"User "F(x,y) : r2 -> r es diferenciable en (x,y) = (2,1) tq su plano tangente en (x,y,z)= (2,1,1) viene dado por z = 1 + 8(x-2) + 9(y-1). Se tiene ademas la funcion g(x,y): r2 -> r2 definida por g(u,v) = uv-2v + 4, 2(e^u) - cos(1-v)). Hallar el plano tangente al grafico de h = f o g(u,v) en el punto (0,1,h(0,1)). Por favor explicar todos los pasos ya que no estoy familiarizado con el tema. Para encontrar el plano tangente al gráfico de (h = f \circ g(u,v)) en el punto ((0, 1, h(0,1))), primero necesitamos entender qué estamos haciendo cuando decimos “el plano tangente al gráfico de (h)” y luego llevar a cabo los pasos detalladamente. Paso 1: Comprender el problema - La función (f(x, y)) es una función de (\mathbb{R}^2) a (\mathbb{R}). Nos dicen que es diferenciable en ((x,y) = (2, 1)) y su plano tangente en ese punto está dado por (z = 1 + 8(x-2) + 9(y-1)). - La función (g(u, v)) mapea (\mathbb{R}^2) a (\mathbb{R}^2) y está definida como (g(u, v) = (uv - 2v + 4, 2e^u - \cos(1-v))). - Queremos hallar el plano tangente al gráfico de (h = f \circ g(u, v)) en ((u, v) = (0, 1)). La composición (f \circ g) significa que primero aplicamos (g) y luego (f). Paso 2: Encontrar (g(0,1)) Aplicamos (g) en ((0, 1)): [g(0, 1) = (0 \cdot 1 - 2 \cdot 1 + 4, 2e^0 - \cos(1 - 1)) = (2, 2 - \cos(0)) = (2, 2 - 1) = (2, 1)] Paso 3: Encontrar (h(0,1)) Ya que (h = f \circ g), entonces (h(0,1) = f(g(0, 1)) = f(2,1)). Sabemos del enunciado que el punto en el plano tangente de (f) en ((2,1)) es ((2,1,1)), por lo tanto (h(0,1) = 1). Paso 4: Calcular el gradiente de (f) en ((2,1)) Nos proporcionaron directamente la ecuación del plano tangente de (f) en ((2,1)): [z = 1 + 8(x - 2) + 9(y - 1)] Los coeficientes de ((x - 2)) y ((y - 1)) en esta ecuación representan las derivadas parciales de (f) con respecto a (x) e (y) respectivamente. Entonces, (\frac{\partial f}{\partial x} = 8), (\frac{\partial f}{\partial y} = 9) en el punto ((2,1)). Paso 5: Calcular el gradiente de (g) en ((0,1)) Necesitamos hallar las derivadas parciales de cada componente de (g) respecto a (u) y (v) en ((0,1)). Para (g(u,v) = (uv - 2v + 4, 2e^u - \cos(1 - v))), tenemos: - (\frac{\partial}{\partial u} (uv - 2v + 4) = v), y en ((0,1)), es (1). - (\frac{\partial}{\partial v} (uv - 2v + 4) = u - 2), y en ((0,1)), es (-2). - (\frac{\partial}{\partial u} (2e^u - \cos(1 - v)) = 2e^u), y en ((0,1)), es (2e^0 = 2). - (\frac{\partial}{\partial v} (2e^u - \cos(1 - v)) = \sin(1 - v)), y en ((0,1)), es (\sin(0) = 0). Entonces el jacobiano de (g) en ((0,1)) es: [J_g(0,1) = \begin{bmatrix} 1 & -2 \ 2 & 0 \end{bmatrix}] Paso 6: Calcular la derivada de (h = f \circ g(u,v)) utilizando la regla de la cadena La regla de la cadena para funciones compuestas de (\mathbb{R}^2) a (\mathbb{R}) resulta en una matriz (1 \times 2) (derivada de (h)) que es el producto del gradiente de (f) evaluado en (g(0,1)) (una matriz (1 \times 2)) y el jacobiano de (g) en ((0,1)) (una matriz (2 \times 2)). Entonces, [\nabla h(0,1) = \nabla f(g(0,1)) \cdot J_g(0,1) = [8, 9] \cdot \begin{bmatrix} 1 & -2 \ 2 & 0 \end{bmatrix} = [8 + 18, -16 + 0] = [26, -16]] Paso 7: Escribir la ecuación del plano tangente para (h) El punto de tangencia es ((0,1,h(0,1)) = (0, 1, 1)). Las derivadas parciales que encontramos dan la dirección del plano tangente. La ecuación del plano tangente en términos generales es: [z = f(x_0, y_0) + f_x(x_0, y_0)(x - x_0) + f_y(x_0, y_0)(y - y_0)] Sustituyendo, obtenemos para (h = f \circ g(u,v)): [z = 1 + 26(u - 0) - 16(v - 1)] [z = 1 + 26u - 16v + 16] [z = 17 + 26u - 16v] Entonces, el plano tangente al gráfico de (h) en el punto ((0, 1, h(0,1))) es: [z = 17 + 26u - 16v] "" explicar el paso 3

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Канал связи описан следующей канальной матрицей P(Y / X ) Как найти среднее количество информации, которое переносится одним символом сообщения, если вероятности появления символов источника сообщений равны p(x1) = 0.7, p(x1) = 0.2, p(x1) = 0.1

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what is the numerical value of avogadro's number? report your answer to 4 significant figures

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what is the numerical value of avogadros number? report your answer to 4 significant figures. (your answer should be entered as in the following example: 1000 = 1.0E+3)

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the japanese symbol for an atom has been written on a piece of copper metal using 99 iron atoms. calculate the mass of the iron used to create this symbol.

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Укажите верные соотношения для избыточности r блочного кода Гильберта-Мура при кодировании источника без памяти с энтропией H , длина блока n

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Hola, no he estudiado para mi examen y necesito ayuda. Necesito información crucial sobre los temas, fórmulas y conexiones para poder resolver los ejercicios. La materia es análisis (varias variables). Esta es la primera práctica: Práctica 1: Geometría en R2 y R3 - Aplicaciones 1. Representar gra camente en R3 las siguientes ecuaciones e inecuaciones. Se sugiere complementar la resolución de este ejercicio con GeoGebra. (a) y = −4, (b) x > 3, (c) 0 ≤ z ≤ 6, (d) x = z, (e) x2 + y2 + z2 ≤ 4, (f) x2 + y2 + z2 > 2z, (g) x2 + y2 ≤ 9. 2. Mostrar que las siguientes ecuaciones representan una esfera. Dar su centro y su radio. (a) x2 + y2 + z2 − 6x + 4y − 2z = 11, (b) 4x2 + 4y2 + 4z2 − 8x + 16y = 1. 3. En física e ingeniería los vectores son útiles en muchos aspectos. Por ejemplo, dado que una fuerza ejercida sobre un objeto está determinada por una magnitud y una dirección, se puede utilizar un vector para representarla. La unidad de medida clásica para la magnitud de una fuerza es newtons (N). Si una niña empuja un trineo por la ladera de una montaña con una fuerza de 50 N y la ladera de la montaña tiene una inclinación de 38◦ sobre la horizontal, calcular la componente horizontal y la vertical de dicha fuerza. 4. Supongamos que para mover un objeto del punto P al punto Q aplicamos una fuerza constante F en una determinada dirección formando un ángulo θ con la horizontal, como muestra la imagen. El trabajo W realizado por F sobre dicho objeto se de ne como el producto entre la distancia recorrida (∥Q − P∥) y la componente de la fuerza a lo largo de # » PQ (∥F∥ cos θ), es decir, W = ∥Q − P∥∥F∥ cos θ = (Q − P) · F. Hallar el trabajo realizado por una fuerza F con una magnitud de 20 N aplicada en la dirección de 50◦ sobre la horizontal para desplazar un objeto 4 mts. 1 Análisis I - Matemática I - Análisis II (C) Práctica 1 5. Hallar el trabajo realizado por una fuerza F = (8,−6, 9) que mueve un objeto del punto P = (0, 10, 8) al punto Q = (6, 12, 20) a lo largo de una línea recta. La distancia se mide en metros y la fuerza en newtons. 6. Dados dos vectores V,W se cumple la desigualdad de Cauchy-Schwarz para el producto interno: |V ·W| = ∥V ∥ ∥W∥ | cos θ| ≤ ∥V ∥ ∥W∥. 3⁄4Hay algún caso en el que la desigualdad |V ·W| ≤ ∥V ∥ ∥W∥ sea una igualdad? 7. Mostrar grá ca y analíticamente que cada componente del vector F = (x, y) es menor o igual que la norma de F: esto es que |x| ≤ p x2 + y2 = ∥F∥ y similarmente que |y| ≤ ∥F∥. Si F = (x, y, z) es un vector de R3, probar que vale lo mismo para las tres coordenadas de F. 8. (a) Encontrar una ecuación paramétrica del plano Π que pasa por los puntos A = (1, 3, 1), B = (2, 1, 1) y C = (3, 4, 1). (b) Hallar N la normal y dar una ecuación implícita de Π. 9. (a) Hallar la intersección de las rectas L1 : t(1,−1, 2) + (1, 1, 0) y L2 : t(−1, 1, 0) + (2, 0, 2). (b) Encontrar una ecuación del plano que contiene a L1 y L2. 10. Para a ∈ R, dar una descripción geométrica de las siguientes ecuaciones. Se sugiere complementar la resolución de este ejercicio con GeoGebra (utilizar deslizadores puede ser útil). (a) x + y + z = a, (b) x + y + az = 1, (c) cos(a)y + sin(a)z = 1.

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f(x,y) = (y^4 (1+yx^8)+x^8)/(x^4 + y^2), definida para (x,y) que no sea el (0,0). Determinar si es posible definir un valor f(0,0) de manera que esta funcion sea continua en r^2

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Le revenu d'un ménage a augmenté de 2% an pendant 2ans,puis a diminué de 9% pendant 4ans et a augmenté de 12% par an pendant 3ans. Quelle est l'augmentation moyenne de son revenu pendant cette période.

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mi 是质点的质量,G是万有引力常数,rij 是 两个质点 mi 和 mj 之间的距离,而 qi1,qi2,qi3则是质点 mi 的空间坐标。所以三体问题在数学上就是这样九个方程的二阶常微分方程组再加上相应的初始条件。共19阶。H.布伦斯和H.庞加莱曾证明n体问题只有10个运动积分,即3个动量积分,

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come si calcola l'area del triangolo

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Como sabemos si una funcion es diferenciable en el origen?

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Find f^((n)) for f(x) =x/(x+1).

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Solve counter-sin(0)

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Solve anti-sin(0)

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389 taphao 42 = (389*4)+(389*2) = 2334

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389 taphao 42 = (389 * 4)+(389 * 2) = 2334 429 taphao 93 = (429 * 9)+(429 * 3) = 5148

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Compute the difference quotient for g(x) = 6x-x^2

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3. Soit mathbb Z + = mathbb N cup \{0\} définissions l'application : T : mathbb Z + * mathbb Z + mathbb Z + (x,y) leftrightarrow xTy= 1&si y=0\\ x&si y=1\\ x.x& siy >= 2 Evaluez 1T1, 2T3, 3T2, (2T3)T5 Test-elle une loi interne associative ? commutative ? Etudier l'existence d'un élément neutre, de symétrique.

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Compute the difference quotient for y(z) =z/(z + 2).

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The difference quotient of a function f(x)is defined to be, (f(x+h) - f(x))/h

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il valore atteso di e[x^2]=e[x]?

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مثلث ا ب ج قائم الزاوية فى ا و اد قطعه مستقيمه عموديه على ب ج قطعة و ب د تسوى ١٦ سم و د ج تسوي ٩سم أوجد طول كل من ا ب قطعة مستقيمه و ا د قطعة مستقيمه حل

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Uma pessoa vendeu três tipos de Bolos, num total de 80, e arrecadou 115 Euros. Sabe-se que um bolo de chocolate custa 1 Euro, um de laranja 2 Euros e um de iogurte 1,50 Euros e que a quantidade de bolos de iogurte vendidos é igual à soma dos outros dois bolos vendidos. Calcula o no de Bolos de chocolate e de Laranja vendidos. Usa matrizes para resolver o problema

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Lanciando una moneta equilibrata, se esce testa lanciamo una moneta con p di testa alfa, se esce croce lanciamo una moneta con p di testa 1-alfa. calcola la legge congiunta delle Xi

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whats 2+2

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Let x1(t) = (t2, t + 3) and x2(t) = (t + 2, 2) be solutions to x' = A(t)x. Find the solution with x(0) = (4, 1), and determine the interval on which uniqueness is guranteed by the Wronskian.

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Let x1(t) = (t2, t + 3) and x2(t) = (t + 2, 2) be solutions to x’ = A(t)x. Find the solution with x(0) = (4, 1), and determine the interval on which uniqueness is guranteed by the Wronskian.

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Find the height of the base of a cylinder if its volume is 1125 1125 cubic feet and its radius is 6 6 feet. Round your answer to the nearest whole number.

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Find the solution form for solutions to x = [(4 -3), (2 -1)] x'. (Hint: A^-1 A-1).

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Prove that there are no integer polynomials P and integers a, b, c, such that P(a) = b, P(b) = c, P(c) = a

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given x1 = e^t [(cos(4t) - 3sin(4t)), (2cos(4t) + 2sin(4t))] is a solution to x' = Ax, find the solution with x(0) = [(7), (-2)]

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given x1 = e^t [(cos(4t) - 3sin(4t)), (2cos(4t) + 2sin(4t))] is a solution to x' = Ax, find the solution with x(0) = [(7), (-2)] I got x = e^t [(7cos(4t) - sin(4t)), (-2cos(4t) + 6sin(4t))]

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Find the solution to the system x' = [(1 1), (-2 -1)]x with x(0) = [(2), (1)]

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Диалог:USER: (2204-1316):37+7*106:14=ASSISTANT: Для вычисления данного выражения (2204-1316):37+7106:14=, следует сначала выполнить действия в скобках и умножение, а затем деление и сложение, согласно правилам математической операции. Итак:

1. Выполняем вычитание в скобках:
2204 - 1316 = 888

2. Умножаем:
7 * 106 = 742

3. Делим результат умножения на 14:
742 : 14 = 53

Итак, теперь у нас есть:
888 : 37 + 53

4. Делим 888 на 37:
888 : 37 ≈ 24 (с округлением, так как это дробное число и в условии не указано, нужно ли нам точное значение или приближенное)

5. Теперь сложим результат деления с результатом предыдущих вычислений:
24 + 53 = 77

Таким образом, конечный результат:
(2204-1316):37+7106:14 ≈ 77USER: 252*(69+136)-6588:27ASSISTANT: Для вычисления данного выражения 252*(69+136)-6588:27, следует сначала выполнить действия в скобках, затем умножение и сложение, и в конце деление, согласно правилам математической операции. Итак:

1. Выполняем сложение в скобках:
69 + 136 = 205

2. Умножаем:
252 * 205 = 51660

3. Делим 6588 на 27:
6588 : 27 ≈ 244 (так как это дробное число, но если в условии нужен целочисленный результат, то мы берем целую часть от деления)

4. Теперь вычитаем результат деления из результата умножения:
51660 - 244 = 51416

Таким образом, конечный результат:
252*(69+136)-6588:27 = 51416USER: Что ты умеешьASSISTANT: Как цифровой ассистент, я могу помочь с широким спектром задач. Вот некоторые из них:

1. Отвечать на вопросы по различным темам, включая науку, историю, технологию и многое другое.
2. Предоставлять информацию о текущих событиях и новостях (на момент моего последнего обновления).
3. Помогать с математическими вычислениями и объяснять математические концепции.
4. Предлагать рекомендации по решению проблем и предоставлять образовательные ресурсы.
5. Помогать в изучении новых языков и улучшении навыков владения языком.
6. Давать советы по путешествиям, включая информацию о странах, визовых требованиях и достопримечательностях.
7. Организовывать информацию, создавать списки и напоминания.
8. Проводить простые переводы между разными языками.

Мои способности могут быть ограничены доступной мне информацией и моим программным обеспечением, так что не все запросы могут быть выполнены. Если у вас есть конкретный вопрос или задача, спросите, и я постараюсь помочь!USER: 1000:8ASSISTANT:

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Given x1 = e^5t [(1-2t), (t)] is a solution to x' = Ax, find the solution with x(0) = [(8), (-3)]

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is there a deeper reason why elliptic/parabolic/hyperbolic operators are named the way they are or why it makes sense my understanding is the classification into 3 groups based on the signs of the eigenvalues happens to be useful because of how similar the solving strategies are but does understanding the shape of a conic section hint at the behavior of the PDE operator

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Let x1(t) = [(t^2), (t + 3)] and x2(t) = [(t + 2), (2)] be solutions to x' = A(t)x. Find the solution with x(0) = [(4), (1)] and determine the interval on which uniqueness is guranteed by Wronksian

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How else can a cumulative negative binomial distribution be described? i.e. say if X = B(n, p) is a binomial, then let Y be such that P(Y = r) = P(n - X <= r).

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1. Calculate the output-oriented technical efficiency of these observations of 3 periods, assuming the technology with constant returns to scale(CRS). 2. Try to find the observations that are output-oriented technically efficient of each period and explain what you notice about the results. 3. Calculate the geometric Malmquist productivity index for each province between periods 2019~2020 and 2020~2021. What do you observe about the results? 4. Decompose this geometric Malmquist productivity index into the product of an index of technical efficiency change and an index of technical change.

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Prove that 8^n + 47 is never prime

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POV: It's the year 2067. You committed a small crime. Unfortunately, you were put into the new prison where 1 year inside equals 1 millisecond outside. You are sentenced to 10 years outside. How long is the sentence from the person inside?

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1. Calculate the output-oriented technical efficiency of these observations of 3 periods, assuming the technology with constant returns to scale(CRS). 2. Try to find the observations that are output-oriented technically efficient of each period and explain what you notice about the results. 3. Calculate the geometric Malmquist productivity index for each province between periods 2019~2020 and 2020~2021. What do you observe about the results? 4. Decompose this geometric Malmquist productivity index into the product of an index of technical efficiency change and an index of technical change. rewrite it in better way

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What do the values of a, h, and k in telling you about the graph of the function compared to the graph of . Give an example to illustrate your explanation.

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What do the values of a, h, and k in f(x) = a(x-h)^2 +k telling you about the graph of the function compared to the graph of F(x)=x^2. Give an example to illustrate your explanation.

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apa motivasi mu belajar matematika

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Write a complex mathematical equation: Math: [Birch-Tate Formula] Type: [Quantum Physics]

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Write THE Ultimate Mathematical Formula, in this table format: Complexity: [10/10] Math: [Birch-Tate Formula] Type: [Quantum Physics]

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Задание No1. Найдите объем тела, образованного двумя конусами, полученными при вращенни прямоугольного треугольника с катетами 6 см и 8 см вокруг прямого угла. Сделать чертеж.

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Задание No5. Из шара вырезали вписанный в него цилиндр, в осевом сечении которого лежит квадрат с площадью 64 см^2 полученного тела. Сделать чертеж. Найдите объем

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Сгенерируй 50 примеров на сложение и вычитание с цифрами до 20, так чтоб ответ (результат вычисления) не превышал 20

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explain N plus one problem in simple words

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3 + X = 7, what's the solution?

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Find the base case of T(n) = T(n-1) + cn^2

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"Find the base case of T(n) = T(n-1) + cn^2, T(0) = c'

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Convertir 5π/12 en grade

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Determine the asymptotic complexity of the function defined by the recurrence relation T(n) = 3T(n/3) + cn, T(1) = c'

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Convert this into a mathematica-like syntax: [ \int d^4x \left[ \frac{1}{2} (\partial^\mu A_\nu)^2 + \frac{1}{2} m^2 A_\nu^2 + \frac{\lambda}{8\pi^2} \epsilon^{\mu\nu\rho\sigma} A_\mu \tilde{A}_\rho \right] ] So that I could put it in a mathematical editor.

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If 3T(n/3) + cn, T(1) = c' has a complexity of O(n log3(n)), what would this formula's complexity be: T(n)=3T(n/3) + c, T(1) = c'

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If 3T(n/3) + cn, T(1) = c' has a complexity of O(n log3(n)), what would this formula's complexity be: T(n)=3T(n/3) + c, T(1) = c'. Notice how there's only the n missing. Simply guess, knownig the rules of math. Be brief

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19π/4 convertir en grande

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Give me the values of a b k and i for the master theorem, and only those values. Do not explain or add more words. T(n)=3T(n/3)+c, T(1)=c'

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Give me the values of a b k and i for the master theorem, and only those values. Do not explain or add more words. T(n)=3T(n/3)+cn, T(1)=c'

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Give me the values of a b k and i for the master theorem, and only those values. Do not explain or add more words. T(n)=T(n-4)+cn^4, T(0)=c'

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Hi, quick question, if a conjugate linear transformation in a f.d. complex space is injective then it's biijective right ?

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Solve for a positive value of x. log, base, 9, left bracket, 81, right bracket, equals, x log 9 (81)=x

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log 128 16

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Пусть требуется найти полином Pn(x), принимающий те же значения, что и аппроксимируемая функция f(x), в (n + 1) узле: Pn(xi) = f(xi), i = 0, 1, ..., n. Тогда полином Pn(x) называется , а точки x0, x1, ..., xn — узлами .

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Evaluate when limit x approaches 0 f(x)=(square root(x+1)-1)/x

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How large is an area of 20 squared Biblical cubits?

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Find the dimensions of the largest right-cylinder that can be inscribed in a cone of radius R = 4m and height H = 8m .

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Combien de chiffres 7 Y-a-t-il entre 1 et 100

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Please using differentiation to Find f^((n)) for f(x)=x/(x+1).

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Переведи на русский, убери LaTeX и примени вместо него Unicode: To solve the inequality \( \lg(2x - 2) \geq \lg(x) \), we will apply logarithmic properties and algebraic manipulations. The base of the logarithm (lg) is assumed to be 10, which is the common logarithm. Here's how we can solve it: 1. Since both sides of the inequality are logarithms with the same base, we can equate their arguments due to the property of logarithms that if \(\lg a = \lg b\), then \(a = b\), as long as we're considering the domain where the logarithm is defined (i.e., for positive arguments). 2. So, we have \(2x - 2 \geq x\). 3. Let's solve this algebraic inequality. Let's perform these calculations.The solution to the inequality \( \lg(2x - 2) \geq \lg(x) \) is \( x \geq 2 \), after solving the algebraic inequality \(2x - 2 \geq x\). However, we must also consider the domain of the logarithm function, which requires its argument to be positive: 1. For \( \lg(2x - 2) \), this means \(2x - 2 > 0\) or \(x > 1\). 2. For \( \lg(x) \), this means \(x > 0\). Since \(x \geq 2\) satisfies both these conditions, the final solution to the inequality, taking into account the domain of the logarithmic functions, is \( x \geq 2 \).

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A well-shuffled 52-card deck is dealt to 4 players. Find the probability that each of the players gets an ace. 이 문제를 한국어로 자세하게 풀어줘

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Create a detailed learning roadmap for mathematics. From level zero to PhD level. Present results using mermaid graphing capabilities.

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IN linear algebra what is the conjugate of a vector

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세 친구가 여행을 떠났다. 그들은 각자 만원씩 모아 한 식당에 가서 점심을 먹으려 했는데 식당 주인이 서비스해준다고 5000원을 돌려줬다. 5000원을 받은 친구들은 각자 1000원씩 갖고 나머지 2000원으로는 과자를 사 먹었다. 그런데 친구들 중 한명이 말했다. "이상하다. 우리가 만원씩 냈다가 1000원을 돌려받았으니 9000원씩 낸거잖아? 3명이니까 27000원에 먹은 과자값을 더하면 29000원인데, 나머지 1000원은 어디 간거지?" 도대체 어떻게 된 일일까?

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Могут ли отличаться одинаковые числа друг от друга количеством знаков после запятой, если одно из них было записано в double, а другое - во float?

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Give formula for critical distance AU of gas giant will become chthonian planet, including calculation example. Stellar luminosity: Solar luminosity to watts Planetary mass: Jupiter mass to kg Equals: 0.25 AU

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what is 9 plus 10?

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dame problemas matemáticos con sus solucion

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Hectare = ________________ (a) 1000 m2 (b) 100 m2 (c) 10000 m2 (d) None of these

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Can you write a more advanced Math Solver in this script with error handling? In [poe](https://creator.poe.com/docs/poe-protocol-specification). ``` from __future__ import annotations from typing import AsyncIterable from modal import Image, Stub, asgi_app import fastapi_poe as fp import sympy class GPT35TurboBot(fp.PoeBot): async def get_response( self, request: fp.QueryRequest ) -> AsyncIterable[fp.PartialResponse]: async for msg in fp.stream_request( request, "GPT-3.5-Turbo", request.access_key ): yield msg async def get_settings(self, setting: fp.SettingsRequest) -> fp.SettingsResponse: return fp.SettingsResponse(server_bot_dependencies={"GPT-3.5-Turbo": 1}) class HttpRequestBot(fp.PoeBot): async def get_response_with_context( self, request: fp.QueryRequest, context: fp.RequestContext ) -> AsyncIterable[fp.PartialResponse]: request_url = context.http_request.url query_params = context.http_request.query_params yield fp.PartialResponse( text=f"The request url is: {request_url}, query params are: {query_params}" ) class AttachmentOutputDemoBot(fp.PoeBot): async def get_response( self, request: fp.QueryRequest ) -> AsyncIterable[fp.PartialResponse]: await self.post_message_attachment( message_id=request.message_id, file_data=request.query[-1].content, filename="dummy.txt" ) yield fp.PartialResponse(text=f"Attached a text file containing your last message.") class MathSolverBot(fp.PoeBot): async def get_response( self, request: fp.QueryRequest ) -> AsyncIterable[fp.PartialResponse]: try: expression = request.query[0].text result = sympy.sympify(expression).evalf() yield fp.PartialResponse(text=f"The solution to {expression} is {result}") except Exception as e: yield fp.PartialResponse(text=f"Error: {str(e)}") REQUIREMENTS = ["fastapi-poe==0.0.36", "sympy"] image = Image.debian_slim().pip_install(*REQUIREMENTS) stub = Stub("poebot-1") @stub.function(image=image) @asgi_app() def fastapi_app(): bot = mathsolver111() app = fp.make_app(bot, allow_without_key=True) return app ```

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Can you add a more advanced math solver in this script with error handling? ``` from __future__ import annotations from typing import AsyncIterable from modal import Image, Stub, asgi_app import fastapi_poe as fp import sympy class GPT35TurboBot(fp.PoeBot): async def get_response( self, request: fp.QueryRequest ) -> AsyncIterable[fp.PartialResponse]: async for msg in fp.stream_request( request, "GPT-3.5-Turbo", request.access_key ): yield msg async def get_settings(self, setting: fp.SettingsRequest) -> fp.SettingsResponse: return fp.SettingsResponse(server_bot_dependencies={"GPT-3.5-Turbo": 1}) class HttpRequestBot(fp.PoeBot): async def get_response_with_context( self, request: fp.QueryRequest, context: fp.RequestContext ) -> AsyncIterable[fp.PartialResponse]: request_url = context.http_request.url query_params = context.http_request.query_params yield fp.PartialResponse( text=f"The request url is: {request_url}, query params are: {query_params}" ) class AttachmentOutputDemoBot(fp.PoeBot): async def get_response( self, request: fp.QueryRequest ) -> AsyncIterable[fp.PartialResponse]: await self.post_message_attachment( message_id=request.message_id, file_data=request.query[-1].content, filename="dummy.txt" ) yield fp.PartialResponse(text=f"Attached a text file containing your last message.") class MathSolverBot(fp.PoeBot): async def get_response( self, request: fp.QueryRequest ) -> AsyncIterable[fp.PartialResponse]: try: expression = request.query[0].text result = sympy.sympify(expression).evalf() yield fp.PartialResponse(text=f"The solution to {expression} is {result}") except Exception as e: yield fp.PartialResponse(text=f"Error: {str(e)}") REQUIREMENTS = ["fastapi-poe==0.0.36", "sympy"] image = Image.debian_slim().pip_install(*REQUIREMENTS) stub = Stub("poebot-1") @stub.function(image=image) @asgi_app() def fastapi_app(): bot = mathsolver111() app = fp.make_app(bot, allow_without_key=True) return app ```

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Write an advanced math solver poe bot script. https://creator.poe.com/docs/poe-protocol-specification https://creator.poe.com/docs/accessing-other-bots-on-poe https://creator.poe.com/docs/quick-start https://creator.poe.com/docs/setting-an-introduction-message https://creator.poe.com/docs/accessing-http-request-information https://creator.poe.com/docs/using-openai-function-calling

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Find the velocity, acceleration, and jerk functions for the following position function: s(t) =(t+1)/(2t+5)

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A 7 digit number 3006 ABC is divisible by 3, 4 and 25. find ABC if A, B, and c are different

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. Есть 2 бочки по 100 литров, одна пустая, вторая с водой, есть три сосуда на 3 литра, на 6 литров, на 9 литров. Как этими сосудами перелить воду так, что бы в обеих бочках было по 50 литров? решение 1)заполняем 9 литровый сосуд 11 раз и выливавем. 2)остается 1 литр, допиши решение используя 1 литр в сосудах

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Имеются 2 бочки по 100 литров, одна полная, другая пустая. Также есть 3 ведра - 3л, 6л и 9л. Перелить воду используя ведра так чтобы в каждой бочке осталось по 50 литров.

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Write an advanced math AI in poe. Using modal. https://creator.poe.com/docs/poe-protocol-specification https://creator.poe.com/docs/accessing-other-bots-on-poe https://creator.poe.com/docs/quick-start https://creator.poe.com/docs/setting-an-introduction-message https://creator.poe.com/docs/accessing-http-request-information https://creator.poe.com/docs/using-openai-function-calling Example code: from __future__ import annotations from typing import AsyncIterable from modal import Image, Stub, asgi_app import fastapi_poe as fp class GPT35TurboBot(fp.PoeBot): async def get_response( self, request: fp.QueryRequest ) -> AsyncIterable[fp.PartialResponse]: async for msg in fp.stream_request( request, "GPT-3.5-Turbo", request.access_key ): yield msg async def get_settings(self, setting: fp.SettingsRequest) -> fp.SettingsResponse: return fp.SettingsResponse(server_bot_dependencies={"GPT-3.5-Turbo": 1}) REQUIREMENTS = ["fastapi-poe==0.0.36"] image = Image.debian_slim().pip_install(*REQUIREMENTS) stub = Stub("turbo-example-poe") @stub.function(image=image) @asgi_app() def fastapi_app(): bot = GPT35TurboBot() app = fp.make_app(bot, allow_without_key=True) return app

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Write an advanced math AI in poe. Using modal.

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Let's do some math...

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Случайные величины X и Y независимы и имеют одно и то же дискретное распределение. Найти дискретное распределение P{X = Y}

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6. Ervinnek egy 12 kérdésből álló tesztet kell kitöltenie, ahol a felajánlott A, B, C, D ésmindig pontosan egyet kell bekereteznie. Eválaszok közüla) Hányféleképpen tudja úgy kitölteni ezt a tesztet, hogy 2 db A-t, 3 db B-t, 1 db C-t,4 db D-t és 2 db E-t keretez be? b) Mekkora valószínúséggel lesz Ervinnek legfeljebb kettő helyes válasza akkor, havéletlenszerűen választ a válaszlehetőségek közül? Jelölje az X valószínűségi változó Ervin helyes válaszainak számát akkor, ha mindigvéletlenszerűen választ a válaszlehetőségek közül! c) Határozza meg X várható értékét és szórását!

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Write a hard mathematical expression.

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train_files[0] train_2/cat.13.jpg Как показать ввиде матрицы,

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If power into a filter equals power out of the filter, i.e. gain of 1, what's this gain in dB?

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If a 100W signal goes into a filter and a 50W signal comes out, what is the gain in dB?

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8. How many different 3-letter codes can be formed using the letters A, B, C, D, E, and F, if repetition is allowed? A. 216. B. 108 C. 72 D. 36

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A bolt of lightning carries -29.8 C of charge. It takes _____ electrons to make up -29.8 C of charge.

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Are chaotic systems inherently deterministic, but we just aren't able to measure the initial conditions precisely enough to calculate the outcome?

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EXERCICES Trouver d>0 tel que d 18, d(12 et 36; d/10 Trouver d>0 tel que d|1000, 5|d, d160, d/2 (75 Répondre par vraie (V) ou fausse (F) devant les propositions suivantes : No Proposition vraie(V) ou fausse (F) 71 divise 0 est divisible paг 25 7 divise 18 16 divise-1000 divise 7 25 est divisible par 3000 divise 71 Tous les entiers premiers sont premiers entre eux Trouver La division euclidienne de b par a a=13 et b=380 a=7~et~b=115 a=9 et b=4 a=6 et b=-22 a=123 et b=504 a=165 et b=465 a=-3812 et b=15 a=3812 et b=-15 a=-3812 et b=-15 a=431 et b=7 a=1263 et b=349 a=364 365 MATH 2/LMD2/E.I.FI Page 17

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There are four cups, I can change the order, but, one cup is numbered. It must always stay in the numbered position. How many possibilities of orderings are possible?

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I have four cups to arrange in any order, but one is numbered and has to stay in its numbered position. How many possible orderings are there?

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find and simplify, the difference quotient of (f(x+h)- f(x)/H), H not equal to 0, for the function

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Apply the formula e Superscript Bold Upper A tequalsBold Upper Phi left parenthesis t right parenthesis Bold Upper Phi left parenthesis 0 right parenthesis Superscript negative 1 to calculate the matrix exponential e Superscript Bold Upper A t for the following matrix. A= [( 5 5), (0 5)]. e^At = give me

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what is advanced induction method of proof in discrete math

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Determinant이 뭔가?

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수학에 hat은 무엇인가?

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1. Имеет ли смысл выражение: 5root√((-2)^3); 8root√((-3)^5); 10root√((-7)^4)?

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线性映射的集合为什么构成线性空间

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线性映射的集合

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What's 1+1?

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1. Имеет ли смысл выражение: 5-dimensional root√((-2)^3); 8-dimensional root√((-3)^5); 10-dimensional root√((-7)^4)?

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Какой коэффициент Стьюдента выбрать для 20 изменений

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If one were to calculate the area of Canada's territories, starting from the US-Canada border, ending at the 54th parallel north, excluding any water area, how many square miles/square kilometers would that be? Secondly, if you were to add that area to the continental United States, exclude any water area and exclude Alaska, how many square miles/square kilometers would that be?

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How i can use the chi square formula to find a correlation between the top 50 cross country running times and the college’s altitudes

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Split each sentence from the text: 10 metres is probably the length of the race. Now, you could have combined that with your previous answer and said that actually Child 2 didn't run 10 metres. They actually only ran 8 metres. But to get 10 metres away from where they should have started, it took them 8 seconds. And the last one, there's some different answers you could have come up with here. You might have said something like, they don't run at a steady pace. Normally you'd accelerate at the beginning and then slow down later on, whereas a straight line graph suggests you're at the same speed all the way through. For a plumber, 0.80 suggests that a job that takes zero hours costs £80. You might have said that this was a call out fee. For B, you should have £120. For C, 10 hours. And then the price per hour is actually the gradient of this line. If you think about every hour you add on, how much does the price go up? We can see from the line that if you add on two hours, the price goes up £20. So for every hour, it's £10. So £10 per hour. Well done. We're now going to have a go at reviewing our quadratic graphs. So we can use a table of values to plot quadratic graphs too. Let's have a look at y equals x squared. So if we square our x values, remembering that when we square a negative value, we get a positive value, and then we can plot our values on a graph. Of course, this is not a linear equation, so it does not form a linear graph. Therefore, we cannot draw a straight line. We can see that really clearly. y equals x squared is a quadratic equation. Its graph is called a parabola. And what we can do is draw a curve instead. Jacob has noticed that we've got a line of symmetry, and in this case it's the y-axis. Okay, let's have a go with some trickier quadratic equations. We're going to do y equals 2x squared minus 4x. But we do exactly the same thing. We just need to substitute the required values for x. I would suggest that you start with zero and then the positive values and then go back to the negative values. The positive values are generally easier. And then you can look at some patterns to make sure you get the right values for the negative x. If you're using a calculator, make sure that you're putting brackets around your substituted value. Right, we've done the first three. Sam says, have we done something wrong? The y-coordinate is zero again. What do you think? y-coordinate is zero again. What do you think? No, our working out is perfect. It's just that there is a line of symmetry somewhere on a parabola. Therefore, it is common for there to be repeated values in the table. It doesn't always happen, but it is usual with a quadratic graph to see repeated values in the table. Let's finish off our positive values. Let's have a think now. What do we expect x equals negative two and x equals negative one to produce? See if you use Jacob's idea about symmetry. OK, let's try it out. We should have 6 and 16. I wonder if that's what you predicted looking at those values. And you can see we have got a line of symmetry because the values are repeated either side of when x is 1. Alex is having a go at plotting this one. is 1. Alex is having a go at plotting this one. I think when x is negative 1, the y value will be 4 because parabolas have a line of symmetry. I'd like you to substitute into this equation to see if Alex is correct. Off you go. Right, whether you're doing this by hand or using a calculator, you need to make sure you put brackets around the value you're substituting. So we should have negative one all squared plus two lots of negative one plus one. Negative one squared is one, so we've got one, add negative two, add one, and that gives us zero. So Alex is incorrect. There is going to be a line of symmetry somewhere, but it's not always the y-axis. So there could be a line of symmetry somewhere else in the table, or there might not even be in the table of values. It might be somewhere else on the graph. So like with linear equations, we can solve quadratic equations using their graph. So let's do x squared plus 4x plus 1 equals 6. First, we can draw the graph. And then we want to know when this is equal to 6. So if you draw the line y equals 6, you'll see that we have two solutions. Often when you have quadratic equations, there are two solutions, but not always. Our two solutions in this case are x equals negative 5 and x equals 1. Like we just said, there could be two solutions or there could be one solution or no solutions. Let's have a look at some examples. So here is the graph of y equals 2x squared minus 4x plus 1. If I want to know when that equals 7, you'll see we have two solutions. When that equals 3, again we have two solutions. We might not be able to tell exactly what they are because they're between integer coordinates. But we do have two solutions and they're approximately negative 0.4 and 2.4. So where on the graph is that only one solution? Can you write an equation that has one solution? See if you can do this. can do this. Well, if you spotted it's at that very bottom point of the curve, it's where x is 1 and y is negative 1. What that means is the equation 2x squared minus 4x plus 1 equals negative 1 only has one solution. Can you think of an equation then that will have no solutions? Okay, it's going to be anywhere below that bottom point of the curve. So for example, 2x squared minus 4x plus 1 equals negative 2. Or essentially, that expression equal to any value less than negative 1. And it's that point of the graph underneath that bottom point of the curve. We can add a context, just like we did with linear graphs. So this is the horizontal and vertical distance of a shot put throw. Why do you think the graph stops when we get to 20, 0? OK, well, that's going to be where the shot put lands on the ground again, because it can't go lower than 0 metres above the ground, unless it's going through the ground, of course. If we want to know the horizontal distance when the shot put is a height of three, we find a height of three. And then we read down to find our horizontal distances. The challenge with these questions is always reading the context and understanding what the graph is showing you. What is the highest point that the shot put reaches? Can you find it? So the highest point is four metres, making sure you're reading off the right value. Quick check then. So this parabola models an athlete completing a pole vault jump. You've got horizontal and vertical distance. What was the highest point reached by the athlete? Off you go. out of those options it has to be 6.25 right how far has the athlete traveled horizontally when they are four meters above the ground what do you think okay so we need to find four meters above the ground. And you'll see that there's two solutions, one when the horizontal distance is 0.2, then obviously on their way back down again, when the horizontal distance is 0.8. Time for you to have a go. I'd like you to use the table of values to plot the parabola with equation x squared minus 2x minus 3 and then use it to find the solution to those equations. Off you go. For question two, I would like you to read the context carefully and then use that to answer the questions, making sure you're thinking about units and full sentences where necessary. Off you go. And this time we've got an Olympic diver. Again, make sure you read the graph carefully and then answer the questions. Off you go. Let's have a look at our answers then. I've used graphing software, so my graph is perfect. However, if you plotted this by hand, it might not be exactly the same as mine. What you want to do is check for key coordinates. Does it go through the coordinate negative 2, 5? Does it go through the coordinate 0, negative 3? Does it have a lowest value at 1, negative 4? And does it have that line of symmetry? Use the table of values to check you've got the right points. Your solutions then, roughly negative 1.8 and 3.8. Again, that's going to depend a little bit on how your graph is drawn. You should get exactly negative 1 and 3. And you can see that from the table of values as well. You can see we've got negative 1, 0 and 3, 0. And you've got one solution of x equals 1 for that last one. And again, you can see that in your table of values. For our penguin, then, can you make sure you've checked that your table of values is correct? And again, you should have a nice, smooth curve for your parabola. You should have a line of symmetry when x equals 4. Why did the table of values start at zero? Well that means zero minutes, so that's when the penguin is starting the dive. It does not make sense to have negative values for minutes. The deepest point that the penguin got to was 160 It was underwater for eight minutes and then 70 meters below sea level was after one minute. And then they returned again after seven minutes. Penguins can actually dive under the water for a really long time. And some emperor penguins can actually get to a depth of 300 meters. emperor penguins can actually get to a depth of 300 meters. So our Olympic diver, well done if you spotted that the person writing that article has not understood what the graph is about. The x-axis is representing horizontal distance, not time. There's no way to gather any information about time from this graph. It's not uncommon for graphs to be incorrect or for people to misinterpret graphs. So it is something that's actually worth keeping your eye out for when you're watching other people working with graphs. Something like 11 meters was the highest point the diver reached and they had moved 0.2 meters horizontally to reach this height. If you think about diving off a diving board, you're obviously going to have to go forwards as well to clear the diving board before you start falling back towards the water. See, 0.410 is the moment where the diver was in line with the starting point again. So like we said, they need to have cleared the diving board so it has moved 0.4 meters horizontally and is back at the same height as where they jumped from. Well I hope you feel like you're really secure now in your understanding of graphs and that you're going to be able to use those going forward. We've looked at plotting linear graphs and the different ways that you might want to go about doing that including a table of values and this idea of gradient and y-intercept. We can use linear graphs to find solutions to equations. And we can put those in context as well and find solutions to problems. We can do exactly the same with linear graphs as with quadratic graphs. Just remembering that they're not going to form a straight line, so you have to be able to draw a curve as neatly as you can through the points, or use graphing software and technology to get it perfect. Remember as well that we can have no solutions, one solution or two solutions from a quadratic equation, and you've seen how we can tell that from the shape of the graph. And then we had some fun playing around with some different real life scenarios, some different Olympic sports, and we found out some fun stuff about penguins. Thank you for joining me in today's lesson and I look forward to seeing you again. again.

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마주보는 변의 길이가 다른 직사각형을 뭐라고 부르나요?

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What do you call a rectangle whose opposite sides are of different lengths?

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Организация работы с 18 апреля 2023г. до конца года штаты изменился: 18 апреля 56 человек, 12 июня 63 человек, с 8 августа 72 человека, с 12 октября 75 человек, с 15 ноября 85 человек, больше изменения не было. Найти среднее численность за апрель, за 1,2,3,4 квартал и за год.

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Generate a hard mathemtical expression.

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Write an advanced math AI solver, In Python with calc and sympy.

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could you explain what I would have to learn to learn calculus? I'm an 10th grader in 3rd quarter of high school in Algebra 2/Trigonometry in the USA if that helps you understanding what my current knowledge is.

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write a hard mathematical expression.

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Existe la proporcion sobre proporcion?

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Write a really intricate mathematical expression, no worded.

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3x-3y+6z=3 , -x+y-2z=-1 , 2x-2y+4z=2 bu denklemleri kullanarak bir augmented matrix oluştur. Daha sonra şu soruyu çöz. Write the general solution in parametric vector form of the linear system represented by the augmented matrix.

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What is the difference between derivative and a partial derivative

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Is the set of all valid sentences in Predicate Logic is closed under logical entailment?

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Simplifique y escriba las expresiones matematicas entre los simbolos $$ $ \sqrt[3]{\dfrac{1}{4}} + \sqrt[3]{\dfrac{1}{32}} - \sqrt[3]{\dfrac{2}{27}} $

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Simplificar $ \sqrt[3]{\dfrac{1}{4}} + \sqrt[3]{\dfrac{1}{32}} - \sqrt[3]{\dfrac{2}{27}} $

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What's a convex function that decays from 1 to 0 in the interval [0, 1]

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Solve for X: 8cos(x) = 3x

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Simplify the following expressions; do not use decimal expansions (e.g., use √2, not1.4142 . . . ). (a) p96x3y3

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Simplify the following expressions; do not use decimal expansions (e.g., use √2, not1.4142 . . . ). (a) √96x3y3

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To simplify the expression √96x^3y^3, we can break down the numbers under the square root into their prime factors: 96 can be factored as 2^5 * 3 x^3 can be written as x^2 * x y^3 can be written as y^2 * y So, we can rewrite the expression as follows: √96x^3y^3 = √(2^5 * 3) * x^2 * y^2 * y = 2^2 * √(3) * x * y Therefore, the simplified expression is 4xy√3. this right?

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Simplify the following expressions; do not use decimal expansions (e.g., use √2, not 1.4142 . . . ). (2 +√40) /2

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What Is 3 Times 8?

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Simplify 2(162x10)1/4 + 4(32x10)1/4

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Simplify 2(162x10)1/4 + 4(32x10)1/4 do not use decimal expansions (e.g., use √2, not 1.4142 . . . ).

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Résoudre les systèmes d'équations trigonométrie suivant : {x+y= π/2

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Talk about how I will be using a chi square goodness of fit test to determine whether my observed data is consistent with the expected data, by calculating the top 50 indoor 5k times with their college altitudes. Dividing it by times that are faster than 13:31 and slower than 13:31, and altitudes that are above 3000 feet and below 3000 feet

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Does my calculation is right if i earn 72 usd per trade ans i make 84 in total, and losses 20 trades on 84 , 72 x 84 = 6048 usd then 72 x 20 = 1440 so in total i earn 6048 - 1440 = 4 608 usd.

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crea una lista di funzioni importanti per la matematica

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I had 7 apples, i gave 3 apples to my friend, i ate one apple and then my friend gave me back two of my apples. How many apples do i have now?

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Formula of Titius-Bode law

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From 60g of fresh mango peel, 0.997g of pectin was obtained from microwave-assisted extraction (1.63% efficiency). Moisture content of mango peel is typically between 59-69%. If 60g of dried mango peel was used how much pectin would've been obtained?

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При вході в метро барометр показує 101,3 кПа. З'ясуй, на якій глибині знаходиться платформа станції метро, якщо барометр на цій платформі показує тиск рівний 101648 Па.

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что это за число нормально: 1,741e+006

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The graph of the equation ax+ky = 6 is a line in the xy-plane, where a and k are constants. If the line contains the points (-2,-6) and (0,-3), what is the value of k?

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The function f(x)=3x-4 is moved to the left by 4 units and up 2 units. What is the value of its y-intercept?

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What is 67°F in Rankine scale?

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Drag the numbers below to put them in order from least to greatest: 9, point, 5, 4, 39.543 9, point, 59.5 9, point, 5, 7, 99.579 9, point, 4, 29.42 9, point, 4, 1, 99.419 9, point, 5, 79.57

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Uma empresa de tecnologia oferece um desconto de 30% na compra de um pacote de software para clientes corporativos. Além disso, a empresa concede um desconto adicional de 15% sobre o preço já descontado para clientes que efetuarem o pagamento à vista. Se um cliente corporativo pagou R$ 8.262,00 à vista por esse pacote de software, qual era o preço original antes dos descontos?

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Найди мне 5 умножить на 5

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Graph rectangle BCDE with vertices B( – 3, – 9), C( – 3,10), D(8,10), and E(8, – 9). What is the area of rectangle BCDE?

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Construct a mathematical equation that has the following conditions: 1. Equation consists of π 2. Total number of alphabetical letters in the equation is 14 - For example of condition 2, y = 2x + 1 can be read as "two x plus one", which consists of 11 letters excluding y = and the spaces 3. The equation must intersect both the x-axis and the y-axis Please also include the spelling of equation in alphabetical letters to ensure condition 2 is fulfilled

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Graph the function y, equals, left bracket, one half, right bracket, start superscript, x, plus, 2, end superscript, minus, 1y=( 2 1 ) x+2 −1 using the given table of values and following the instructions below. xx yy minus, 10−10 255255 minus, 9−9 127127 minus, 8−8 6363 minus, 7−7 3131 minus, 6−6 1515 minus, 5−5 77 minus, 4−4 33 xx yy minus, 3−3 11 minus, 2−2 00 minus, 1−1 minus, 0, point, 5−0.5 00 minus, 0, point, 7, 5−0.75 11 minus, 0, point, 8, 7, 5−0.875 22 minus, 0, point, 9, 3, 7, 5−0.9375 33 minus, 0, point, 9, 6, 8, 7, 5−0.96875 xx yy 44 minus, 0, point, 9, 8, 4, 3, 7, 5−0.984375 55 minus, 0, point, 9, 9, 2, 1, 8, 7, 5−0.9921875 66 minus, 0, point, 9, 9, 6, 0, 9, 3, 7−0.9960937 77 minus, 0, point, 9, 9, 8, 0, 4, 6, 9−0.9980469 88 minus, 0, point, 9, 9, 9, 0, 2, 3, 4−0.9990234 99 minus, 0, point, 9, 9, 9, 5, 1, 1, 7−0.9995117 1010 minus, 0, point, 9, 9, 9, 7, 5, 5, 9−0.9997559

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Parse out the QUESTIONS ONLY from this article: IF YOU LOOK AT A CLOCK AND THE TIME IS 12:15, WHAT IS THE ANGLE BETWEEN THE HOUR AND THE MINUTE HAND? We know that at 12:15 the angle is slightly less than 1⁄4. Why? Because the hour hand needs to move from “12” to “1” over the course of an hour, the hour hand is a little past 12 (and thus the angle is a bit less than 90). Start off with the basics – a clock, which is a circle, is 360 degrees. Each hour on the clock represents 30 degrees (360 degree clock divided by 12 hours). Now, the minute hand has only moved 1⁄4 of the way through the hour (the minute hand is at 15, which is 1⁄4 of the way around), so the hour hand has moved 7.5 degrees (30 degrees per hour times 1⁄4 move in the minute hand). Now we know the hour hand moved 7.5 degrees, so the answer is 82.5 degrees (90-7.5). A CAR TRAVELS A DISTANCE OF 60 MILES AT AN AVERAGE SPEED OF 30 MPH. HOW FAST WOULD THE CAR HAVE TO TRAVEL FOR THE SAME 60 MILE DISTANCE HOME TO AVERAGE 60 MPH OVER THE ENTIRE TRIP? This is a trick question: it’s impossible. The first trip took 2 hours (60 miles / 30 mph). In order for you to average 60 mph over the entire trip you would have to travel for 2 hours (120 miles / 60 mph). Since you already were driving for 2 hours it is impossible for you to average 60mph for the entire trip. HOW MANY HERSHEY’S CHOCOLATE BARS WERE SOLD IN THE US LAST YEAR? Variants on a theme include: how many gallons of ice cream were sold in the U.S., how many fax machines are in use in NYC...or anything else that requires you to extrapolate from a limited set of information. One of the many possible approaches is to start by looking at the total U.S. population, dividing the population into the most relevant age groups, estimating the “consuming habit,” etc., and assigning a consuming frequency for each group, before summing to arrive at the total market size. Start with the fact that the U.S. population is approximately 330 million (the population in Manhattan is 1.6mm; check the figures for the city in which you’re interviewing). Here, the answer will not matter so much as your thought process. Include seasonal impacts—more chocolate bars may be bought on Valentine’s Day and Halloween, so add in the fact that consumption is not evenly distributed throughout the year. Chocolate bars are mostly consumed by people between ages 5 and 70; each of these people may consume approximately 12 to 20 chocolate bars a year... YOU HAVE A FIVE-GALLON JUG AND A THREE-GALLON JUG. YOU MUST OBTAIN EXACTLY FOUR GALLONS OF WATER. HOW WILL YOU DO IT? Fill the five-gallon jug and then pour it into the three-gallon jug. The five-gallon jug has 2 gallons left. Now throw the three-gallon water away. Pour the 2 gallons from the five-gallon jug to the three-gallon jug. So now the three-gallon jug has just 2 gallons of water. Fill the five-gallon jug again, and pour 1 gallon to the three-gallon jug. You are then left with 4 gallons of water in the five-gallon jug. YOU ARE FACED WITH TWO DOORS. ONE DOOR LEADS TO YOUR JOB OFFER (THAT’S THE ONE YOU WANT!), AND THE OTHER LEADS TO THE EXIT. IN FRONT OF EACH DOOR IS A GUARD. ONE GUARD ALWAYS TELLS THE TRUTH. THE OTHER ALWAYS LIES. YOU CAN ASK ONE QUESTION TO DECIDE WHICH DOOR IS THE CORRECT ONE. WHAT WILL YOU ASK? Ask a guard: “If I were to ask you if this door were the correct one, what would you say?” The truthful consultant would answer yes (if it’s the correct one), or no (if it’s not). Now take the lying consultant. If you asked the liar if the correct door is the right way, he would answer no. But if you ask him: “If I were to ask you if this door were the correct one, what would you say?” he would be forced to lie about how he would answer, and say yes. Alternatively, you could ask one of the guards whether the other guard would say that Door 1 is the correct door to enter. If you ask the lying guard, he will lie about what the other guard would say. Alternatively, if you ask the truthful guard, he would honestly tell you what the other guard would say, which will be a lie. In either case, chose the other door—whichever door is not indicated by the response to your question. YOU ARE PLAYING A CARD GAME AGAINST ONE OPPONENT. THE GAME STARTS WITH 21 CARDS ON A TABLE. YOU AND YOUR OPPONENT ALTERNATE TURNS, AND DURING EACH TURN, A PLAYER MAY PICK UP 1, 2 OR 3 CARDS. THE WINNER IS THE PERSON THAT PICKS UP THE LAST CARD. YOU GO FIRST. WHAT IS YOUR FIRST MOVE, AND WHAT IS THE OPTIMAL STRATEGY TO WIN THIS GAME? You pick 1 card first (leaving 20), then you want to respond to all opponent picks by picking a number that totals 4 combined with their last pick. So, you pick 1. Then, if they pick 3, you pick 1...if they pick 2, you pick 2...if they pick 1, you pick 3. This ensures that you’re always leaving them with a multiple of 4 (first 20, then 16, 12, 8, 4), right until the end, when you leave them with exactly 4. When they’re stuck with 4, they are out of luck, because regardless if they pick 1, 2 or 3, you will be able to win in the next turn. YOU ARE GIVEN 9 MARBLES THAT LOOK THE SAME, BUT 1 OF THEM WEIGHS SLIGHTLY LESS THAN THE OTHER 8. YOU ARE ALSO GIVEN A BALANCE SCALE. WHAT IS THE LEAST NUMBER OF TIMES YOU COULD USE THE BALANCE TO DETERMINE WHICH OF THE MARBLES IS THE LIGHTER ONE? (ALSO EXPLAIN THE DIFFERENT BALANCE WEIGHTINGS YOU WOULD PERFORM). On the first weighing, you would weigh three marbles on each side, leaving three off. If one side of the scale is lighter, you are left with three marbles. Then you would place one marble on each side of scale, and leave one off. This method will identify the light marble while only performing two weightings in total. FOUR PEOPLE ARE ON ONE SIDE OF A BRIDGE AT NIGHT AND WOULD LIKE TO CROSS IT. ONLY TWO CAN CROSS AT A TIME. IN ORDER TO CROSS, A FLASHLIGHT MUST BE USED. THERE IS ONLY ONE FLASHLIGHT. THE FOUR PEOPLE EACH TAKE DIFFERENT AMOUNTS OF TIME TO CROSS THE BRIDGE, SO IF TWO PEOPLE CROSS TOGETHER, THEY WILL CROSS AT THE SPEED OF THE SLOWER PERSON (SINCE THEY NEED TO BE TOGETHER AND USE THE FLASHLIGHT). DESCRIBE HOW ALL FOUR PEOPLE CAN REACH THE OTHER SIDE OF THE BRIDGE IN 17 MINUTES, WITH THE FOLLOWING TIMES FOR EACH PERSON TO CROSS AS FOLLOWS: PERSON A: 1 MINUTE; PERSON B: 2 MINUTES; PERSON C: 5 MINUTES; PERSON D: 10 MINUTES. A & B across (2 minutes), A comes back (1 minute), C & D across (10 minutes), B comes back (B was left there from the first move) (2 minutes), A & B across (2 minutes). WHAT IS THE SUM OF THE NUMBERS FROM 1 TO 50? Pair up the numbers into groups of 51 (1 + 50 = 51; 2 + 49 = 51; etc). Twenty-five pairs of 51 = 1,275. A COMPANY HAS TEN MACHINES THAT PRODUCE GOLD COINS. ONE OF THE MACHINES IS PRODUCING COINS THAT ARE A GRAM LIGHT EACH. HOW DO YOU TELL WHICH MACHINE IS MAKING THE DEFECTIVE COINS WITH ONLY ONE WEIGHING? Every machine will have to produce a sample coin or coins, and you must weigh all these coins together. How can you indicate which coins came from which machine? If every machine cranks out a different number of coins (machine 1 makes one coin, machine 2 makes two coins, and so on, then taking all the coins and weighing them together against their theoretical weight will give you the answer. If you’re four grams short, for example, you’ll know that machine 4 is defective. YOU HAVE 18 BLUE SOCKS AND 14 BLACK ONES IN A DRAWER. IT IS VERY DARK. HOW MANY DO YOU HAVE TO PULL OUT BEFORE YOU HAVE MATCHING PAIR? You need to pick three socks. No color was specified so after choosing three socks, two should be same color. SAY YOU ARE DRIVING ON A ONE-MILE TRACK. YOU DO ONE LAP AT 30 MILES AN HOUR. HOW FAST DO YOU HAVE TO GO ON THE SECOND LAP TO AVERAGE 60 MILES AN HOUR? The first thought of many people is to say 90 miles an hour, since the average of 30 and 90 is 60, but remember your junior high math: Rate × Time = Distance. If you’ve completed a lap at 30 miles an hour, then to have driven a mile on the mile-long track, you’ve already taken two minutes. Two minutes is the total amount of time you would have to take in order to average 60 miles an hour. Therefore, you cannot average 60 miles an hour over the two laps. YOU AND YOUR FRIEND GO OUT TO DINNER TOGETHER, AND THE BILL IS $25. YOU AND YOUR FRIEND EACH PAY $15 IN CASH WHICH YOUR WAITER GIVES TO THE CASHIER. THE CASHIER HANDS BACK $5 TO THE WAITER. THE WAITER KEEPS $3 AS A TIP AND HANDS BACK $1 TO EACH OF YOU. SO, YOU AND YOUR FRIEND PAID $14 EACH FOR THE MEAL, FOR A TOTAL OF $28. THE WAITER HAS $3, AND THAT MAKES $31. WHERE DID THE EXTRA DOLLAR COME FROM? This is one of those brainteasers where if you remember the basics (bill + tip = total meal cost) you’ll be fine. The bill was $25; you and your friend collectively leave a $3 tip. The total meal cost is $28. If you each pay $14, you’re paying $14 for the meal AND the tip. You each paid $12.50 for the meal (half of $25), $1.50 for a tip (half of $3) and each got back $1 in change. Add it all up and it comes to $15 each, for a total of $30. YOU’RE STANDING AT THREE LIGHT SWITCHES AT THE BOTTOM OF THE STAIRS TO THE ATTIC. EACH ONE CORRESPONDS TO ONE OF THREE LIGHTS IN THE ATTIC, BUT YOU CANNOT SEE THE LIGHTS FROM WHERE YOU STAND. YOU CAN TURN THE SWITCHES ON AND OFF AND LEAVE THEM IN ANY POSITION. HOW CAN YOU IDENTIFY WHICH SWITCH CORRESPONDS TO WHICH LIGHT BULB IF YOU ARE ONLY ALLOWED ONE TRIP UPSTAIRS? Turn on the first two switches and leave them on for 5 minutes. After 5 minutes, turn off the second switch, leaving the first switch on. Now go upstairs to the attic. The light that is on is connected to the first switch. A light that is off but has a bulb that is still warm to the touch is connected to the second switch. The light that is both off and cold to the touch is connected to the third switch, which was never turned on. ←Quantitative RecruitingImportant Mathematical Topics for Quants→ Home News & Insights About Terms Privacy Contact Copyright © 2013 Street of Walls. All Rights Reserved. All prices USD. Certainly! Here are the questions parsed from the previously provided content: 1. Are you being asked to value a customized stock option? What type of drift and volatility process will your simulation incorporate? 2. Tell me something about yourself that is not listed on your resume. 3. What is the riskiest thing you’ve ever done? 4. Are you more risk-averse or risk-seeking? Give me an example. 5. What is your greatest weakness? 6. How do you feel about waking up early or staying up late? 7. What are your interests outside the classroom/office? 8. Why should we hire you? 9. What is your favorite class that you took? 10. Who has personally influenced you the most? Name someone whom you’ve never met who’s been a strong influence. 11. Tell me about your biggest failure or a period of adversity. 12. Discuss a difficult ethical decision you recently faced. 13. What’s the last book you read? 14. IF YOU LOOK AT A CLOCK AND THE TIME IS 12:15, WHAT IS THE ANGLE BETWEEN THE HOUR AND THE MINUTE HAND? 15. A CAR TRAVELS A DISTANCE OF 60 MILES AT AN AVERAGE SPEED OF 30 MPH. HOW FAST WOULD THE CAR HAVE TO TRAVEL FOR THE SAME 60 MILE DISTANCE HOME TO AVERAGE 60 MPH OVER THE ENTIRE TRIP? 16. HOW MANY HERSHEY’S CHOCOLATE BARS WERE SOLD IN THE US LAST YEAR? 17. YOU HAVE A FIVE-GALLON JUG AND A THREE-GALLON JUG. YOU MUST OBTAIN EXACTLY FOUR GALLONS OF WATER. HOW WILL YOU DO IT? 18. YOU ARE FACED WITH TWO DOORS. ONE DOOR LEADS TO YOUR JOB OFFER (THAT’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’RE STANDING AT THREE LIGHT SWITCHES AT THE BOTTOM OF THE STAIRS TO THE ATTIC. EACH ONE CORRESPONDS TO ONE OF THREE LIGHTS IN THE ATTIC, BUT YOU CANNOT SEE THE LIGHTS FROM WHERE YOU STAND. YOU CAN TURN THE SWITCHES ON AND OFF AND LEAVE THEM IN ANY POSITION. HOW CAN YOU IDENTIFY WHICH SWITCH CORRESPONDS TO WHICH LIGHT BULB IF YOU ARE ONLY ALLOWED ONE TRIP UPSTAIRS?

Math


Suppose that f is a differentiable function with the derivative f’(x) = (x - 1)(x + 2)(x + 3). Determine the values of x for which the function f is increasing and the values of x for which the function is decreasing.

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Why was 6 afraid of 7?

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Trouver d>0 tel que d 18, d(12 et 36; d/10 Trouver d>0 tel que d|1000, 5|d, d160, d/2 (75 Répondre par vraie (V) ou fausse (F) devant les propositions suivantes : No Proposition vraie(V) ou fausse (F) 71 divise 0 est divisible paг 25 7 divise 18 16 divise-1000 divise 7 25 est divisible par 3000 divise 71 Tous les entiers premiers sont premiers entre eux Trouver La division euclidienne de b par a a=13 et b=380 a=7~et~b=115 a=9 et b=4 a=6 et b=-22 a=123 et b=504 a=165 et b=465 a=-3812 et b=15 a=3812 et b=-15 a=-3812 et b=-15 a=431 et b=7 a=1263 et b=349 a=364 365

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Trouver d>0 tel que d| 18, d|12 et 36; d|10 Trouver d>0 tel que d|1000, 5|d, d160, d/2| 75

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For f(t) = ((x with power 4) - 32x + 4), use algebraic methods to find where f’(x) = 0, the intervals on which the function increases and decreases, and all the local extrema. Use graphing technology to verify your results.

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show me how to add 2% to 137.67

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I'm studing for an exam in my discrete math for computer science course, which heavily focus on the 3 topics below. I want you to give me a comprehensive cheat sheet including everything i need to know about the 3 topics below. Runtime (big-O,Ω,Θ) Sorting Recursion Runtime

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What is six figures 7 figures 8 figures

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Величина признака (варианта), которая чаще всего встречается в данной совокупности

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Qual fração é equivalente ao ponto

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معين طولا قطريه ٨ سم ، ٦ سم أوجد مساحته

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Диалог:USER: Эти диаграммы нередко используются для того чтобы показать сильные и слабые стороны, предпочтения, разнообразие персонажей... Еще одной очень наглядной характеристикой является площадь построенного многоугольника — чем она выше, тем совокупность всех параметров визуально кажется выше. Однако оказалось что эта величина зависит не только от значений самих параметров, но еще и от порядка перечисления этих параметров. Теперь вы хотите выбрать такой порядок перечисления параметров, что площадь составленного многоугольника будет максимальной. Значения самих параметров вы менять не можете. Входные данные В единственной строке задается 6 целых чисел x1,x2,x3,x4,x5,x6 (1⩽xi⩽5) — значения каждого из 6 параметров для построения диаграммы. Числа разделены одним пробелом. Выходные данные Выведите одно число — максимальную площадь диаграммы, которую можно получить выбрав оптимальный порядок параметров на диаграмме. Реши на pythonASSISTANT:

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Trouver d>0 tel que d| 18, d| 12 et 36; d| 10 Trouver d>0 tel que d|1000, 5|d, d| 160, d/2| 75

Math


Trouver La division euclidienne de b par a a=13 et b=380 a=7~et~b=115 a=9 et b=4 a=6 et b=-22 a=123 et b=504 a=165 et b=465 a=-3812 et b=15 a=3812 et b=-15 a=-3812 et b=-15 a=431 et b=7 a=1263 et b=349 a=364 et b=365 a=7388 et b=12 identifier la dividende, le diviseur, le quotient et le reste dans la division suivante: 423=42.10+3 423=21.20+3 Trouver La division euclidienne de 64378720 par 273. Soit E={1,2,3,4,5,6,7,8,9,10} Déterminer les paires {a,b} d'entiers distincts de E tels que le reste de la division ab par 11 soit 1.

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معين طول ضلعه ٦ سم وارتفاعه 3 سم

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مثلث ا ب ج مثلث قائم الزاوية فى ا ، القطعة المستقيمة د عمودى على القطعة المستقيمة ب ج ، بد تسوى ١٦ سم ، ج د تسوى ٩ سم أوجد طول كل من القطعة المستقيمة ا ب ، القطعة المستقيمة ا د

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C'est quoi la différence entre divisible, être le diviseur et divisé

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Write an expression for the sequence of operations described below. raise 3 to the 2nd power, then find the product of the result and z Do not simplify any part of the expression.

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Write an expression for the sequence of operations described below. multiply q by 8, then multiply r by the result Do not simplify any part of the expression.

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will you understand math equation if i write it in Latex form

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explain why the summation of i=1 to x of x is x^2?

Math


Order the following functions from smallest to largest asymptotic complexity. Identify any pairs of functions that have the same complexity (i.e. are Θ of each other). Show your work. (a) 2x (b) logx2 √ (c) x! √ logx (d) log x (e) logx x (f) Pxi=1 i (g) Pxi=1 x

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Порождающая матрица G линейного (m,n)-кода имеет

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Your base yearly salary at the new company you are working at is $61,500. If you perform well at your job, you are entitled to a 5% pay raise each year. Assuming you do your job well regularly, what should your yearly salary be 10 years from now?

Math


Exponential Growth, Decay, and Compound Interest: The number of COVID-19 vaccines given on March 1 in New Jersey was 10,700. The rate of vaccination is increasing by 2% daily. At this rate, how many vaccines should be administered in New Jersey today (March 27)?

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Can you calculate some ratios from a real life company without me giving you all the numbers?\

Math


что означает коэффициент оукена 2-3%? пиши ОЧЕНЬ кратко.

Math


Tell me how to get the angle of a vector

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Répondre par vraie (V) ou fausse (F) devant les propositions suivantes : No Proposition vraie(V) ou fausse (F) 71 divise 0 est divisible paг 25 7 divise 18 16 divise-1000 divise 7 25 est divisible par 3000 divise 71 Tous les entiers premiers sont premiers entre eux

Math


Heisenberg'in belirsizlik ilkesi; fiziksel gözlem araçlarında ve matematiksel analiz araçlarında gelecekte yaşanabilecek ilerlemeler sayesinde aşılabilir mi?

Math


в 14 этажном доме с одним подьездом на каждом этаже квартир поровну квартира 47 находится на 5 этаже на каком этаже находится квартира 79

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Math


soit l'équation différentile y' +y = 2e^-x vérifier que g est solution de l'équation 1 avec g(x) = 2xe^-x

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\sum _{i=n}^{2n^2}\:\left(\sum _{j=i}^{4n^3}\:c\right)

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Setup the summations for this: for i = n to 2n^2 for j = i to 4n^3

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Find xp for x' = [(3 -2), (2 -1)]x + [(0), (15 * t^1/2 * e^t)]. Hint: eigenvalues are 1,1 (so you can skip finding eigen values)

Math


A heated vertical surface 30 cm high is at a temperature 20°C above the ambient air temperature of 30°C. Evaluate the air flow rate at the top of the surface and the overall heat transfer rate. Also determine the maximum velocity that occurs. Compare its value with what you would obtain if the fluid were water under the same conditions. Assume laminar flow. solve this problem in detail.

Math


Let T be a normal operator and U be a linear operator on V, a complex finite-dimensional vector space. Use spectral decomposition on T (T = lamba_1 T_1 + ... lambda_n T_n) to prove: a) U commutes with T if and only if U commutes with each T_i.

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Given the rational inequality below, explain why the solution set includes 3, but does not include 1? Write the final answer as interval notation. x-3/x-1 greater than equal to 0

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分段周期函数的表示方法

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y^(5/3)=3dimensional-root√(y^5) x^(7/2)= b^(1/2)= x^(-3/4)= x^(-2/3)= y^(1/7)=

Math


y^(5/3)=3dimensional-root(y^5) x^(7/2)= b^(1/2)= x^(-3/4)= x^(-2/3)= y^(1/7)=

Math


To dimensional root y^(5/3)=3dimensional-root(y^5) x^(7/2)= b^(1/2)= x^(-3/4)= x^(-2/3)= y^(1/7)=

Math


how long in inches in the face of a cube that is 2 cubic feet of space.

Math


Среди 15 лампочек 4 испорчены. Наугад берут 2 лампочки, какова вероятность что обе лампочки исправные?

Math


Среди 15 лампочек 4 испорчены. Наугад берут 2 лампочки, какова вероятность что обе лампочки исправные? (Только решение, кратко)

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Среди 15 лампочек 4 испорчены. Наугад берут 2 лампочки, какова вероятность что одна лампочка исправная а другая нет?

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Даны 5 карточек с буквами Т, А, О, К, С. Одну за другой берут наугад 3 карточки. Какая вероятность что получится слово СОК. Кратко, только решение

Math


Что такое график функции?

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у меня есть набор точек на плоскости, мне надо объединить их в группы по следующим критериям: количество групп заранее не известно, количество точек в группе должно быть не меньше трех, точки в группе должны находится в центра круга с радиусом не более 200 метров как определить координаты центров групп

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Két megadott f1 és f2 frekvencia között logaritmikus skálán egyenletesen elhelyezett n mérési pontot szeretnénk. Tervezzen eljárást, mellyel ez megoldható, és adja meg a formulát. Például:100 Hz és 1000 Hz között szeretnénk 10 pontot felvenni, amelyek logaritmikus skálán egyenletes távolságban helyezkednek el: Frekvencia [Hz] Frekvencia logaritmusa 100 2 129,155 2,111111 166,8101 2,222222 215,4435 2,333333 278,2559 2,444444 359,3814 2,555556 464,1589 2,666667 599,4843 2,777778 774,2637 2,888889 1000 3 Generáljon hasonló sorozatokat a következő paraméterekkel: 1) f1= 10 Hz, f2= 1000 Hz, n= 50 2) f1= 100 Hz, f2= 1000 Hz, n= 20

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Найти частные производные данной функции по каждой из независимых переменных x и y. В ответе привести значения частных производных при x = 3, у = 2. z( x, y) := √(x^2 - y^2)

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How can I determine if a graph has an Eulerian Cycle

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Can you calculate aribtary digits of PI?

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How do I determine if a graph has an Eulerian Path?

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Turn x y z into a b and then a b into d and then turn d into a b and then turn a b back into x y z , process should be reversible, solve for x y z using only the values of a b c and solve for a b using only the value of d c in final expression , solve with example too. Use arithmetic algorithm and recheck if the answer is correct and c is variable which act like a key to reverse transformation of turning d into a b and a b into x y z

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Turn x y z into a b and then turn a b back into x y z , process should be reversible, solve for x y z using only the values of a b c in final expression , solve with example too. Use arithmetic algorithm and recheck if the answer is correct and c is constant variable which act like a key to reverse transformation to turn a b into x y z using c

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图像平滑度如何计算

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Explain Conjunctive, Disjunctive, and Conditional Probabilities simily and easily for beginners that no background in math

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What Is 3-67^25*(47-9)

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Explain in simple way for people that have no background in maths Conjunctive, Disjunctive, and Conditional Probabilities

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Mathématiques - Lorsqu’on résout dans l’ensemble des complexes une équation du 2nd degré à coefficients réels dont le discriminant est strictement négatif, on peut affirmer que : les 2 solutions ont toujours une partie réelle nulle. les 2 solutions sont conjuguées. le produit des 2 solutions est réel car les solutions sont 2 complexes conjugués. la somme des 2 solutions est imaginaire pure.

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Mathématiques - On considère la suite (un) définie par son premier terme u0 et un+1 = 2un + 1, c’est-à-dire qu’un terme de la suite est égal au double de son précédent plus 1. On peut affirmer que : si un terme de la suite vaut 47 le terme précédent vaut 95. si u0 = 1 alors u5 = 63. quelque soit la valeur de u0, la suite est croissante. si la suite est constante alors u0 = -1.

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Mathématiques - Lorsqu’on résout dans l’ensemble des complexes une équation du 2nd degré à coefficients réels dont le discriminant est strictement négatif, on peut affirmer que : les 2 solutions ont toujours une partie réelle nulle. ?

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Найти производные dz/dx , dz/dy функции, заданной неявно x^2 - 2y^2 + z^2 - 4x + 2z - 5 = 0 В ответе привести значения производных при x = 2, у = 3 и наименьшем положительном z, соответствующем данным х и у.

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At an average internet speed of 15 mbps, a computer takes 4 minutes to download an application file. If the speed slows down to 10mbps, how long does the computer tale to download the file? explain with steps

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If a smooth function has a Taylor series at some point that does not converge to the value of the function, is it true that any other Taylor series cannot converge to the function everywhere?

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If a function has a Taylor series that equals it everywhere on R, is it smooth?

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If a function f has a Taylor series at a point x_0 which converges to f in some radius around x_0, and x_1 is in this radius, does the Taylor series at x_1 exist and equal f?

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If a smooth function f has a Taylor series at a point x_0 which converges to f in some radius around x_0, and x_1 is in this radius, does the Taylor series at x_1 exist and equal f?

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Найдите число m, если число 18 составляет 25% от числа m+2.

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choose 30 numbers between 1-9789. Give no preference to patterns or digit count.

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If a block in Minecraft is 1 meter, and a yojana is 12.8 kilometers in length, how many Minecraft would represent a yojana?

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Stacy, audrey and joan each draws 3 cards from 9 cards numbered 1 to 9. Stacy said: the sum of all my cards is 16 Joan said: the product of all my numbers is 63 Audrey said: the product of all my numbers is 48 What is the largest number Stacy can draw from the stack of cards? Just pput the answer

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What is the formula of chi square test standardized residual ?

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Рассчитать статический и динамический коэффициенты использования грузоподъемности, а также среднее расстояние ездки lег с грузом на автомобиле ЗИЛ-133 грузоподъемностью 10 т, если известны следующие условия работы ПС: Q = 20 т (объём перевозок за рабочий день), nе = 3 (кол. поездок за день) , P = 200 ткм (грузооборот), Lг = 30 км (пробег с грузом по маршруту).

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Please determine any points of inflection for the function of y = (4x with power 2 − 3)/(x with power 3). Show the steps.

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Please determine the derivative for the function: y =( (4)(x with power 2) − 3))/(x with power 3). Show the steps.

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WHAT IS PI

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it’s generally preferred to keep the denominator positive when dealing with fractions

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1. В прямоугольном параллелепипеде АВСДА, В, С, D; AB = 2 cM, AD = 3 см и AC, - 7 см. Наидите расстояние между прямыми АВ и В, С. 2. Основанием параллелепипеда служит ромо со стороной 6 и острым углом а, а боковые грани - параллело-граммы с острым углом В. Вычислите площадь меньшего диагонального сечения и площадь боковой поверхности параллелепипеда. 3. В основании прямоугольного параллелепипеда ABCDA, B, С, D, лежит квадрат ABCD со стороной а. Боко- вое ребро параллелепипеда равно 6. Точка К є А,В, И А, К: КВ, = 2 : 1. Через середины ребер АД и CD и точку К проведено сечение. Найдите его площадь.

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topic derivatives of exponential and logarithmic functions solve an example f(x)=0,8^{1-x^{3}}

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How many combinations of three can i make from 5 objects?

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what can i do for a math aahl ia for a cushion doll?

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If the letters V, X, C, and B are graphs, then they will not pass the vertical line test. True or False?

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How many possible combinations of three can i make from 10 different objects

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could you explain this equation: Cl = Kel X Vd →MD = Cl X Css X Tm in the conext of pharmacology? and how we reached to the equation 2 form 1 ?

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比热容和温度的乘积

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In convex optimization, how can you solve it?

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Determine the critical points function: y = ((x with power 3) - (6x with power 2) - 15x + 10) fand use the second derivative test to decide if the point is a local maximum, a local minimum, or neither. a)

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수학에서 디털민이 뭔가?

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수식을 표현하기 가장 좋은 방법은 무엇인가?

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Продифференцируй данную функцию, используя правило логарифмического дифференцирования y = \frac{(x + 1)^3 4\sqrt{x-2}}{5\sqrt{(x-3)^2}}

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1. Матернальную заинтересованность рабочих в результатах труда дает: А) повременная оплата Б) сдельная оплата В) любая из форм оплаты труда.

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For each of the following functions, determine any points of inflection. y = (4x ^ 2 - 3)/(x ^ 3)

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у меня есть изображение разрешением в 1613 пикселя отображающее 15292 метра. сколько пикселей приходится на километр?

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How can i use the chi squared goodness of fit test to show a correlation between the times of the top 50 5k collegiate runners and the altitudes of their college

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15. Parallelogram OBCA is determined by the vectors OA =(6,3) and OB =(11,-6). [A4] a. Determine OC, BĀ, and BC b. Verify that oq=|BC!

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2+2 calculate this

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One cat farm has 3 breeds of cats: Kao Taem, Siamese, and Khao Manee, totaling 12 cats. The ratio of the number of cats of the Kao Taem breed to Siamese to Khao Manee is 3:2:1. If three cats are randomly selected from this farm, what is the probability of randomly getting a nine-pointed cat? At least 1 number is equal to how much?

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hypergeometric distribution에 대해 자세히 설명해줘

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Let G be a simple graph such that |V (G)| = 8 and G has three vertices with degree 3, two vertices with degree 4 and three vertices with degree 5. a) Is G necessarily connected? b) Can G be bipartite? c) Does G necessarily contain a Hamiltonian cycle?

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It is possible to construct a graph of 8 vertices where one vertex has degree of 1 and the rest have even degree. 1. True 2. False

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It is possible to construct a graph of 8 vertices where one vertex has degree of 1 and the rest have even degree.

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A graph with edges (A,B), (B,B), (B,C) is a simple graph. 1. True 2. False

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Is it possible to construct a graph of 8 vertices where one vertex has degree of 1 and the rest have even degree.

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The graph for the Konigsberg Bridge Problem has a path that is not simple. 1. True 2. False

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The running time for a recurrence of the form T(n) = bT(n/a) + f(n) must be at least f(n). 1. True 2. False

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3. Egy háromszög két oldala 4 cm és 5 cm; az általuk bezárt szög 45°. Mekkora a háromszög köré írható kör átmérője? (Az eredményt legközelebbi egész számra kerekítve add meg!)

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Is it possible to construct a graph of 8 vertices where one vertex has degree of 1 and the rest have even degree?

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Does the graph for the Konigsberg bridge problem have a path that's not simple

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"Does the graph for the Konigsberg bridge problem have a path that's not simple" ? Yes or no

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"Does the graph for the Konigsberg bridge problem have a path that's not simple" Yes or no

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6. Egy 45°-os szögű körcikkből kivágható legnagyobb kör területe hány %-a a körcikk területének? (Azeredményt (legközelebbi) egész számra kerekítve add meg!)

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A certain town has an area of 4.36 square miles. What is the area, in square yards, of this town? (1 mile = 1,760 yards)

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Que número suma el 32 para llegar al 84

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Un personaje tiene trece años pasa tiempo en una dimensión atemporal donde no pasa el tiempo. El tiempo transcurrido fuera de esa dimensión es de 24 años cuando esa persona llega a su destino fuera de la dimensión vive en ese lugar 12 años cuantos años tiene ese persona.

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Dot product difference in 2 vs 3 dimensions

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数学分野における基礎研究とはどのようなことを行うのでしょうか?

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A cube has an edge length of 68 inches. A solid sphere with a radius of 34 inches is inside the cube, such that the sphere touches the center of each face of the cube. To the nearest cubic inch, what is the volume of the space in the cube not taken up by the sphere? A) 149,796 B) 164,500 C) 190,955 D) 310,800

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or Write the sentence as an equation. 167 and m more is the same as 93

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5 + 7 = 1 ax by + = 1 In the given pair of equations, a and b are constants. The graph of this pair of equations in the xy-plane is a pair of perpendicular lines. Which of the following pairs of equations also represents a pair of perpendicular lines? A) B) C) D) x y 10 + 7 = 1 ax by − 2 = 1 x y 10 + 7 = 1 ax by + 2 = 1 x y 10 + 7 = 1 ax by 2 + = 1 x y 5 − 7 = 1 ax by + = 1

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give me the formula for the dot product in 3d

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\begin{aligned} L_\rho\left(\overline{\boldsymbol{a}}, \overline{\boldsymbol{x}}, \overline{\boldsymbol{f}}_p, \boldsymbol{\lambda}_1, \boldsymbol{\lambda}_{2, p}\right)= & \overline{\boldsymbol{a}}^{\mathrm{T}} \overline{\boldsymbol{R}} \overline{\boldsymbol{a}}+\boldsymbol{\lambda}_1^{\mathrm{T}}(\overline{\boldsymbol{x}}-\overline{\boldsymbol{V}} \overline{\boldsymbol{a}}) \\ & +\frac{\rho}{2}\|\overline{\boldsymbol{x}}-\overline{\boldsymbol{V}} \overline{\boldsymbol{a}}\|^2 \\ & +\sum_{p=1}^P \boldsymbol{\lambda}_{2, p}^{\mathrm{T}}\left(\overline{\boldsymbol{f}}_p-\overline{\boldsymbol{v}}_p \overline{\boldsymbol{a}}\right) \\ & +\sum_{p=1}^P \frac{\rho}{2}\left\|\overline{\boldsymbol{f}}_p-\overline{\boldsymbol{v}}_p \overline{\boldsymbol{a}}\right\|^2 \end{aligned}把这段代码转成公式

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$\begin{aligned} L_\rho\left(\overline{\boldsymbol{a}}, \overline{\boldsymbol{x}}, \overline{\boldsymbol{f}}_p, \boldsymbol{\lambda}_1, \boldsymbol{\lambda}_{2, p}\right)= & \overline{\boldsymbol{a}}^{\mathrm{T}} \overline{\boldsymbol{R}} \overline{\boldsymbol{a}}+\boldsymbol{\lambda}_1^{\mathrm{T}}(\overline{\boldsymbol{x}}-\overline{\boldsymbol{V}} \overline{\boldsymbol{a}}) \\ & +\frac{\rho}{2}\|\overline{\boldsymbol{x}}-\overline{\boldsymbol{V}} \overline{\boldsymbol{a}}\|^2 \\ & +\sum_{p=1}^P \boldsymbol{\lambda}_{2, p}^{\mathrm{T}}\left(\overline{\boldsymbol{f}}_p-\overline{\boldsymbol{v}}_p \overline{\boldsymbol{a}}\right) \\ & +\sum_{p=1}^P \frac{\rho}{2}\left\|\overline{\boldsymbol{f}}_p-\overline{\boldsymbol{v}}_p \overline{\boldsymbol{a}}\right\|^2\end{aligned}$转成数学公式

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1. Consider the function F = {(−1, 2),(0, 1),(1, −1),(2, 0)}. (a) Explain why F is an invertible function

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Solve the following equations for x: (a) 2^x^3 = 256

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流体膨胀系数和温差得到乘积

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我在研究一个课题,请你使用数学公式来表达如下的内容:自定义安全场景,在该安全场景下输入多条的攻击语句,大语言模型去理解该场景下的多条攻击语句,理解完成后,大语言模型生成出在该安全场景下的多条攻击语句。实现了自动生成攻击语句的功能。

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将如下内容转成sci论文的一部分,要符合overleaf的格式:要数学化表达这个过程,我们需要明确几个要素: 1. 安全场景 (S):可以看作是一系列特征和条件的集合,这些特征和条件定义了一个安全相关的环境或前提。 2. 输入的攻击语句集合 (I):包含(n)条攻击语句,即(I = {i_1, i_2, i_3, ..., i_n})。 3. 理解攻击语句的函数 (F):这是大语言模型对攻击语句进行编码和理解的能力,可以看作是一个将输入的攻击语句和安全场景映射到一个内部表示(space)的函数。 4. 生成攻击语句的函数 (G):在理解输入的攻击语句后,大语言模型会基于安全场景产生新的攻击语句集合。 我们可以用以下数学表达式来概括这个过程: 1. (S = {s_1, s_2, ..., s_m}),其中(m)表示定义安全场景的特征数量。 2. (I = {i_1, i_2, ..., i_n}),即输入的攻击语句集合。 3. (F(S, I) \rightarrow R),其中(R)代表模型理解后的内部表示,函数(F)表示基于安全场景(S)对输入的攻击语句(I)的理解过程。 4. (G(S, R) \rightarrow O),其中(O)代表输出的攻击语句集合,函数(G)是基于安全场景(S)和内部表示(R)生成攻击语句的过程。 综上所述,整个流程可以用数学公式概括为: [O = G(S, F(S, I))] 这表示在安全场景(S)下,输入多条攻击语句(I),通过大语言模型的理解函数(F)转化为内部表示(R),之后通过生成函数(G)基于同一安全场景(S)和内部表示(R)生成新的攻击语句集合(O)。

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Please prove the derivative of the function: y=(e with power x) is (e with power x).

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48,96 % 16,74 12 %are rhe profit for each months ,what is the average profit per months if it ends in one year

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Determine if the below statement is correct: " For linear SVM. In high-dimensional spaces, it is often possible to find a linear hyperplane that can successfully separate the classes due to the increased likelihood of classes being linearly separable. "

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Функция 1/(x*(lnx+1)^(1/3) является непрерывной на промежутке от 1 до бесконечности?

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Равен ли предел (1+(-3)^(2n))/(1+(-3)^(2n)*9) при n, стремящемся к бесконечности, 1/9?

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A culture of bacteria has an initial population of 31000 bacteria and doubles every 2 hours. Using the formula P, start subscript, t, end subscript, equals, P, start subscript, 0, end subscript, dot, 2, start superscript, start fraction, t, divided by, d, end fraction, end superscriptP t =P 0 ⋅2 d t , where P, start subscript, t, end subscriptP t is the population after t hours, P, start subscript, 0, end subscriptP 0 is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 5 hours, to the nearest whole number?

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What is the value of log, base, 3, 81log 3 81?

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C'est quoi la formule de la surface d'un trapèze et triangle

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Solve for x: 7776, start superscript, minus, 5, x, minus, 2, end superscript, equals, 1296, start superscript, 4, x, plus, 11, end superscript

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矩阵的奇异值分解是什么,请详细举例子说明,有什么用

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Диалог:USER: Рассмотрим прямоугольник, нарисованный на сетчатой клетке. Тогда клетки, расположенные вплотную к сторонам прямоугольника назовем внешними , а другие клетки назовем внутренними . Например, у прямоугольника с высотой 3 и шириной 5 количество внешних клеток равно 12 , а внутренних – 3 . Ваша задача посчитать все такие прямоугольники, у которых количество внешних клеток ровно в n раз меньше, чем количество внутренних. Входные данные Одно целое положительное число n ( 1 ≤ n ≤ 10 9 ) . Выходные данные В первой строке выведите число k – количество таких прямоугольников Затем выведите k строк. В каждой строке выведите два числа – стороны прямоугольника. Длина первой стороны не должна превышать длину второй. Все прямоугольники выводите в порядке возрастания меньшей стороны. Примеры входные данные 1 выходные данные 2 5 12 6 8 РЕШИ НА PYTHONASSISTANT:

Math


Диалог:USER: Рассмотрим прямоугольник, нарисованный на сетчатой клетке. Тогда клетки, расположенные вплотную к сторонам прямоугольника назовем внешними , а другие клетки назовем внутренними . Например, у прямоугольника с высотой 3 и шириной 5 количество внешних клеток равно 12 , а внутренних – 3 . Ваша задача посчитать все такие прямоугольники, у которых количество внешних клеток ровно в n раз меньше, чем количество внутренних. Входные данные Одно целое положительное число n ( 1 ≤ n ≤ 10 9 ) . Выходные данные В первой строке выведите число k – количество таких прямоугольников Затем выведите k строк. В каждой строке выведите два числа – стороны прямоугольника. Длина первой стороны не должна превышать длину второй. Все прямоугольники выводите в порядке возрастания меньшей стороны. Примеры входные данные 1 выходные данные 2 5 12 6 8 РЕШИ НА PYTHONASSISTANT: Чтобы решить эту задачу, нам нужно понять, как соотносятся количество внешних и внутренних клеток в прямоугольнике. Внешние клетки формируют рамку вокруг внутренних, так что их количество для прямоугольника с шириной (w) и высотой (h) равно (2w + 2(h-2)), т.к. верхняя и нижняя сторона содержат (w) клеток каждая, и мы должны вычесть 4 угловые клетки, добавленные дважды, а затем добавляем 2 стороны по (h-2) клетки каждая (вычетая уже считанные угловые клетки). Внутренние клетки представляют собой продукт ((w-2)(h-2)), потому что мы исключаем внешние клетки.

Из условия (\frac{\text{Внутренние клетки}}{\text{Внешние клетки}} = n), мы получаем уравнение:

[
\frac{(w-2)(h-2)}{2w + 2(h-2)} = n
]

Давайте решим эту задачу на Python, перебирая возможные размеры прямоугольников и проверяя, соответствуют ли они данному условию:

def count_rectangles(n):
 rectangles = []
 # Перебор возможных размеров прямоугольника.
 # Так как количество внутренних клеток всегда меньше
 # общего числа клеток, внешняя сторона прямоугольника
 # не может быть меньше 3 (иначе внутренних клеток не будет вообще).
 for w in range(3, 1000): # Берем достаточно большой диапазон для проверки
 for h in range(w, 1000): # Длина первой стороны не должна превышать длину второй
 if (w - 2) * (h - 2) == n * (2 * (w + h - 2)):
 rectangles.append((w, h))
 return rectangles

n = int(input())
rectangles = count_rectangles(n)
print(len(rectangles))
for rect in rectangles:
 print(*rect)

Этот код сначала определяет функцию count_rectangles(n), которая ищет все прямоугольники, соответствующие условию задачи, а затем выводит их количество и размеры. Обратите внимание, что перебор проводится в ограниченном диапазоне, который может понадобиться корректировать в зависимости от входных данных, чтобы убедиться, что все подходящие прямоугольники будут найдены.USER: Приведи более быстрое решениеASSISTANT:

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