table today. It was below my eyeline and about 5 feet away. The dimensions were about 12" x 18", and as I looked at it, the side edges appeared to be wider apart at the back side... | 677.169 | 1 |
1) Is insufficient - This length doesn't help us except to tell us that BCD is not a right isosceles triangle. 2) x = 60. This means that Angle BCD = 180-60 =120. The remaining angle CBD = 180-120-30 = 30. This tells us that the triangle is isosceles. BC = CD = 6.
As it's DS question no need for actually finding the va... | 677.169 | 1 |
Name some phenomena that may be characterized by graphs of the shape you produced. With each phenomenon, describe in what units the horizontal and vertical measurements might be made. [Sample answers: Height of a rider on a Ferris wheel: vertical measurement of height, horizontal measurement of time. Wave in the water:... | 677.169 | 1 |
Of course, you don't have to -- I know you have better things to do than to teach mathematics to some Canadian who really should have been paying more attention in school. ;-)
(You can probably safely assume that I have an upper level of understanding of math, however -- I did take entry-level Calculus in school, and I... | 677.169 | 1 |
Hi! My son has been working independently on the Geometric Approach so I am somewhat lost when he comes to me with a question (even after I try to review the earlier lessons leading up to the problem). I am hopeful you will be able to catch me up so I can help him with the chart on Worksheet 9-1. I see that the chart's... | 677.169 | 1 |
Archimedes had reduced the problem of finding a regular hexagon to that of finding two points that divided a line segment into two mean proportionals. He then used a construction somewhat like that of the painting to find a line segment divided as desired. Crockett Johnson's papers include not only photocopies of the r... | 677.169 | 1 |
Toward the end of his life, Crockett Johnson took up the problem of constructing a regular seven-sided polygon or heptagon. This construction, as Gauss had demonstrated, requires more than a straight edge and compass. Crockett Johnson used compass and a straight edge with a unit length marked on it. Archimedes and Newt... | 677.169 | 1 |
Three very similar paintings in the Crockett Johnson collection are closely related to the Crockett Johnson described the construction of his isosceles triangle in the diagram reproduced. The horizontal line segment below the circle on the painting corresponds to unit length BF in the figure, and the triangle is ABF. T... | 677.169 | 1 |
Examples of Pythagorean triples include (3, 4, 5) and (5, 12, 13). There are infinitely many such triples,[2] and methods for generating such triples have been studied in many cultures, beginning with the Babylonians[3] and later ancient Greek, Chinese and Indian mathematicians.[4] The traditional interest in Pythagore... | 677.169 | 1 |
First, it takes an x coordinate for the center of the shape, not the edge. Second, it takes a y coordinate for the center of the shape. The third parameter is the radius of the shape. The fourth parameter describes the beginning angle in radians. The fifth parameter describes the ending angle in radians, and the sixth ... | 677.169 | 1 |
For convex two-dimensional shapes, the centroid can be found by balancing the shape on a smaller shape, such as the top of a narrow cylinder. The centroid occurs somewhere within the range of contact between the two shapes. In principle, progressively narrower cylinders can be used to find the centroid to arbitrary acc... | 677.169 | 1 |
If you don't know what a cross product is try this alternative method for evaluating the area of the triangle. Lets say we have a triangle whose vertices are lattice points. As shown in the picture below draw a vertical line from A so that this line intersects at .
Use coordinated of and to write down an equation of th... | 677.169 | 1 |
Notation
The following notations hold for all six trigonometric functions: sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). For brevity, only the sine case is given in the table.
Definitions
Periodicity, symmetry, and shifts
These are most easily shown from the unit circle:
Fo... | 677.169 | 1 |
(OMK 2008, Bongsu) Ali(OMK 2008, Bongsu) An equilateral triangle with sides 2 units is inscribed in a circle. Find the area of the circle.
(OMK 2008, Muda) Given that ABC is an isosceles triangle with angle ABC = angle ACB = 80 degrees. Two points E and F are on AB and AC, respectively, such that angle ABF = 10 degrees... | 677.169 | 1 |
Attached is a chart I made for connecting beams at right angles for the various orientations of the two beams.
For each of the three ways that two beams can meet at a right angle, the bold numbers indicate which connectors might be used for a rigid connection. The non-bold numbers can also make the connection but it wo... | 677.169 | 1 |
CIRCLE: Draw a large circle from top to bottom with your two index fingers (each finger draws half of the circle.
CENTER: Point both fingers forward together in the center of the circle you just drew.
RADIUS: From the "center" gesture, move one finger from the center to the edge of the circle (the other stays put).
DIA... | 677.169 | 1 |
A (convex) polytope is the convex hull of some finite set of points. Each polytope of dimensions d has as faces finitely many polytopes of dimensions 0 (vertices), 1 (edge), 2 (2-faces), · · · , d-1 (facets). Two-dimensional polytopes are usually called polygons, three-dimensional ones polyhedra. Two polytopes are said... | 677.169 | 1 |
No. |a + b| is not generally equal to |a| + |b|, although there are important relationships called the triangle inequality and the polarization identity relating the two expressions, and it is good to know the geometry of when they are equal.
You must first calculate the vector a + b by adding components, and then take... | 677.169 | 1 |
Tip #17 to Get a Top ACT Math Score
You couldn't ask for easier points to boost your score. Every ACT has a midpoint and/or distance question. If you don't know the formulas, you don't stand much chance. But if you memorize them, right here and now, you will gain points, guaranteed! In fact, take a few minutes right no... | 677.169 | 1 |
Pre-Calc I made a sketch, and y = |9x| consists of two lines first: y = 9x starting at the origin, and the second: y = -9x also starting in the origin, resulting in a graph looking like a V If I understand the question correctly, you now want the area of the triangle in the second ...
Tuesday, December 7, 2010 at 11:19... | 677.169 | 1 |
David Singmaster.Off the rails.The Weekend Telegraph (18 Feb 1989) xxiii&(25 Feb 1989) xxiii.Gives the Ripley and Always results and asks which is correct and whether the wrong one can be corrected -- cf Ripley above.
5 comments:
I got the same answer, but with a different approach. I put A at the origin and D on the p... | 677.169 | 1 |
Parallel postulate
The Parallel postulate, also called Euclid's Fifth Postulate on account of it being the fifth postulate in Euclid's Elements. It states:
If a line segment intersects two straight lines forming two interior angles on the same side sum to less than two right angles then the two lines segments, if exten... | 677.169 | 1 |
above is not working properly, review the anatomy for
the
course. You may need to update your browser or download a free media
plug-in.
To record direction, use north, east, south, west, northeast
etc. until you learn to use azimuth. Azimuth is
measured in degrees around the horizon (0 degrees when facing due
North to ... | 677.169 | 1 |
A characteristic of horizontal lines, such as the edges of an overhang, in reference to a point of interest, such as a point on a façade or the interior of a space. The profile angle is the altitude from the point of interest to the intersection of the horizontal line with the normal to it plane passing through the poi... | 677.169 | 1 |
Math (Geometry) Square ABCD has M as the midpoint of AB, N as the midpoint of BC, P as the midpoint of CD and Q as the midpoint of MP. If the area of AMNPDQ is 20, what is the area of ABCD?
Wednesday, May 1, 2013 at 6:42am by Hale
Math (Geometry) Square ABCD has M as the midpoint of AB, N as the midpoint of BC, P as th... | 677.169 | 1 |
Figure 3
In the right-angled triangle, we refer to the lengths of the three sides according to how they are placed in relation to the angle θθ. The side opposite to the right angle is labeled the hypotenuse, the side opposite θθ is labeled opposite, the side next to θθ is labeled adjacent. Note that the choice of non-9... | 677.169 | 1 |
Parallelogram?
Start with any general quadrilateral, and connect the midpoints of
consecutive sides, making an inscribed quadrilateral as in the diagram. That
inscribed quadrilateral, in the diagram, seems to be a parallelogram. Let me
conjecture that this inscribed quadrilateral is a parallelogram with half the
area o... | 677.169 | 1 |
In fact there are fifteen triangles with the same shape as (1,2,3) (including (1,2,3) itself). They are: (1,2,3), (2,3,4), (3,4,5), (4,5,6), (5,6,7), (6,7,8), (7,8,9), (8,9,10), (9,10,11), (10,11,12), (11,12,13), (12,13,14), (13,14,15), (1,14,15) and (1,2,15). Each of these triangles can be obtained from (1,2,3) by rot... | 677.169 | 1 |
Proving Diagonals Perpendicular
Date: 07/28/2003 at 09:10:05
From: Dan16etta
Subject: Perpendicular diagonals
Given the points a(-4,1), b(2,3), c (4,9) and d (-2,7), show that
quadrilateral abcd is a parallelogram with perpendicular diagonals.
Date: 07/28/2003 at 13:35:48
From: Doctor Barrus
Subject: Re: perpendicular ... | 677.169 | 1 |
Stated this way, compass and straightedgeconstructions appear to be a parlor game, rather than a serious practical problem.
The set of ratios constructible using compass and straightedge from such a set of ratios is precisely the smallest field containing the original ratios and closed under taking complex conjugates a... | 677.169 | 1 |
Question 45424
The angle of depression from the top of a building to apoint on the groudn is 32 deg 30'. How far is the point on the ground from the top of the building if the buildlng is 252 m high?
Draw the picture.
You have a right triangle with an acute angle of 32 deg 30' and
a side opposite the acute angle of len... | 677.169 | 1 |
In that moment a math student will saw the problem, figure out, and jump out of the window.
Avistew
05/14/2010, 07:17 am
That's not mathese at all. That's what I would have said too, if you hadn't used number and confused me. Something doesn't qualify as mathese if I can understand it :p
EDIT: by the way, my whole reas... | 677.169 | 1 |
How to find Euler's angles?
How to find Euler's angles?
I have read about Euler's angles and matrices, including zxz,zyz, etc . I am not obliged to use a specific rotation but rather I want to figure out what angles I need to use for alpha,theta, gamma in the specific matrix. For example, I have a vector from the centr... | 677.169 | 1 |
Perpendicular
Perpendicular is a geometric term that may be used as a noun or adjective. The fundamental meanings pertain to the position of straight lines relative to one another, in which two lines are positioned at an angle of ninety degrees, which is defined as a right angle. Any two lines in Euclidean space which ... | 677.169 | 1 |
In this lesson we will look at the basic definition and properties of the right angled triangle.
Right Angled Triangle
'Right Angled Triangle' is a triangle with one internal angle equal to 90 degrees (right angle).
The side opposite to the right angle is called "hypotenuse" and hypotenuse is the longest
side of the ri... | 677.169 | 1 |
Since the sum on angles in triangle is 180 then the ratio of degrees is 180/9 = 20
2*20:3*20:4*20 = 40:60:80
sufficient
statement II
In order for all the angles of the triangle ABC be smaller than 90 degrees you cannot have a right angle. If you did then you could express the ratio of this triangle sides by the Pythago... | 677.169 | 1 |
Then, since BC is to GH as GH is to CF, and, if three straight lines are proportional, then the first is to the third as the figure on the first is to the similar and similarly situated figure described on the second, therefore BC is to CF as the triangle ABC is to the triangle KGH.
Therefore also the triangle ABC is t... | 677.169 | 1 |
Vectors- How do you number to use to multiply by cos and sin? 257cos198? how do you get 198?
Johnny asked
An airplane flies 257 km in a straight line in a direction of 18.0 degrees North of West. It then changes direction and flies in a straight line for 233 km in a direction of 78.0 degrees South of West. Find the tot... | 677.169 | 1 |
A circle is a special form of this... I won't show it again.
A straight line - the single body problem again.
Two straight lines - parallel this time. This is something new.
No intersection at all. The kōan of conics.
This is new, but whether it is something is a question I will not attempt to address.
Now for the proo... | 677.169 | 1 |
I used two equations and two unknowns and came up with x =50 degrees and y = 40 degrees. that doesn't work when i use y=40 in the second picture with the angle DBC = (y-50)degrees. This would make that angle a negative number. Click here to see answer by ankor@dixie-net.com(15624)
Question 213077: Another unit of angle... | 677.169 | 1 |
In the figure above, s is the length of the side
opposite the 3, so s = 3.
• Square
A square is a rectangle with 4 equal sides.
If PQRS is a square, all sides are the same length
as QR. The perimeter of a square is equal to four
times the length of one side.
• Trapezoid
A trapezoid is a quadrilateral with one pair of
p... | 677.169 | 1 |
Ellipse #9
This is the same method as Ellipse #6, and
shows that an entire family of ellipses can be drawn with a spirograph. Notice
that the endpoints of the line move in straight lines, and the midpoint moves
in a circle. The outer boundary of this family of ellipses is called an
Astroid.
The above Java animation was... | 677.169 | 1 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.