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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
How do you prove Leibniz formula for the nth derivatives?
Prove it by induction on n, use 0 or 1 as base cases.
Why resistor do not have positive or negative terminal?
cuz a resistor is basically a long wire , that resists some of the charges flowing across it.
it has resistive properties which stops some of the current from flowing from one terminal to the other.
so....as it is just a piece of wire....it doesn't need a +ve or a -ve terminal
How do you work out the volume of a cuboid if only given the areas of the faces of a cuboid?
If the areas of the three faces are x, y and z then the volume is sqrt(x*y*z).
Proof:
Suppose the sides of the cuboid are a, b and c.
Then the different areas of the faces are ab, bc and ca.
If these are called x, y and z, then x*y*z = ab*bc*ca = (a*b*c)^2
and that, as yuo will notice, is the square of the volume.
How do you prove that there is a prime between n and 2n?
To be pedantic, the question should say "for all n >= 2". A detailed proof is given here: http://mathforum.org/library/drmath/view/51527.html The proof is quite long, but it only uses properties of logarithms, exponents, and the binomial theorem, so if you know about these and have enough mental stamina, you can probably make sense of it.
Which theorem is used to prove the AAS triangle congruence postulate theorem?
The first thing you prove about congruent triangles are triangles that have same side lines (SSS) is congruent. (some people DEFINE congruent that way).
You just need to show AAS is equivalent or implies SSS and you are done.
That's the first theorem I thought of, don't know if it works though, not a geometry major.
The exponential function, logarithms or trigonometric functions are functions whereas a complex variable is an element of the complex field.
Each one of the functions can be defined for a complex variable.
Reverse and negation of an if-then statement?
The reverse and negation of an if-then statement is as follows:
if (...) then statement;
reversed becomes
if (not (...)) then statement;
Let the triangle be ABC and suppose the median AD is also an altitude.AD is a median, therefore BD = CD
AD is an altitude, therefore angle ADB = angle ADC = 90 degrees
Then, in triangles ABD and ACD,
AD is common,
angle ADB = angle ADC
and BD = CD
Therefore the two triangles are congruent (SAS).
And therefore AB = AC, that is, the triangle is isosceles.
In how many different ways can the letters of the word coniohser be arranged?
Coniohser has 9 letters. So the solution is permutation of nine that means 1*2*3*4*5*6*7*8*9 =362880
Does every statement have a counterexample?
No. Not if it is a true statement. Identities and tautologies cannot have a counterexample.
What are other differences of postulate and theorem?
The phrase "other differences" implies that you already have some differences in mind. However, you have not bothered to share that information. Consequently, there is no way for me to know if a difference that I mention is one that you already know or if it is another one.
How do you prove the formula for the volume of a square pyramid?
You really can't "prove" the formula. You use it. You first square the base 'b'. Then, you multiply that number by the height 'h'. Then, you divide the product of the base squared and height by 3. Boom! You get your answer. In my school, we get a formula sheet with all the formulas we will need to use. If you didn't understand the description above, here is the formula for a square pyramid:1/3b2 h.
Hope this helped!
The question cannot be answered without more information about the points e, f and g.
When 8 is subtracted from two times a number the result is 10 what is the number?
8-(2x)=10
-(2x)=10-8
-(2x)=2
x=2/(-2)
x= -1
