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Proofs
Proof means sufficient evidence to establish the truth of something. It is obtained from deductive reasoning, rather than from empirical arguments. Proof must show that a statement is true in all cases, without a single exception.
1,294 Questions
Not in general. Imagine making a pentagon out of sticks connected with hinges for the vertexes. You can bend it all around, making pentagons that are not congruent to the original, even though the sides remain the same length.
A similar triangle would be rigid, even if the corners were connected with hinges.
What did the first roman fraction used look like?
It used to look like a coin. The basic unit was an assarius, assis or as, which was a coin that was divided up into multiples of 1/12ths, where 1/12th of an assis was an uncia (from which we derive the words "inch" and "ounce"), before being divided further.
The first fraction is more than likely to have been the semis, or half (1/2), since it is the simplest fraction of all.
The names of each fraction also became the names for the coins themselves:
1/12 of an assis was an uncia, denoted by a single dot: •
2/12 (1/6) of an assis was a sextans, denoted by ••
3/12 (1/4) of an assis was a quadrans, denoted by •••
4/12 (1/3) of an assis was a triens , denoted by ••••
5/12 of an assis was a quincunx, denoted by •••••
6/12 (1/2) of an assis was a semis , denoted by the letter S. (1/2 an as)
7/12 of an assis was a septunx , denoted by S•
8/12 (2/3) of an assis was a bes, denoted by S••
9/12 (3/4) of an assis was a dodrans, denoted by S•••
10/12 (5/6) of an assis was a dextans, denoted by S••••
11/12 of an assis was a deunx, denoted by S•••••
The dots themselves weren't necessarily lined up; they could be spread out, a bit like the dots on dominos. However, other common fractions in the duodecimal system were:
- 1/8, sescuncia, Є•.
- 1/24, semuncia Є.
- 1/36, binae sextulae, ƧƧ.
- 1/48, sicilicus, Ɔ.
- 1/72 sextula, Ƨ.
- 1/144, dimidia sextula, Ƨ.
- 1/288, scripulum, ℈.
- 1/1728, siliqua, ».
Why personality is not a theorem to be proven but a postulate to be accepted?
Personality is subjective and so cannot be proven. However, it should not be accepted without challenge either.
How many 4 letter codes are there if letters are not repeated?
If letters cannot be repeated, then there are 26 options for the first letter. There are then 25 options for the second letter. There are then 24 options for the third letter, and 23 for the fourth. This means that in total there are 26x25x24x23 options for the code. 26x25x24x23 = 358,800. Thus, there are 358,800 possible 4 letter codes.
When do you use law of sines and law of cos sines?
Use Law of Sines if you know:
- Two angle measures and any side length or
- Two side lengths and a non-included angle measure.
Use Law of Cosines if you know:
- Two side lengths and the included angle measure or
- Three side lengths.
What is the contribution of Indian mathematicians in the field of pie?
Many Indian mathematicians have made lot of effort on pi.
1)Madhava of Sangamagrama has also made huge contributions on pi.
He was able to estimate π as 3.14159265359, which is correct to 11 decimal places.
2)In the beginning of the 20th century, the Indian mathematician
Srinivasa Ramanujan found many new formulas for pi.
This formula was used to set several
π computing records in the end of the 1980s, including the first calculation of over one billion (1,011,196,691) decimals in 1989. It remains the formula of choice for π calculating software that runs on personal computers.
What is the x-intercept for y equals 4x-16?
y = 4x - 16
At the x-intercept, y=0.
0 = 4x - 16
Add 16 to each side:
16 = 4x
Divide each side by 4:
x = 4
Is inductive or deductive reasoning the best way to approach a geometric proof?
Please remember proof gives absolute truth, which means it HAS to be true for all cases satisfying the condition. Hence, inductive reasoning will NEVER be able to be used for that ---- it only supposes that the OBSERVED is true than the rest must, that's garbage, if it's observed of course it's true (in Math), no one knows what will come next. But it's a good place to start, inductive reasoning gives a person incentive to do a full proof.
Do NOT confuse inductive reasoning with inductive proof.
Inductive reasoning: If a1 is true, a2 is true, and a3 is true, than a4 should be true.
Inductive Proof: If a1 is true (1), and for every an, a(n+1) is true as well (2), then,
since a1 is true (1), then a2 is true (2), then a3 is true (2).
You see, in inductive proof, there is a process of deductive reasoning ---- proving (1) and (2). (1) is usually, just plugin case 1. (2) provides only a generic condition, asking you to derive the result (a (n+1) being true), that is deductive reasoning.
In other words, proof uses implications a cause b, and b cause c hence a cause c.
Inductive says though a causes c because I saw one example of it.
What is the estimate of covariance for d effect-sizes for a meta analysis?
In a meta-analysis, the estimate of covariance for effect sizes is often calculated to assess the degree to which the effect sizes are correlated across studies. This covariance can be estimated using a random-effects model, which accounts for both within-study and between-study variability. Typically, it involves using the inverse of the variance of each effect size as weights in a weighted average. Understanding covariance helps in evaluating the overall heterogeneity and potential publication bias in the meta-analysis.
He had an enlarged heart that caused a irregular heartbeat
How do you prove that the sum of a rational number and its additive inverse is zero?
I can give you an example and prove it:
eg. take the rational no. 2......hence its additive inverse ie. its opposite no. will be -2
now lets add:
=(2)+(-2)
=2-2
=0
it means that the opposite no.s. get cancelled and give the answer 0
this is the same case for sum of a rational no. and its opposite no. to be ZERO
What is the angle between lines of force and equipotential lines in an electrical field?
The angle is a right angle.
- give me examples of est
imate
What does rotation mean in termsof inverse of orthogonal matrix?
The inverse of a rotation matrix represents a rotation in the opposite direction, by the same angle, about the same axis.
Since M-1M = I, M-1(Mv) = v. Thus, any matrix inverse will "undo" the transformation of the original matrix.
Can it be possible limit of logarithmic functions equal to logarithmic function of limit?
Yes it is possible.
If limit(f) > 0 then limit(loga(f)) = loga(limit(f)).
All logarithmic functions loga(x) are continuous as long as x > 0. Where-ever a function is continuous, you can make that kind of swap.
Why negative times negative is equal to positive?
Using the distributive property of multiplication over addition, x*[x - x] = x*[x + (-x)] = x*x + x*(-x)LHS = x*0 = 0
RHS = x^2 + x*(-x)
Therefore x*(-x) = -x^2 and, by commutativity, -x*x = -x^2
Next
-x*[x - x] = -x*[x + (-x)] = -x*x + -x*(-x)
LHS = -x*0 = 0
RHS = -x^2 + -x*(-x)
Therefore (RHS) -x times -x = +x^2 (LHS).
Let ABC and DEF be triangles which are right angled at A and D, such that the hypotenuses BC and EF are equal and, without loss of generality, angle B = angle E.Then
Then by the sine rule, BC/sin(A) = AC/sin(B) and EF/sin(D) = DF/sin(E)
Since angle A = angle D = pi/2 radians, then sin(A) = sin(D) = 1
so that BC/sin(A) = BC while EF/sin(D) = EF
therefore, since the hypotenuses BC and EF are equal, the left hand sides of the two equations are equal.
Therefore, AC/sin(B) = DF/sin(E)
then, since angle B = angle E, then sin(B) = sin(E) so that AC = DF.
Also, angle C = pi/2 - angle B
and angle F = pi/2 - angle E
the right hand sides are equal so angle C = angle F.
Then in a manner similar to the above, we can show that AB = DE.
Thus all three pairs of corresponding sides are equal and all three pairs of corresponding angles are equal so that the two triangles are congruent.
Prove diagonals are equal in a rectangle?
Suppose ABCD is a rectangle.Consider the two triangles ABC and ABD
AB = DC (opposite sides of a rectangle)
BC is common to both triangles
and angle ABC = 90 deg = angle DCB
Therefore, by SAS, the two triangles are congruent and so AC = BD.
What is an oval shape mersman table with the number 7339 on it worth?
50$ at a flea market,100$ at a antique show,200$ at a antique shop,
