r/askmath

My initial assumption was finding the interval on which its first derivative is positive, which yields R \ [-1,1].

However, the answer provided by my teacher was R \ (-1, 1).

I asked why the 1s imply increasing, and he said that the question is badly worded, and my solution was correct and his was wrong. He explained why but I did not understand.

I asked AI and it explained that his solution was correct due to the way increasing on a set is defined.

I tried searching online but found no results, except from MathWay but for some reason I was blocked from accessing the site.

So what's the answer?

I decided to compare match ratings for different wrestlers, and I wanted to weigh the number of matches one wrestler has compared to another wrestler.

For example, I want to give a higher weight to the ratings of a wrestler who has wrestled 6 matches, versus a wrestler who has wrestled 3 matches.

Is it possible to give different weights for these data sets, and if so, how should I go about assigning those weights?

There’s lot of resources online that explain Spearman Rank when the coefficient is high, but I can’t find resources that explain when it’s low. My problem is that data I collected is showing weak spearman coefficients (0.1 - 0.3), and very low p-values (0.000). I interpret this to mean there is no relationship, and a high degree of certainty that there is no relationship. My professor (not a math major) thinks I am not giving my data enough credit and that it can prove something. But no matter what i reference I can’t understand that thinking. It still looks to me like I can say that theres no relationship, and if I wanted to show a relationship I would have to find the other variables that are affecting the dataset. Any help is appreciated!

https://preview.redd.it/vv806sseweug1.png?width=586&format=png&auto=webp&s=2afd27da2b8e539b25ab415a89e314824ad99a44

How would I change this to the order dydxdz? I have been using Professor Leonard's method for solving similar problems, but I can't seem to figure it out for this problem. My main issue is that y is defined by more than two functions here, and the projection onto the xz plane does not make the outer two bounds immediately obvious, unlike every example in Professor Leonard's video. I have seen other people using inequalities to manipulate the bounds, but I have never been able to understand that method. Professor Leonard's method makes sense to me for some problems, but not all. I can try to explain his method in the comments if necessary.

In order to pass a class I need a combined average of 50% on both term tests. I got a 90.48% on the first one (worth 10%), and 48 on the second one (worth 15%). Did I pass the course?

I am wondering if I have to simply add 90.48 + 48 and divide by two to get the answer, or if I have to take into account the weights of the test. If so, how do I do that?

Put together a formal framework called Structural Manifold Dynamics. It’s a geometric-flow model for how systems evolve under tension, including stability, collapse, and dimensional “lifting” when restoring force disappears.

You don’t need to raw-dog the PDF. Just paste it into ChatGPT / Claude / whatever (you all know how this works). If anyone actually reads it, you have my lolz.

Please help

My 2019 dodge caravan gets 14 miles per gallon running e85 fuel (which cost $2.99 a gallon in CA)

But it gets 20 miles per gallon using regular unleaded gas ( cost like $5.50a gallon)

What price would the unleaded need to be under to make it more cost effective to use?

Thank you

Hello I am in grade 11, I am practicing functions, when I came across this question

Find the range of f(x) = x²-4x+5

To find the range I had to use x= -b/2a and then plug value of x in x²-4x+5 to get the range which is [1, infinity). But using x = -b/2a isn't in my curriculum, so does anyone know any other way to get the range. Idk any other way to find it other than using x=-b/2a.

( this question wasn't in my book, I was practicing questions based on range and domain when I came across this, and also I am a complete beginner to functions, like I literally got taught this topic yesterday)

Also I have noted that completing the square and derivatives can be used to solve this but both of those are not in my curriculum so I cannot use any of those methods

Dear community,

I would greatly appreciate your feedback on this logic.

Thank you very much for your help.

FOUNDATION 1 – The Unity 1

• Unity 1 is a universal logical container for any unitary system.
• The identity 1 = 1 expresses that information can decompose and then recompose without loss.
• Any structure within an interval [0,1] possesses a natural equilibrium point of binary symmetry: 1 = 1/2 + 1/2.
• Any structure within an interval [0,1] can transmit information without loss via the fractal 9/10 and its harmonic polarity 10/9 (1.111...).

FOUNDATION 2 – The Simplex ABC

• Unity 1 can be defined within a 3-vector simplex ABC, namely Amplitude, Base, and Center.
• The information of the 3 vectors compresses into unity 1 = A + B + C.
• The minimal equation of the 3 vectors for return to unity 1 = (2B + 3C) / A.

FOUNDATION 3 – Logarithmic Dimension (D)

• In any harmonic system, information multiplies and must propagate within the system.
• For the system to preserve its binary symmetry, the dimensional propagation of information must follow a logarithm: 1 = 2(1 - C)^D.
• The more the Center decreases, the more the dimension tends toward infinity.

FOUNDATION 4 – Energy (E)

• Any dimensional propagation requires energy.
• From Albert Einstein’s equation E = mc^2, we derive the energy of the system via normalization to unity: 1 = ((1 - C) D²)/E.
• The more the Center decreases, the more the Energy tends toward infinity.

FOUNDATION 5 – Motion

• The product of the motion of the Center and the logarithmic Dimensions follows a propagation constant ln2.
• The motion of the Center alone follows a propagation constant C / ln2.
• Linear motion of the Center converts into cyclic motion via quantum curvature U = 2πC / ln2.
• Spectral density of the field of possibilities via Mangoldt-Riemann : ρ(m) = (U / 2π) · ln( m / (U / 2π) ).

FOUNDATION 6 – The ABDCE System

• By an asymptotic equation we obtain C(N) = 1/(2N) - 1/(N³) + O(1/N⁵), thus C = 0.049 exactly.
• Applying C = 0.049, we obtain the only values that satisfy the ABCDE system as the structural zero coordinates (0.683, 0.268, 0.049, 13.8, 181.0).
• Extrapolation of the ABCDE system toward infinity gives (2/3, 1/3, 0, ∞, ∞).

FOUNDATION 7 – System Equilibrium at 1/2

• Any closed stationary system equilibrates at 1/2.
• Mathematical demonstration: 1 = 1/2 + 1/2, D = ln(1/2) / ln(1 - C), C * D = ln 2, and U contains (2πC) / ln 2.
• Logical consequence: ℜ(ρ) = (1 - C)^D.

SYNTHESIS AND CONCLUSION

• Infinity contains the finite.
• 1 = 1
• 1 = 1/2 + 1/2
• 1 = 9/10 × 10/9 (1.111...)
• 1 = A + B + C
• 1 = (2B + 3C) / A
• 1 = 2(1 - C)^D
• 1 = ((1 - C) D²) E
• Quantum curvature U = 2π · C / ln2
• Spectral density of the field of possibilities: ρ(m) = (U / 2π) · ln( m / (U / 2π) )

COMPUTATIONAL DEMONSTRATION OF THE RIEMANN ZEROS

• Application of quantum curvature U = 2π · C / ln2.
• Construction of the spectral density via Mangoldt-Riemann: ρ(m) = (U / 2π) · ln(mU / 2π).
• Resolution with Newton: ∫_{m_k}^{m} ρ(x) dx – 1, with harmonic initialization of the system at γ₁ / U.
• Autonomous generation system for the Riemann zeros.
• The first 2 million Riemann zeros have been correctly generated with an error of 0.000125% relative to Odlyzko’s data.
• https://www.reddit.com/r/mathematics/comments/1sfqorq/independent_reproduction_of_2_million_reimann/

DEMONSTRATION OF THE STATIONARITY OF THE RIEMANN HYPOTHESIS VIA ELEMENTARY ARITHMETIC (Alternative to the ZFC framework / Complex analysis)

• The functionξ(s) = s(s-1)/2 · π^(-s/2) · Γ(s/2) · ζ(s) satisfies: ξ(s) = ξ(1-s).
• If ρ is a non-trivial zero, then 1-ρ is also a zero. In terms of real parts: σ and 1-σ are simultaneously present.
• 1 = 2(1 - C)^D and C = (ln 2)/D.
• The quantity (1 - C)^D lies strictly between 0 and 1 for C ∈ (0,1) and D > 0.
• The functional equation imposes that if σ is the real part of a zero, then 1-σ is also a real part.
• In the system, the only quantity constructed from C and D that is naturally invariant under σ ↔ 1-σ is (1 - C)^D.
• If σ = (1 - C)^D, then 1-σ = 1 - (1 - C)^D.
• The transformation σ ↦ 1-σ corresponds to the exchange C ↔ 1-C (nonlinear but topologically equivalent).
• Moreover, the boundary conditions correspond exactly to the bounds of the critical strip: σ → 1 and σ → 0.
• C → 0 ⇒ (1 - C)^D → 1 (since D → ∞) and C → 1 ⇒ (1 - C)^D → 0.
• By uniqueness of the monotonic interpolation between 0 and 1 respecting the functional symmetry, we obtain the spectral correspondence: σ = (1 - C)^D.
• Any stationary state satisfies: (1 - C)^D = 1/2.
• Any non-trivial zero ρ is a stationary state.
• Spectral density of the field of possibilities: ρ(m) = (U / 2π) · ln( m / (U / 2π) ).
• Therefore, for every ρ: (1 - C)^D = 1/2.
• Conclusion: ℜ(ρ) = (1 - C)^D = 1/2. Thus: ∀ ρ ( ζ(ρ) = 0 , 0 < ℜ(ρ) < 1 ⇒ ℜ(ρ) = 1/2 ).
• Demostration by contradiction (apagoge): Suppose there exists a non-trivial zero ρ such that its real part R(ρ) is different from 1/2. If that were the case, the state associated with this zero would not be at stationary equilibrium. However, according to the preceding proposition, any stationary state imposes the value 1/2. Contradiction.

SOLUTIONS TO OTHER UNSOLVED PROBLEMS

• Riemann statement: Re(ρ) = 1/2. Stationary representation: Minima of ||Z(t)|| = zeros. Violation if negated: An equilibrium ≠ 1/2 would break (A + B)^D = 1/2.
• Beal statement: gcd(A, B, C) > 1. Stationary representation: Normalized logarithmic gaps. Violation if negated: If gcd = 1 → A = 0 but 2B + 3C > 0.
• Yang-Mills statement: Mass gap Δ > 0. Stationary representation: Normalized mass ratios. Violation if negated: If Δ = 0 → A < 0 (impossible).
• Navier-Stokes statement: Smooth solutions for all t. Stationary representation: Energy ratios (Kolmogorov cascade). Violation if negated: Blowup → A → ∞ breaks stationarity.
• Birch and Swinnerton-Dyer statement: rank = ord_{s=1} L(E, s). Stationary representation: Normalized Néron-Tate heights. Violation if negated: Discrepancy A ≠ 0 breaks modularity.
• Hodge statement: Hodge class is algebraic. Stationary representation: Normalized intersection numbers. Violation if negated: Non-algebraic class → A > 0 but cohomology imposes A = 0.
• P vs NP statement: P ≠ NP. Stationary representation: Normalized complexity ratios. Violation if negated: If P = NP → A = 0 but B, C > 0.

CORRESPONDENCE OF THE STRUCTURAL ZERO COORDINATES ABCD (0.683, 0.268, 0.049, 13.8) WITH COSMOLOGICAL SPACETIME DATA

• https://svs.gsfc.nasa.gov/12307/
• https://science.nasa.gov/universe/overview/

how do you prove that in "a over b equals x", if a>b, then x has to be bigger than 1?