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solution stringlengths 1 6.9k ⌀ | question stringlengths 40 2.42k ⌀ | cot_type stringclasses 3
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User avatar #1 - servbot (03/06/2012) [-]
Is your username a smashing pumpkins reference?
User avatar #2 to #1 - thepumpkinsrock (03/06/2012) [-]
yes indeed.
User avatar #3 to #3 - servbot (03/06/2012) [-]
Dude, I ******* love the smashing pumpkins. Billy Corgan is a god.
User avatar #4 to #4 - thepumpkinsr... |
null | null | null | null | null | null | null | null | Calculating incremental response
May 01, 2005 9:30 PM By
When measuring the effectiveness of a promotion, it’s not enough to know the overall response and revenue. What you really need to measure is the incremental order activity generated by the promotion.
Confused? Let’s say that you mail a print catalog, then fo... |
810 | On square $ABCD$ , point $E$ lies on side $AD$ and point $F$ lies on side $BC$ , so that $BE=EF=FD=30$ . Find the area of the square $ABCD$ . | math | qq8933/AIME_1983_2024 | {'ID': '2011-II-2', 'Year': 2011, 'Problem Number': 2, 'Part': 'II'} | null | [
"\nThe problem asks for the area of a square $ABCD$, given some conditions about points $E$ and $F$ on its sides. Let the side length of the square be $s$. We can set up a coordinate system with the origin at $A$, such that $A=(0,s), B=(s,s), C=(s,0), D=(0,0)$.\n\nLet the coordinates of the points be:\n$A = (0, s)$... | Solution:
Let the square $ABCD$ have side length $s$. We set up a coordinate system with $A=(0,s), B=(s,s), C=(s,0), D=(0,0)$.
Point $E$ lies on side $AD$, so $E=(0, y_E)$ where $0 \le y_E \le s$.
Point $F$ lies on side $BC$, so $F=(s, y_F)$ where $0 \le y_F \le s$.
We are given $BE=EF=FD=30$.
Using the distance formu... | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
On square $ABCD$ , point $E$ lies on side $AD$ and point $F$ lies on side $BC$ , so that $BE=EF=FD=30$ . Find the area of the square $ABCD$ .<|im_end|>
<|im_start|>assistant
<|im_start|>think
The problem a... |
null | null | null | null | null | null | null | null | I just finished New Moon, and I'm trying to get through Eclipse. Can someone please tell me what all the darn rage is about? In New Moon, she could have told that story in half the book. Why does she take so long to get to the point?
It will be nice to get back to my BDB series. |
null | null | null | null | null | null | null | null | Harry Potter Wiki
Ravenclaw family
12,003pages on
this wiki
Revision as of 00:18, July 7, 2012 by Jiskran (Talk | contribs)
Helena Ravenclaw
Ravenclaw family
Family heritage
Blood status
wizarding family of unknown degree
Notable family members
Ravenclaw is the surname of a wizarding family that existed circ... |
469 | Suppose that $a$ , $b$ , and $c$ are positive real numbers such that $a^{\log_3 7} = 27$ , $b^{\log_7 11} = 49$ , and $c^{\log_{11}25} = \sqrt{11}$ . Find \[a^{(\log_3 7)^2} + b^{(\log_7 11)^2} + c^{(\log_{11} 25)^2}.\] | math | qq8933/AIME_1983_2024 | {'ID': '2009-II-2', 'Year': 2009, 'Problem Number': 2, 'Part': 'II'} | null | [
"\nThe problem asks for the value of the expression $a^{(\\log_3 7)^2} + b^{(\\log_7 11)^2} + c^{(\\log_{11} 25)^2}$, given certain conditions on $a, b, c$. Let's analyze each term separately.\n\nFirst, consider the term $a^{(\\log_3 7)^2}$. We are given $a^{\\log_3 7} = 27$.\nLet $x = \\log_3 7$. Then the given eq... | Solution:
We are given that $a, b, c$ are positive real numbers such that $a^{\log_3 7} = 27$, $b^{\log_7 11} = 49$, and $c^{\log_{11}25} = \sqrt{11}$. We need to find the value of $a^{(\log_3 7)^2} + b^{(\log_7 11)^2} + c^{(\log_{11} 25)^2}$.
Consider the first term, $a^{(\log_3 7)^2}$. We are given $a^{\log_3 7} = 2... | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Suppose that $a$ , $b$ , and $c$ are positive real numbers such that $a^{\log_3 7} = 27$ , $b^{\log_7 11} = 49$ , and $c^{\log_{11}25} = \sqrt{11}$ . Find \[a^{(\log_3 7)^2} + b^{(\log_7 11)^2} + c^{(\log_... |
null | null | null | null | null | null | null | null | Code Pink Journals CodePINK Journals
Monday, May 05, 2008
Grandmothers say "TAKE ME, NOT MY GRANDCHILD"
We had a wonderful Grandmothers action at the MRS today! Grandmothers showed up, walked the picket line, and blocked the doorway!
The marine recruiters locked the front doors and refused to speak with our Grandm... |
230 | Given $f(z) = z^2-19z$ , there are complex numbers $z$ with the property that $z$ , $f(z)$ , and $f(f(z))$ are the vertices of a right triangle in the complex plane with a right angle at $f(z)$ . There are positive integers $m$ and $n$ such that one such value of $z$ is $m+\sqrt{n}+11i$ . Find $m+n$ . | math | qq8933/AIME_1983_2024 | {'ID': '2019-I-12', 'Year': 2019, 'Problem Number': 12, 'Part': 'I'} | null | [
"\nThe problem asks for the value of $m+n$, where $m$ and $n$ are positive integers, and $z = m+\\sqrt{n}+11i$ is a complex number such that $z, f(z), f(f(z))$ form a right triangle with the right angle at $f(z)$.\n\nThe vertices of the right triangle are $A=z$, $B=f(z)$, $C=f(f(z))$. The right angle is at $B$, whi... | Solution:
Let the vertices of the triangle be $A=z$, $B=f(z)$, $C=f(f(z))$. The right angle is at $B$, so the vectors $\vec{BA} = z - f(z)$ and $\vec{BC} = f(f(z)) - f(z)$ are orthogonal. This means that the ratio $\frac{z - f(z)}{f(f(z)) - f(z)}$ is purely imaginary.
We have $f(z) = z^2 - 19z$.
$z - f(z) = z - (z^2 -... | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Given $f(z) = z^2-19z$ , there are complex numbers $z$ with the property that $z$ , $f(z)$ , and $f(f(z))$ are the vertices of a right triangle in the complex plane with a right angle at $f(z)$ . There are... |
null | null | null | null | null | null | null | null | Ideas that could be patented
Ca. 6233 ord.
- but which cannot be patented as I have published the ideas here.
Battery powered container vessels
Shipping by sea pollutes very little if measured by the CO2 produced to move 1 kg payload 1 kilometer. However, even so shipping still produces a lot of CO2. This could be... |
1. **Define the function \( g_n(m) \):**
Let \( g_n(m) = f(n-m, m) \). This transformation helps us to simplify the problem by reducing it to a single variable function.
2. **Boundary conditions:**
From the given conditions, we have:
\[
g_n(0) = f(n, 0) = 0 \quad \text{and} \quad g_n(n) = f(0, n) = 0
\]... | Let $P$ denote the set of all ordered pairs $ \left(p,q\right)$ of nonnegative integers. Find all functions $f: P \rightarrow \mathbb{R}$ satisfying
\[ f(p,q) \equal{} \begin{cases} 0 & \text{if} \; pq \equal{} 0,
1 \plus{} \frac{1}{2} f(p+1,q-1) \plus{} \frac{1}{2} f(p-1,q+1) & \text{otherwise} \end{cases}
\]
... | math | AI-MO/NuminaMath-CoT/aops_forum | {'source': 'aops_forum', 'messages': [{'content': 'Let $P$ denote the set of all ordered pairs $ \\left(p,q\\right)$ of nonnegative integers. Find all functions $f: P \\rightarrow \\mathbb{R}$ satisfying\n\\[ f(p,q) \\equal{} \\begin{cases} 0 & \\text{if} \\; pq \\equal{} 0, \n1 \\plus{} \\frac{1}{2} f(p+1,q-1) \... | null | [
"\nThe problem asks for all functions $f: P \\rightarrow \\mathbb{R}$, where $P$ is the set of ordered pairs of nonnegative integers, satisfying a given functional equation. The set $P = \\{(p, q) \\mid p \\ge 0, q \\ge 0, p, q \\in \\mathbb{Z}\\}$.\n\nThe functional equation is:\n\\[ f(p,q) = \\begin{cases} 0 & \\... | Solution:
Let the given functional equation be
\[ f(p,q) = \begin{cases} 0 & \text{if } pq = 0 \\ 1 + \frac{1}{2} f(p+1,q-1) + \frac{1}{2} f(p-1,q+1) & \text{if } pq \neq 0 \end{cases} \]
Consider the function $h(p,q) = pq$. If $pq=0$, then $h(p,q) = 0$.
If $pq \neq 0$,
\begin{align*} 1 + \frac{1}{2} h(p+1,q-1) + \frac... | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $P$ denote the set of all ordered pairs $ \left(p,q\right)$ of nonnegative integers. Find all functions $f: P \rightarrow \mathbb{R}$ satisfying
\[ f(p,q) \equal{} \begin{cases} 0 & \text{if} \; ... |
null | null | null | null | null | null | null | null | Indeed job search
Cocoa jobs
job title, keywords or company name
city, state or zip code (optional)
Advanced Job Search
Search 3,566 Cocoa jobs from job sites, newspapers, associations and company career pages.
Cocoa jobs
The Cocoa, FL job market is strong compared to the rest of the US. Over the last year, job po... |
Suppose the center of the largest teacup is at the origin in the complex plane, and let $z=\frac{2}{3} e^{\pi i t / 6}$. The center of the second disk is at $5 e^{\pi i t / 6}$ at time $t$; that is, \frac{15}{2} z$. Then the center of the third disk relative to the center of the second disk is at \frac{15}{2} z^{2}$, a... | Alice is sitting in a teacup ride with infinitely many layers of spinning disks. The largest disk has radius 5. Each succeeding disk has its center attached to a point on the circumference of the previous disk and has a radius equal to $2 / 3$ of the previous disk. Each disk spins around its center (relative to the dis... | math | KbsdJames/Omni-MATH | {'domain': ['Mathematics -> Algebra -> Intermediate Algebra -> Complex Numbers', 'Mathematics -> Calculus -> Differential Calculus -> Applications of Derivatives'], 'difficulty': 5.25, 'answer': '18 \\pi', 'source': 'HMMT_2'} | null | [
"\nThe problem describes a system of infinitely many rotating disks, where each disk is attached to the circumference of the previous one. We need to find the trajectory of a point (Alice) located at the limit point of this system.\n\nLet the disks be numbered $D_0, D_1, D_2, \\ldots$, where $D_0$ is the largest di... | Solution:
Let the position of Alice at time $t$ be $z(t)$ in the complex plane. The position of Alice is the limit point of the centers of the disks, which can be expressed as:
$z(t) = \sum_{j=1}^{\infty} 5 (2/3)^{j-1} e^{i j \omega t}$, where $\omega = \pi / 6$.
This is a geometric series, and its sum is $z(t) = 5 \fr... | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Alice is sitting in a teacup ride with infinitely many layers of spinning disks. The largest disk has radius 5. Each succeeding disk has its center attached to a point on the circumference of the previous ... |
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