text stringlengths 6 976k | token_count float64 677 677 | cluster_id int64 1 1 |
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A triangle has sides of length 6 cm and 8 cm. The angle between the two known sides is 75°. Find the length of the unknown side. [c ≈ 8.669104433…]
A triangle has sides of length 14, 19, and 27 units. What is the area of each defect on the two smaller sides? [The area of the square on the largest side is 272 = 729 squa... | 677.169 | 1 |
I do not think it is likely because it is impossible to trisect an angle exactly in geometry. Since you can not do that I do not know how you could make a construction of right triangles that would lead to a triangle with exactly 1/3 of the original angle in it.
Question: What is the relationship between trisecting an... | 677.169 | 1 |
You can put this solution on YOUR website! Your question is a bit confusing, but here's some about the coordinate systems:
Cartesian are square like. Pick an arbitrary point and call that 0,0,0. From there, you can go left / right, up / down, or front / back. The amount of each would be the directions of x , y , z. Gen... | 677.169 | 1 |
Rhombohedral
In crystallography, the rhombohedral (or trigonal) crystal system is one of the 7 lattice point groups. A crystal system is described by three basis vectors. In the rhombohedral system, the crystal is described by vectors of equal length, all three of which are not mutually orthogonal. The rhombohedral sys... | 677.169 | 1 |
Tuesday, May 10, 2011
Constructive Triangles
I am in the process of reviewing all the lessons in each of my albums for the upcoming Oral Exams which complete my Montessori training with the Montgomery Montessori Institute. This is no small task, and each night the studying lasts a couple of hours (at which point I can ... | 677.169 | 1 |
that, but the coordinates 0, 0 refer to "top left" as well. Think of a clock, or a box. You start at 12:00 then move to 3:00 then 6:00 then 9:00 and back to 12. With a box, you normally start in the upper left hand corner, draw a line to the right, then go down, stop and draw a line to the left, and then go back up aga... | 677.169 | 1 |
Vectors Geometry
Chapter 1
Euclidean Geometry and Vectors
1.1 Euclidean Geometry
1.1.1 The Postulates of Euclid
The two Greek roots in the word geometry, geo and metron, mean "earth"
and "a measure," respectively, and until the early 19th century the de-
velopment of this mathematical discipline relied exclusively on o... | 677.169 | 1 |
r = x ˆ + y + z κ;
ı (1.1.4)
the numbers (x, y, z) are called the coordinates of the point P with respect
ı ˆ
to the cartesian coordinate system formed by the lines along ˆ, , and
ˆ ˆ ˆ
κ. In the plane of ˆ and , the vectors x ˆ+y form a two-dimensional vector
ı ı
space R2 . With some abuse of notation, we someti... | 677.169 | 1 |
where θ is the angle between u and v, 0 ≤ θ ≤ π (see Figure 1.2.1), and
the notation u . v means the usual product of two numbers. If u = 0
or v = 0, then u · v = 0.
v# v w
....
... .................θ
.. θ .....
.. ..
..
.
.. E . E
u u
Fig. 1.2.1 Angle Between Two Vectors
Alternative names for the inner product are dot... | 677.169 | 1 |
In other words, the scalar triple product does not change under cyclic per-
mutation of the vectors or when · and × symbols are switched.
C
Exercise 1.2.15. Verify that the ordered triplet of non-zero vectors u, v, w
is a right-handed triad if and only if (u, v, w) > 0.
Recall that v × w = v · w sin θ is the area of th... | 677.169 | 1 |
Trigonometry Basics Test - Sin, Cos, Tan
Choose the best answer. Trigonometric ratios are rounded to the nearest thousandth.
1. for which of the following triangles?
2. for which of the following triangles?
3. for which of the following triangles?
4. Which trigonometric function can equal or be greater than 1.000?
Sine... | 677.169 | 1 |
10 – PYTHAGORA not a distribution technique but probably the most useful piece of Math of all times :) this allows us to know the distance between 2 points, the angle between them and to deduce a whole lot of measures, distances, ratios aso
11 – POISSON DISK distribution, using the distance between 2 circles this allow... | 677.169 | 1 |
KneadToKnow
02-06-2008, 10:24 AM
Any opinions? Thanks!
The teacher is only thinking of corners by thinking of the corners of a room. You're thinking more analytically and I encourage you to teach your child to do so as well while also helping her to understand that some people won't be able to see these things.
oldboy
... | 677.169 | 1 |
Question 535976: a ladder 9m long is placed against a wall 2m away from its base. what is the height reached by the ladder?
find the approximate distance that will be saved by walking diagonally across a field 450m by 250m instead of walking along the two adjacent sides.
A flagpole is to be made firm. how much wire wil... | 677.169 | 1 |
Question 462758: 1.The measure of an angle is 30 degrees more than twice the measure of its suppement.Find the measures of the angles.
2.Find the measures of two supplementary angles if the measure of one angle is 5 less than 4 times the measure of the other.
3.What are the measures of two complementary angles if the ... | 677.169 | 1 |
Rotation Tesselation.
Using 1cm dotty paper, poupils are asked to doodle at design in a quarter of a square. This design is then traced and rotated into each other quarter. Finally, the whole thing is rotated around. When coloured, it makes a very beautiful and weird looking tesselation!
Excellent for looking at rotati... | 677.169 | 1 |
I have the Cartesian coordinates of the hypotenuse 'corners' in a right angle triangle. I also have the length of the sides of the triangle. What is the method of determining the coordinates of the third vertex where the opposite & adjacent sides meet.
because it doesn't appear that you worked on the problem before ask... | 677.169 | 1 |
Stewart's Theorem
A theorem in planar Euclidean geometry that gives an algebraic relationship between sides of a triangle and segments of sides when cevians divide a triangle in half. The theorem was discovered by the Scottish mathematician and minister, Matthew Stewart (1717/19 - 1785).
A cevian is a line segment whos... | 677.169 | 1 |
Subject: Mathematics (8 - 12) Title: Quadrilaterals Description: This is an inquiry lesson used to review Algebra 1 objectives by applying them to geometry concepts. Students explore the properties of quadrilaterals and classify them by definition. This lesson can be use in geometry classes. Students in geometry classe... | 677.169 | 1 |
how you know all the dimensions and angles based on how you folded the paper.
That is, you should analyze each step of the folding and discuss what it tells
you about the geometry of the crease lines.
For the flat-foldable analysis: For this analysis you should discuss how
each of our theorems about flat foldability ar... | 677.169 | 1 |
Scaling the Trail Leap Connections
Teacher-Made Supplemental
Resources
Reading Strategies
Cut Down to Size at High Noon: A Math Adventure, by Scott Sundby 11: Similar Triangles (LCC Unit 2 Activity 8)
(GLEs: 7, 29)
Materials List: 6 drinking straws for each pair of students, scissors, pencils, paper, math learning
... | 677.169 | 1 |
The common nine-point circle four orthocentric points. The radius of the common nine-point circle is the distance from the nine-point center to the midpoint of any of the six connectors that join any pair of orthocentric points through which the common nine-point circle passes. The nine-point circle also passes through... | 677.169 | 1 |
Short description: The students are presented with real life situations where trigonometry is used.
Duration of lesson(s): 1 lesson
Grade level(s) and/or target group(s):Students studying trigonometry
Subject(s):Trigonometry
Technologies used:When these problems were presented, a smart board was used to display the dia... | 677.169 | 1 |
And since angle ABF is subtended by the diameter and is therefore right, the side of the pentagon is calculated by an even simpler route:
Based on his circle of diameter 200000 units, Copernicus provides accurate numerical values for the four pentagon related chords corresponding to these angles:
"Since the side of the... | 677.169 | 1 |
the sun was hitting the bottom of one well while it was shining on the sides of the other. measuring the difference in angles from vertical, he was able to conclude that the earth was round and even came up with an acceptable estimate of the earth's diameter (google erathosthenes' experiment.)
but i want a reverse expe... | 677.169 | 1 |
Find a Missing Leg
Explanation
The legs of a right triangle are the sides that are adjacent to its right angle. Sometimes we have problems that ask us to find a missing length of one of these legs. We can use the Pythagorean theorem to find a missing leg of a triangle, but only if we know the length measure of the hypo... | 677.169 | 1 |
In the other limiting case, an entire pizza has its center of mass right at the tip (i.e. center), so
.
To investigate intermediate cases, we start with a slice of angle and imagine cutting it in half lengthwise, creating two skinny pieces of angle . These have their own centers of mass at .
The center of mass of the b... | 677.169 | 1 |
The similarity method for calculating fractal dimension is great if you have a fractal
composed of a certain number of identical versions of itself. However, try using it for
the coast of Britain. Thatís impossible because all lines there have different sizes and
require different magnifications. And we wouldnít sugges... | 677.169 | 1 |
Here various graphs are investigated. The classification is sometimes arbitrary, since a graph may arise as a result of different constructions (stellation, reticulation, truncation, glueing etc.).
Some occuring mathematical terms will be explained later in subsequent chapters.
Tetrahedron Stellation I (Deltoid)
This g... | 677.169 | 1 |
Based on his circle of diameter 200000 units and already established chords of pentagon, hexagon and triangle the calculation effected by Copernicus would have been:
A small rounding error is evident in the result but the corresponding entry (in the Copernican table of half chords ) of 10453 units against 6 degrees is ... | 677.169 | 1 |
Pages
Sunday, February 5, 2012
VFC: Quadrilaterals
Here is a Virtual Filing Cabinet for resources concerning Quadrilaterals.. This is part of an ongoing experiment in how to better share online teaching resources. If you like this post, then make your own post for a particular topic.
What am I missing here? Point me to... | 677.169 | 1 |
Most of the time student these two points one is that "a square is a rectangle, but it's also a rhombus. They are all parallelograms, though, and so what's true of parallelograms is true of them as well" and another is that "students need to see parallel lines with a transversal even when the sides of the quadrilateral... | 677.169 | 1 |
Graphics Trick: Polygon Area
The area of a 2D triangle is easy, it's just half the magnitude of the cross product of two edges where you assume the z component is 0:
|cross((v1−v0),(v2−v0))|
The sign of the cross product tells you if the triangle is front or back facing (counter clockwise or clockwise). If you multiply... | 677.169 | 1 |
Question 149920: Could I please get some help with the following problem:
there is a diagram of a triangle
one side is = 1, another side is = 4 and there is 100 degree angle
I am looking for the value of side C
thank you,
RF Click here to see answer by stanbon(57239)
Question 149918: Sketch one complete period of the g... | 677.169 | 1 |
[65] If you take a square and look at it from some point in space it looks like a quadrilateral. What are the
possible shapes of this quadrilateral?
[66] A regular heptagon (= 7-sided polygon with all angles equal and all sides equal) is randomly placed in
the plane. What is the probability that an observer can see 4 s... | 677.169 | 1 |
This question came from some of the PR practice stuff. In breaking the hexagon into 6 equilateral triangles, I get an area for each triangle to be r root 3 * r (= r^2 root 3), which is then multiplied by 6, for the number of triangles..... But PR says this is not the correct answer???
Curly05 wrote:
Should be broken up... | 677.169 | 1 |
pythagorean triples
The Pythagorean Theorem is a mathematical formula used to determine the length of a side of a right triangle when only two sides are known. Our Pythagorean Theorem calculator is 100% free and guaranteed to save you time and effort. With our Pythagorean Theorem calculator with variables A2 + B2 = C2 ... | 677.169 | 1 |
Can't they be on the same line? 3-4-5 triangle is a very special case. You are doing wrong I think.
I agree this is might be a special case and this is exactly what I am want to know where am I going wrong.
Anyway the points can't be on the same line because as per the 1st statement Z is to left of X and Y is to right ... | 677.169 | 1 |
(mathematics) An endofunction whose square is equal to the identity function; a function equal to its inverse.
irrational
adjective ((compar) more irrational, (superl) most irrational)
Not rational; unfounded or nonsensical.
an irrational decision
(mathematics) (no comparative or superlative) Of a real number, that can... | 677.169 | 1 |
Angle alpha is the angle of longitude of the observer (how far north, or south, of the equator they are). For this example, I will be using a longitude of 50 degrees north (northern France/southern England).
The angle at B is 90 degrees (the angle between the radius from A and the horizon) plus the angle of elevation, ... | 677.169 | 1 |
The point where the axes meet is the common origin of the two number lines and is simply called the origin. It is often labeled O and if so then the axes are called Ox and Oy. A plane with x and y-axes defined is often referred to as the Cartesian plane or xy plane. The value of x is called the x-coordinate or abscissa... | 677.169 | 1 |
A glide reflection is the composition of a reflection across a line followed by a translation in the direction of that line. It can be seen that the order of these operations does not matter (the translation can come first, followed by the reflection).
[edit] General matrix form of the transformations
These Euclidean t... | 677.169 | 1 |
The usual way of orienting the axes, with the positive x-axis pointing right and the positive y-axis pointing up (and the x-axis being the "first" and the y-axis the "second" axis) is considered the positive or standard orientation, also called the right-handed orientation.
A commonly used mnemonic for defining the pos... | 677.169 | 1 |
Related Products
Catenary defines the shape of a line strung between two points. It is not the same math as a parabolic curve. I am looking for a program that will do catenary calculations to determine the change in sag of a line if the line is longer or shorter and takes into account the different elevations of the en... | 677.169 | 1 |
AB = BC = AC => ABC is an equilateral triangle=> angle BAC is 60 degree
that means angle DAC = 60 degree
As per the rule - angle made by the arc on center is twice the angle made by the same arc on the circumference. Here the angle DAC made by the arc DC on the center is 60 degree. So the DBC = 30.
As angle ABC = 60 de... | 677.169 | 1 |
In this lively introduction to shapes and polygons, a bored triangle is turned into a quadrilateral after a visit to the shapeshifter. Delighted with his new career opportunities--as a TV screen and a picture frame--he decides the more angles the better, until an accident teaches him a lesson. Includes special teaching... | 677.169 | 1 |
What are an Oval and an Egg Curve? There is no clear definion. Mostly you define:
......
An oval is a closed plane line, which is like an ellipse or like the
shape of the egg of a hen.
An egg curve only is the border line of a hen egg.
The hen egg is smaller at one end and has only one symmetry axis.
The oval and the e... | 677.169 | 1 |
We have four rods of equal lengths hinged at their endpoints to
form a rhombus ABCD. Keeping AB fixed we allow CD to take all
possible positions in the plane. What is the locus (or path) of the
point D?
Four rods of equal length are hinged at their endpoints to form a
rhombus. The diagonals meet at X. One edge is fixed... | 677.169 | 1 |
There are
two pictures to keep in mind here, the generic right triangle:
First of
all, all physical angles have some size. We cannot visualize
an angle with negative physical size. They do not exist in anything
sufficiently similar to the physical space we live in.
However,
(especially when dealing with the unit circle... | 677.169 | 1 |
Since 30°
is the complementary angle to 60°, we also have computed sin(30°)
and cos(30°).
How
does "wrapping the real number line around the unit circle"
work?
The unit
circle has a circumference of 2p. "Thus", all trig functions
will have the same value when evaluated 2p radians apart. We
say that all trig functions h... | 677.169 | 1 |
3D Shape Properties. Game.
A simple poster with a range of shapes listing their properties. Also, a "cut-out-and-use-as-you-want" sheet with outlined images of various 3D shapes. I've used the first in an introductory lesson and the cut-out sheet for a range of starter activities.
Very helpful resource, thank you. By t... | 677.169 | 1 |
7 is such a sharp number, pushed in between the sensuous curves of 6 and 8. All awkward angles and points, 7 is not a graceful number. It's odd. And sticks out in all the wrong places. 6 and 8 bend like dancers, Swaying or flowing as natural as the breeze. And poor 7 sandwiched in between them, like a middle school kid... | 677.169 | 1 |
Checkpoint
- Course 2, Unit 2
Patterns of Location, Shape, and Size
In each unit, there is a final lesson and Checkpoint that helps students
summarize the key ideas in the unit. The final Checkpoint will generally
be discussed in class, with the teacher facilitating the summarizing,
and students making notes in their M... | 677.169 | 1 |
e)If it is a star, then it is a small pinprick of light in the night sky.
f) A really cool sneaker.
Question 65974: These two definationes are agreed upon:
a vertical lline is a line containing the center of the earth
a horizontal line is a line perpendicular to some vertical line
Which of the following would be true:
... | 677.169 | 1 |
Since the earliest times, mankind has employed the simple geometric forms of straight line and circle, in art, architecture, and mathematics. Originally marked out by eye and later using a stretched cord, in time these came to be made with the simple tools of ruler and compass. This valuable reference book introduces t... | 677.169 | 1 |
Physics suppose that the separation between speakers A and B is 5.80 m and the speakers are vibrating in phase. They are playing identical 135 Hz tones, and the speed of sound is 343 m/s. What is the largest possible distance between speaker B and the observer at C, such that he ...
Tuesday, May 1, 2007 at 9:05pm by Ma... | 677.169 | 1 |
Showing 1 comment
A Parallelogram is a quadrilateral which has two parallel pair of sides.
parallelograms are:
Properties of
--- The opposite sides of a parallelogram are equal in length.
--- The opposite angles are ...
First we will see what the meaning of antiderivation is? An antiderivative of a
function f can be th... | 677.169 | 1 |
Since its a regular polygon its one vertex will be at the mid point of the side of the square by symmetry.
Therefore,
1/4+((1-x)/2)^2=x^2
x= (sqrt(28)-2)/6
if we anlyze dis problem then we are getting four 30-60-90 triangles on four peripherals so as we know 1:2:rt3 ratios we will end up wid 1/rt3 as the side of the he... | 677.169 | 1 |
A hemisphere of radius 8 is inscribed in a cylinder of radius 8 and height 8. The figure shows top and side views of the hemisphere, the cylinder, and a cone whose radius and height are both 8, and whose base and vertex are coplanar with the bases of the cylinder.
Consider that part of the cylinder that is outside (abo... | 677.169 | 1 |
The figure at right shows an outermost 1 × 1 square, within which appears an inscribed circle, within which appears an inscribed square, within which appears another inscribed circle, within which appears another inscribed square. Although the figure does not show it, this process can be continued indefinitely. Let L1 ... | 677.169 | 1 |
Two circles of radii 9 and 17 centimetres are enclosed within a
rectangle with one side of length 50 cm. The two circles touch each
other, and each touches two adjacent sides of the rectangle. Find the
perimeter of the rectangle.
Given a 3,4,5 triangle, and inside it, inscribed, two circles of equal
radii. Both circles... | 677.169 | 1 |
Its C....its necessary to know the angle to be able to draw a circle around a quadrilateral.The sides of a quadrilateral may be equal but if the angles of the sides are obtuse or acute we can't draw a circle.
Vivek.
_________________
"Start By Doing What Is Necessary ,Then What Is Possible & Suddenly You Will Realise T... | 677.169 | 1 |
to follow, and hundreds of others have been given. Here's a nice one given by
Thabit ibn-Qurra (826-901).
Proof: Start with the right triangle ABC with right angle at C. Draw a square
on the hypotenuse AB, and translate the original triangle ABC along this square
to get a congruent triangle A'B'C' so that its hypotenus... | 677.169 | 1 |
Because the two triangles are congruent, this means that their corresponding parts are equal. So their two longer legs are equal which means that AB = DE = 24 cm
This means that AB = 24 cm
Also, their two hypotenuses are equal. So AC = DF = 25 cm which means that DF = 25 cm
----------------------------
Also, congruent ... | 677.169 | 1 |
No Need to change the TriangleError code for either challenge. You just need to check for invalid triangles and raise the error if the triangle isn't.
def triangle(a, b, c)
if a==0 && b==0 && c==0
raise TriangleError, "This isn't a triangle"
end
if a <0 or b < 0 or c <0
raise TriangleError, "Negative length - thats not... | 677.169 | 1 |
reflection with mirrors
reflection with mirrors
You stand 1.80 m in front of a wall and gaze downward at a small vertical mirror mounted on it. In this mirror you can see the reflection of your shoes. If your eyes are 1.95 m above your feet, through what angle should the mirror be tilted for you to see your eyes reflec... | 677.169 | 1 |
Oblique projection
Graphical projection is a protocol by which an image of a three-dimensional object is projected onto a planar surface without the aid of mathematical calculation, used in technical drawing.- Overview :...
Graphical projection is a protocol by which an image of a three-dimensional object is projected ... | 677.169 | 1 |
Looking at functions via multiple representations (graphical, numeric, algebraic, verbal) has always served me well. Some representations shine a different light on the function. Putting 3.5 into the form 7/2, a hint that Dan gave, opened up a new door for making sense of the shape.
I played with the different applets ... | 677.169 | 1 |
Given three points, if they are non-collinear, there are three pairs of parallel lines passing through them – choose two to define one line, and the third for the parallel line to pass through, by the parallel.
Given two distinct points, there is a unique double line through them.
Degenerate ellipse with semiminor axis... | 677.169 | 1 |
No...Angle AOB and BOC...are congruent.....So how do you find the answer?? Thanks
stapel
09-10-2005, 06:20 PM
Yes, AOB and BOC are congruent. And since you say that OC divides BOD "in half", BOC and COD are also congruent.
Eliz.
ToOtSiE_PoP
09-10-2005, 06:46 PM
Oh Okay...Duh..So can you please explain how you got this ... | 677.169 | 1 |
09-10-2005, 08:14 PM
You said that BOD was split in half to form BOC and COD. Don't they have the same angle measure then, since they're each one half of the original angle?
And you said that BOD was a right angle. What is the measure of a right angle? What is half of that?
Eliz.
ToOtSiE_PoP
09-10-2005, 08:22 PM
45 deg... | 677.169 | 1 |
As a concrete example, consider a sphere of radius a, where x = a sin u cos v, y = a sin u sin v, z = a cos u. Here, u and v are the polar angles. In this case, it is easy to see that the normal vector is (sin u cos v, sin u sin v, cos u). The first derivatives are xu = (a cos u cos v, a cos u sin v, -a sin u) and xv =... | 677.169 | 1 |
5/7 Muilti Purpose Ruler
The circle is divided by 72 degree lines into 5 equal segments (yellow lines) and by 52 degree lines into 7 equal segments (blue lines). Repositioning marks enable further division of the circle. At each intersection of lines and circles is a small hole for marking with a fine tip marker.
Ques... | 677.169 | 1 |
falls back to earth, the curved path it follows is a
parabola. It is an open plane curve formed by the
intersection of a cone with a plane parallel to its side.
Hyperbola: It is the curve
produced when a cone is cut by a plane that makes a larger
angle with the base than the side of the cone does.
Mathematics Q.
What i... | 677.169 | 1 |
Probability and Geometry
The activity and two discussions of this lesson connect probability and geometry. The Polyhedra discussion leads to platonic solids, and the Probability and Geometry discussion leads to connections between angles, areas and probability. The subtle difference between defining probability by coun... | 677.169 | 1 |
In the Pentomino problem, we worked with rearranging the shapes on a two-dimensional plane, and we needed to consider how the shapes were alike or different. In this section, we now consider a third dimension of depth as we look for the various possibilities.
The mathematical concepts include visualizing the relationsh... | 677.169 | 1 |
Question 32750
Since you are given two sides of the triangle and you know that neither of the two are the hypotenuse.
You can say that either a=3 and b=4 or the other way where a=4 and b=3. Then by using the pythagorean theorem which states a^2+b^2=c^2 you will be able to get your answer.
So
(3)^2+(4)^2=c^2
9+16=c^2
25... | 677.169 | 1 |
Vectors from 444
We assume vector addition and multiplication of a vector by a scalar (i.e.,
a real number) are well-understood.
Notation: Let I, J, K be (1, 0, 0), (0, 1, 0), (0, 0, 1).
Center of Mass for equal masses
The center of mass of a set of points (with equal masses at each point) is
the mean, or average. Thus... | 677.169 | 1 |
Triangle An emblem of the triad or three-in-one, expressing more than the three dots alone: the points, lines, and the whole figure give a septenate composed of two triads and a monad. The triangle also symbolizes twin rays proceeding from a central point, and when the other ends of these lines are joined, the base lin... | 677.169 | 1 |
Concurrence Ml
concurrent, lines, geometry and triangle
CONCURRENCE (ML. concurrentia, con currence, from concurrcre, to run together, from con-, together + currcrc. to run) AND COL LINEARITY (from Lat. corn-, together + linca, line). If several lines have a point in common they arc said to be concurrent. The common po... | 677.169 | 1 |
Loci: Convergence
Mathematical Treasures
by Frank J. Swetz and Victor J. Katz
Charles Bossut's Traite elementairede geometrie
This is the title page of the Traité élémentaire de géométrie et de la maniere d'appliquer l'algébre a la géométrie (1775), written by Charles Bossut (1730-1814). This work was one of many texts... | 677.169 | 1 |
i am confused in one problem and please help me,i will give picture from problem below
and question says : $AB$ is a diameter of the circle. All triangles above the diameter in the diagram are equal in area. All triangles below the diameter are equal in area.compare total area of triangles above $AB$ and total are belo... | 677.169 | 1 |
Did you try the experiment? If you did not, go do the experiment - we will wait for you!
Welcome back. Did you find a pattern? Good!
OK, here is the pattern between the angle of the mirrors in the Mirror Multiplier and the number of candles you see.
A full circle has a measure of 360 degrees. A single mirror has an ang... | 677.169 | 1 |
My Geometry Lesson Today
We talked about a family today, the Quadrilateral family. It starts off with Big Momma. Big Momma had 4 sides. Big Momma was ugly and boring, so her husband left her. But, before he left her they had 3 babies. Parallelogram, Trapezoid, and Kite. Kite was ugly like her mom. She had 0 pairs of pa... | 677.169 | 1 |
FREE Lesson Plan - 1st of 3 Free Items
Estimating Angles, Area, and Length
Grade Levels: 3 - 7
Objective
Math students in middle school will use estimation to approximate values, angle, and area measurements of a triangle.
Materials
paper
pencil
string
Procedure
Demonstration
Explain to students that they are going to ... | 677.169 | 1 |
Polygons/336504: Suppose that the interior angles of a convex pentagon are five consecutive numbers. What is the measure of the largest angle? 1 solutions Answer 241203 by edjones(7569) on 2010-08-30 00:55:27 (Show Source):
You can put this solution on YOUR website! 180(n-2)=sum of the interior angles of a polygon. n=n... | 677.169 | 1 |
A Little Bit of Trigonometry
Some tasks.
1. Measure side a and side c, and compute a/c. Use a protractor to measure angle A,
and find sin A with a calculator. Does a/c = sin A?
2. Measure side b, and compute b/c. Find cos A with a calculator. Are they
the same?
3. Do the same for angle B: measure b, and compute b/c. Me... | 677.169 | 1 |
I'll refer to this image:
Red vector (named direction) is direction
Two blue vectors represent range where I want to do something
α (alpha) is "falloff" of direction
Purple vector (v) is the vector which I need to check if it's between two blues.
In other words, I need to check if (v) is between (direction-α) and (dire... | 677.169 | 1 |
Quadratic_Equations/417959: One side of a triangle is half the longest side. The third side is 8 meters less than the longest side. The perimeter is 42 meters. Find all three sides. (Enter your answers from smallest to largest.)
? meters
? meters
? meters 1 solutions Answer 292675 by ewatrrr(10682) on 2011-03-06 11:50:... | 677.169 | 1 |
When the midpoints of the sides of a Quadrilateral are joined,
another quadrilateral results. using the diagram helps to see what is
special about this new quadrilateral. Try the Quadrilateral applet for yourself.
The Pythagorean Theorem can be proved in many ways. This
diagram uses shears to show a version of Euclid's... | 677.169 | 1 |
New from the Blog
Geom(ag)etry: Dodecahedrons and Icosahedrons
What follows is an explanation very similar to the one about Cubes and Octahedrons. We are now starting to see how two other Platonic solids are tied together: the Dodecahedron with its 12 pentagonal faces and Icosahedron made up by 20 equilateral triangles... | 677.169 | 1 |
Since the center of each square is the center of the sphere, therefore two sides, EF and FG, along with the one diameter EG of the octahedron form a 45°-45°-90° triangle. Thus, the square on the diameter of the sphere is twice the square on the side of the octahedron.
Coordinates for the vertices of the octahedron
If t... | 677.169 | 1 |
Second equation is x= 2y + 100
You can put this solution on YOUR website! Let M = Mary's age
then because "Susan is six years older than Mary."
M+6 = Susan's age
.
From:"She is twicw as old as Mary"
M+6 = 2M
Solve for M by subtracting M from both sides:
M+6-M = 2M-M
6 years old = M (Mary's age)
.
Susan's age:
M+6 = 6+6... | 677.169 | 1 |
Course Title: Geometry
Grade: 8
Credits: 1
A. Course Description:
Geometry is a survey of Geometry, emphasizing the history of mathematics and proofs.
B. Course Objectives/Methods:
Geometry is a broad overview of the study of shape. It includes a general history of mathematics, the study of line, angle, and a variety o... | 677.169 | 1 |
From the slope and the coordinates of one of the points, we can get the equation of the line. If the coordinates of the third point satisfy that equation, the third point lies on that same line.
The slope of the line connecting (a,0) to (0,b) is
Since the y-intercept is at (0,b), b is the intercept, and we can write as... | 677.169 | 1 |
mathAngle-angle-side congruence between two (or more) triangles. Congruent triangles have sides and angles of identical measure.
Abscissa
The horizontal axis, or the first coordinate in an ordered pair.
Absolute Maximum
The highest point on a graph, especially over a specified domain. It is the greatest value of f(x) o... | 677.169 | 1 |
A function is considered Continuous if its graph has no gaps, no holes, no steps, and no cusps or discontinuities.
Continuous CompoundingContinuous Function
When the graph of a function has no holes, no gaps, no steps, or no discontinuities, then it is considered Continuous. It may have cusps.
Continuously Differentiab... | 677.169 | 1 |
A planar figure that neither crosses itself or contains a gap is a Simple Closed Curve; note that a curve can be "straight" according to the mathematicians.
A number associated with a line graphed in a plane, Slope is the ratio of rise over run, an indication of the steepness of the line. We may write a line as y = mx ... | 677.169 | 1 |
IIT-JEE 2010 Paper I Solutions
Join Us
This section contains 6 multiple choice questions. Each question has 4 choices (1), (2), (3) and (4), out of which ONLY ONE is correct.
1. (1) (2) x (3) (4)
Ans : (3)
2. Consider the two curves C1 : y2 = 4x C2 : x2 + y2 - 6x + 1 = 0 Then, (1) C1 and C2 touch each other only at one... | 677.169 | 1 |
Stage: 3 Challenge Level:
Do you know how to find the area of a triangle? You can count the
squares. What happens if we turn the triangle on end? Press the
button and see. Try counting the number of units in the triangle
now. . . .
Stage: 4 and 5Clearly if a, b and c are the lengths of the sides of a triangle and the t... | 677.169 | 1 |
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