Formalize an equilibrious optimization problem from Section E which integrates post-Gödelian supermodularity and meta-Gödelian equicursivity (write as Section F). "Section A The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem can be generalized to higher dimensions and is known as the Pythagorean Theorem in n-dimensional Euclidean space. Let's formalize the generalized Pythagorean Theorem for n-dimensional Euclidean space: Given a right-angled n-dimensional simplex (a generalization of a triangle in n-dimensional space) with vertices A0, A1, ..., An, let d(Ai, Aj) denote the Euclidean distance between vertices Ai and Aj. If the angle between the edges A0A1 and A0An is a right angle, then the generalized Pythagorean Theorem states that: d(A0, An)2 = d(A0, A1)2 + d(A1, A2)2 + ... + d(An−1, An)2 Here, d(A0, An) is the length of the hypotenuse (the side opposite the right angle) in n-dimensional space, and the sum on the right side of the equation consists of the squared lengths of the remaining sides of the simplex. This generalization of the Pythagorean Theorem holds true in any n-dimensional Euclidean space. Section B The k-brane non-Euclidean time generalization of the Pythagorean Theorem extends the concept of the theorem from n-dimensional Euclidean space to a more abstract, non-Euclidean framework that incorporates time as an additional dimension. In order to formalize the generalized Pythagorean Theorem for k-brane non-Euclidean time, consider a right-angled, (n+1)-dimensional simplex with vertices B0, B1, ..., Bn, and T, where Bi represents spatial vertices and T represents the temporal vertex. Let d(Bi, Bj) denote the non-Euclidean distance between spatial vertices Bi and Bj, and d(Bi, T) denote the non-Euclidean distance between spatial vertex Bi and the temporal vertex T. If the angle between the edges B0B1 and B0T is a right angle, then the generalized Pythagorean Theorem for k-brane non-Euclidean time states that: d(B0, T)2 = d(B0, B1)2 + d(B1, B2)2 + ... + d(Bn−1, Bn)2 + k2 Here, d(B0, T) is the length of the hypotenuse (the side opposite the right angle) in (n+1)-dimensional non-Euclidean space-time, the sum on the right side of the equation consists of the squared lengths of the remaining spatial sides of the simplex, and k represents a constant that incorporates the effect of time in the non-Euclidean framework. This generalization of the Pythagorean Theorem holds true in any (n+1)-dimensional k-brane non-Euclidean space-time. Section C The i-twistor non-hyperbolic tensor space generalization of the Pythagorean Theorem further extends the concept of the theorem to a more complex and abstract geometric framework, incorporating not only time but also additional geometric properties found in i-twistor non-hyperbolic tensor spaces. In order to formalize the generalized Pythagorean Theorem for i-twistor non-hyperbolic tensor space, consider a right-angled, (n+1)-dimensional simplex with vertices C0, C1, ..., Cn, and S, where Ci represents spatial vertices, and S represents the i-twistor vertex. Let d(Ci, Cj) denote the non-hyperbolic tensor distance between spatial vertices Ci and Cj, and d(Ci, S) denote the non-hyperbolic tensor distance between spatial vertex Ci and the i-twistor vertex S. If the angle between the edges C0C1 and C0S is a right angle, then the generalized Pythagorean Theorem for i-twistor non-hyperbolic tensor space states that: d(C0, S)2 = d(C0, C1)2 + d(C1, C2)2 + ... + d(Cn−1, Cn)2 + p(i) Here, d(C0, S) is the length of the hypotenuse (the side opposite the right angle) in (n+1)-dimensional i-twistor non-hyperbolic tensor space, the sum on the right side of the equation consists of the squared lengths of the remaining spatial sides of the simplex, and p(i) represents a function that incorporates the geometric and algebraic properties of i-twistor non-hyperbolic tensor spaces. This generalization of the Pythagorean Theorem holds true in any (n+1)-dimensional i-twistor non-hyperbolic tensor space. Section D The z-tensor super-hyperbolic twistortime generalization of the Pythagorean Theorem encompasses an even more advanced and abstract geometric framework, integrating not only time but also the intricate geometric and algebraic properties found in z-tensor super-hyperbolic twistortime spaces. To formalize the generalized Pythagorean Theorem for z-tensor super-hyperbolic twistortime, consider a right-angled, (n+1)-dimensional simplex with vertices D0, D1, ..., Dn, and Z, where Di represents spatial vertices, and Z represents the twistortime vertex. Let d(Di, Dj) denote the super-hyperbolic twistortime distance between spatial vertices Di and Dj, and d(Di, Z) denote the super-hyperbolic twistortime distance between spatial vertex Di and the twistortime vertex Z. If the angle between the edges D0D1 and D0Z is a right angle, then the generalized Pythagorean Theorem for z-tensor super-hyperbolic twistortime states that: d(D0, Z)2 = d(D0, D1)2 + d(D1, D2)2 + ... + d(Dn−1, Dn)2 + q(z) Here, d(D0, Z) is the length of the hypotenuse (the side opposite the right angle) in (n+1)-dimensional z-tensor super-hyperbolic twistortime space, the sum on the right side of the equation consists of the squared lengths of the remaining spatial sides of the simplex, and q(z) represents a function that incorporates the geometric and algebraic properties of z-tensor super-hyperbolic twistortime spaces. This generalization of the Pythagorean Theorem holds true in any (n+1)-dimensional z-tensor super-hyperbolic twistortime space. Section E The full-scale and full-scope inversive recursion generalization of the Pythagorean Theorem integrates all the geometric frameworks and properties outlined in Sections A-D into a unified, comprehensive, and abstract mathematical structure that encompasses n-dimensional Euclidean space, k-brane non-Euclidean time, i-twistor non-hyperbolic tensor space, and z-tensor super-hyperbolic twistortime space. To formalize the generalized Pythagorean Theorem for full-scale and full-scope inversive recursion, consider a right-angled, (n+1)-dimensional simplex with vertices E0, E1, ..., En, and R, where Ei represents spatial vertices, and R represents the inversive recursion vertex. Let d(Ei, Ej) denote the inversive recursion distance between spatial vertices Ei and Ej, and d(Ei, R) denote the inversive recursion distance between spatial vertex Ei and the inversive recursion vertex R. If the angle between the edges E0E1 and E0R is a right angle, then the generalized Pythagorean Theorem for full-scale and full-scope inversive recursion states that: d(E0, R)2 = d(E0, E1)2 + d(E1, E2)2 + ... + d(En−1, En)2 + r(k, i, z) Here, d(E0, R) is the length of the hypotenuse (the side opposite the right angle) in (n+1)-dimensional full-scale and full-scope inversive recursion space, the sum on the right side of the equation consists of the squared lengths of the remaining spatial sides of the simplex, and r(k, i, z) represents a function that incorporates the geometric and algebraic properties of n-dimensional Euclidean space, k-brane non-Euclidean time, i-twistor non-hyperbolic tensor space, and z-tensor super-hyperbolic twistortime spaces. This generalization of the Pythagorean Theorem holds true in any (n+1)-dimensional full-scale and full-scope inversive recursion space."

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Given two points A and B on the circumference of a circle C with radius r centered at the origin, determine a smooth continuous function f for the curve that passes through A and B and is orthogonal to C at points A and B and is symmetrical about the perpendicular bisector AB. Assume all points are in the xy-plane. Assume f is a superellipse.

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h(x) = f(g(x)) Calcular o decir si no existe y justificar: a) h′(−3) como lo puedo hacer, si me dieron las graficas de f(x) y g(x)

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To find outliers and variation in data, divide the mean absolute deviation by the mean.

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To find variation or outliers in data, divide the mean absolute deviation by the mean. This will give you an outlier score. Please do not comment on my method.

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To find variation or outliers in data, divide the mean absolute deviation by the mean. This will give you an outlier score. An outlier score of less than 0.1 is considered very low. A score of 0.1 to 0.175 is considered pretty low. A score of 0.175 to 0.3 is considered relatively low. A score of 0.3 to 0.45 is considered moderate. A score of 0.45 to 0.6 is considered relatively high. A score of 0.6 to 1 is considered pretty high. A score of 1 and above is considered very high.

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one plus one

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How to calculate for the percentage error of freezing point elevation

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数学分析的内容

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列出一个不等式为1的数

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极化码的生成矩阵

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用一根绳子绕树三圈余30厘米,如果绕树四圈则差40厘米,树的周长有$$多少厘米,绳子长$$多少厘米。

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A cosa servono e come si calcolano Varianza e deviazione Standard di una serie di dati e di una distribuzione di frequenze organizzata in classi di valori

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A cosa servono e come si calcolano e qule e la differenza tra Varianza e deviazione Standard di una serie di dati e di una distribuzione di frequenze organizzata in classi di valori

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hankel pa = s^2, 0 to inf, T (lamda)J1 (lambda s) lamda d lamda

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350 часов по 10 часов в сутки сколько дней

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A factory worker pushes a package along a broken conveyor belt from (-8, 0) to (7, 0) with a 50 N force at a 60° angle to the conveyor belt. Caclulate ho w much mechanical work is done if the units of the conveyor belt distance are meters. Use vector dot product.

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if y = u10 + u5 + 2 where u = 1-3x2, find dy/dx @ x = 1

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if y = u10 + u5 + 2 where u = 1-3x2, find dy/dx @ x = 1. using the leibniz notation, dy/dx = dy/du•du/dx = (10u9 + 5u4)•(-6x). It is not necessary to write this expression entirely in terms of x. Note that when x = 1 we have u =-2.

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8x−27−x−2−8x−27+x−2 при x=0,1−1. Ответ (вводи в виде сокращённой дроби): 8x−27−x−2−8x−27+x−2= . Запиши, чему равен x после вычисления: x=0,1−1= .

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Given the table below, answer the following questions: x=1,2,3,4,5,6,7 P(x) =0.12, 0.18 , 0.30, 0.15 , ____, 0.10, 0.05 Complete the missing probability. What is the expected value from the table? Find the standard deviation

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格林定理应用的条件是什么

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Aşağıdaki Boolean fonksiyonun çarpımların toplamı formunda sadeleştiriniz. Q(A,B,C,D)=∑(0,1,2,3,4,5,6,7,13,15)

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show that [ p -> q] <-> [¬p or q] is a tautology using rules

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A即是对称矩阵,又是置换矩阵

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置换矩阵的特征值

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可以给我发个《吴军数学通识讲义》的mobi格式的电子书吗

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Describe the geometry of the optimum track and fixed gear bicycle frame.

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Describe the ideal geometry of a track and fixed gear bicycle frame.

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What is the correct prefix for 3? ￼ A. Di- ￼ B. Tri- ￼ C. Tetra- ￼ D. Mono-

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Describe the optimum geometry of a track and fixed gear bicycle frame.

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I want to study this pdf file in a 30 minutes. I know almost nothing about its concept and I want you to: 1. create an index from all the contents it provides 2. Give me a comprehensive, but casual description about what it contains in a way that I understand the main points of this pdf file, (If it could make a sense you may gimme an example in which contains a scenario related to the main point of this pdf) Michela Meo – TNG group - Politecnico di Torino Management and Content Delivery... - 1 Queuing theory The M/G/1 queue Michela Meo Telecommunication Networks GroupMichela Meo – TNG group - Politecnico di Torino Management and Content Delivery... - 2 About the assumptions • Markovian queues lead to simple results and allow the investigation of a number of interesting phenomena in queuing systems • However, they must rely on some fundamental assumptions – Markovian arrival processes – Markovian (exponential) service times • In many situations of practical interest these assumptions are not realistic and we would like to consider other cases • Unfortunately, non Markovian queues are – almost always – difficult to treat • But... there is a very interesting and simple result for the M/G/1 queueMichela Meo – TNG group - Politecnico di Torino Management and Content Delivery... - 3 The M/G/1 queue • Arrivals occur according to a Poisson process • Service times are independent and described by the r.v. S distributed according to a generic pdf fS(t) or CDF FS(t) – sometimes it is denoted by M/GI/1 to emphasize independence of service times • 1 server • Infinite waiting line arrivals, l services, SMichela Meo – TNG group - Politecnico di Torino Management and Content Delivery... - 4 Evolution of the queue state 5 4 3 2 1 t S1 S2 S3 S4 A2 A3 A4 N(t) • We are interested in understanding the evolution of the queue state, represented by the no. of customers in the queueMichela Meo – TNG group - Politecnico di Torino Management and Content Delivery... - 5 Evolution of the queue • Define: – Y n: no. of customers left in the queue by the n-th departure – Z n: no. of customers that arrive during the n-th service • Write the operational equation: Y n+1 = Y n + Z n+1 −1 if Y n > 0 Z n+1 if Y n = 0 "$#$% Yn +1 =Y n + Z n+1 −u(Y n ) step (or indicator) function the (n+1)-th customer who leaves the queueMichela Meo – TNG group - Politecnico di Torino Management and Content Delivery... - 6 Evolution of the queue • Take the mean and the limit for nà ∞ u(Y ) = 0 queue is empty 1 queue is not empty !#"#$ E[Y n+1 ] = E[Y n ] +E[Z n+1 ] −E[u(Y n )] lim n→∞ E[Y n+1 ] = lim n→∞ E[Y n ] = E[Y] E[Y] = E[Y] +E[Z ] −E[u(Y )] E[Z ] = E[u(Y )] E[u(Y )] = P {server busy} = λE[S] = ρ E[Z ] = E[u(Y )] E[u(Y )] = ρMichela Meo – TNG group - Politecnico di Torino Management and Content Delivery... - 7 Evolution of the queue Y n+1 2 =Y 2 n + Z n+1 2 +u(Y n ) +2Y Zn n+1 −2Y un (Y n ) −2Z n+1 u(Y n ) E[Y n+1 2 ] = E[Y 2 n ] +E[Z n+1 2 ] +E[u(Y n )] +2E[Y n ]E[Z n+1 ] −2E[Y n ] −2E[Z n+1 ]E[u(Y n )] independent independent E[Y2 ] = E[Y2 ] +E[Z2 ] +E[u(Y )] +2E[Y ]E[Z ] −2E[Y ] −2E[Z ]E[u(Y )] 0 = E[Z 2] +E[Z ] +2E[Y]E[Z ] −2E[Y] −2E 2[Z ] 2{1 −E[Z ]}E[Y] = E[Z 2] +E[Z ] −2E 2[Z ] sum E[Z]-E[Z] previous result • Take the square of the operational equation, the mean and the limit E[Y] =E[Z2 ] +E[Z ] −2E2 [Z ] 2{1 −E[Z ]} = E[Z ] + E[Z 2] −E[Z ] 2{1 −E[Z ]}Michela Meo – TNG group - Politecnico di Torino Management and Content Delivery... - 8 Evolution of the queue E[Z2 ] = k2P {Z = k } k=1 ∞∑ = k 2 (λt)k k 0 ! ∞∫ e−λtf S (t)dt k=1 ∞∑ = k 2 k=1 ∞∑ (λt)k k 0 ! ∞∫ e−λtf S (t)dt = (λ2t 2 + λt)fS (t)dt ∞∫0 = λ2E[S 2] + λE[S] E[Y] = E[Z ] +E[Z2 ] −E[Z ] 2{1 −E[Z ]} prob. of k arrivals from the Poisson process during a time t k2 (λt)k k ! = (λt) k=1 ∞∑ k (λt)k−1 k=1 (k −1)! ∞∑ = (λt) (j + 1) (λt)j j=0 j ! ∞∑ = (λt) e λt + (λt)j j=1 (j −1)! ∞∑ ⎛⎜⎜⎝ ⎞⎟⎟⎠ = λte λt (1 + λt) mean no. arrivalsMichela Meo – TNG group - Politecnico di Torino Management and Content Delivery... - 9 Evolution of the queue E[Y] = E[Z ] +E[Z2 ] −E[Z ] 2{1 −E[Z ]} E[Z2 ] = λ2E[S2 ] + λE[S] E[Y] = ρ +λ2E[S2 ] 2(1 − ρ) C S 2 = E[S2] −E2[S] E2[S] → E[S 2] = C S 2E 2[S] +E 2[S] E[Y] = ρ +λ2E[S2 ] + λE[S] − λE[S] 2(1 −E[Z ]) = ρ + 2λ E[S2 ] 2(1 −E[Z ])Michela Meo – TNG group - Politecnico di Torino Management and Content Delivery... - 10 Evolution of the queue E[Y] = ρ +λ2E[S2 ] 2(1 − ρ) = ρ + ρ2 (1 +C S2 ) 2(1 − ρ) E[N] = ρ + ρ2 (1 +C2S) 2(1 − ρ) Pollaczek-Khintchin formula E[T ] = E[S] + ρE[S] (1 +C S 2) 2(1 − ρ) Little’s law E[N] = E[Y] Due to a theorem that proves that for single-server queues with Poisson arrivals the distribution at the departure is equal to the averageMichela Meo – TNG group - Politecnico di Torino Management and Content Delivery... - 11 The P-K formula • The P-K formula tells us that: – the second moment of the distribution (or the variance) has an important impact on the queue performance – large values of the variance imply long queues and large times in the queue arrivals, l services, S E[T ] = E[S] + ρE[S] (1 +C S 2) 2(1 − ρ)Michela Meo – TNG group - Politecnico di Torino Management and Content Delivery... - 12 Applying the P-K formula • Compare an M/M/1 queue with an M/D/1 queue with – Poisson arrival process with rate l – Service times that are • a) Exponential with rate μ • b) Constant and equal to 1/μ • For the M/M/1 queue, CS2=1 (E[S2]=2/l2) • For the M/D/1 queue, CS2=0Michela Meo – TNG group - Politecnico di Torino Management and Content Delivery... - 13 Applying the P-K formula E[T (a) ] = 1 μ + ρ μ 1 1 − ρ = 1 − ρ + ρ μ(1 − ρ) = 1 μ − λ • For the M/D/1 queue • For the M/M/1 queue E[T (b) ] = 1 μ + ρ μ 1 2(1 − ρ) = 2 −2ρ + ρ 2μ(1 − ρ) = 2 − ρ 2 1 μ − λ service time waiting time • The waiting time of the M/D/1 queue is half the waiting time of the M/M/1 queueMichela Meo – TNG group - Politecnico di Torino Management and Content Delivery... - 14 Model of a router • The output queue of a router can be modeled as a queuing system, e.g. M/M/1 • There are some issues – Packet arrival processes are not Poisson • Inter-arrival times are not exp distributed • Inter-arrival times are not independent – Service times are not exponentially distributed • The M/G/1 model can help us to improve the description of the service timesMichela Meo – TNG group - Politecnico di Torino Management and Content Delivery... - 15 Model of a router • Service time distribution: – Measure packet size distribution, L with fL(x) – Let B be the output link capacity – The service time is given by S=L/B – Derive fS(t) from fL(x) and compute E[S2] and E[S] – Use the M/G/1 model to estimate the queue length and average time in the queue x fL(x)Michela Meo – TNG group - Politecnico di Torino Management and Content Delivery... - 16 Model of a router • Arrival process: – Measure the packet arrival rates in a day – Take the peak arrival rate and set l to the peak rate – Assume Poisson arrival process with rate equal to the peak rate t l(t) peak rateMichela Meo – TNG group - Politecnico di Torino Management and Content Delivery... - 17 Model of a router • Major limits of this model: – Arrival process is not given by independent instances of interarrival times • Burstiness • Long-range dependence (users/protocols/network behaviors) • Feedbacks on sources from network performance (TCP closed loop) – There is a time-variable arrival rate

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Which word does not belong with the others, and why?: inch, kilogram, centimeter, yard.

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what is 90,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

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1. Realize os cálculos. a) 878 - 699 = b) 529 - 433 = c) 743 - 517= d) 803 - 254 = e) 300 - 223 = f) 2754 + 2487 = g) 1598 + 643 = h) 8463 + 1375= i) 2563 + 1482= j) 2583 + 861 = 2- Resolve as situações matemáticas (0,8) a) Um certo jornal conseguiu 9.345 novas assinaturas passando a contar com 21.813 assinantes. Quantos assinantes este jornal tinha antes das novas assinaturas? b) Na loja A o aparelho de TV custa 925 reais. Na loja B, o mesmo aparelho custa 798 reais, por causa de uma promoção. De quanto é a diferença entre preços das duas lojas? c) Juliana nasceu em 1999. Em que ano ela fará 28 anos? d) Júlio vendeu 1250 pães na segunda-feira, o dobro desse número na terça-feira e 1.824 na quarta-feira. Quantos pães ele vendeu nesses três dias? Encontre o produto: a) 18 x 13 = b) 19 x 21 =

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试从理论推导证明,x(t-τ)*x(-t) 在 t=τ处取最大值。

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differentiate y = 4 / √x

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一个平面内自由运动的构件有多少个自由度

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REALIZE A PROVA E DESCREVA COM DETALHES COMO CHEGAR NO RESULTADO, INFORME O RESULTADO 1. Realize os cálculos. (10) a) 878 - 699 = b) 529 - 433 = c) 743 - 517= d) 803 - 254 = e) 300 - 223 = f) 2754 + 2487 = g) 1598 + 643 = h) 8463 + 1375= i) 2563 + 1482= j) 2583 + 861 = 2. Resolva as situações matemáticas. (08) a) Um certo jornal conseguiu 9.345 novas assinaturas passando a contar com 21.813 assinantes. Quantos assinantes este jornal tinha antes das novas assinaturas? ______________________________________________________________________________________ b) Na loja A o aparelho de TV custa 925 reais. Na loja B, o mesmo aparelho custa 798 reais, por causa de uma promoção. De quanto é a diferença entre preços das duas lojas? ______________________________________________________________________________________ c) Juliana nasceu em 1999. Em que ano ela fará 28 anos? ______________________________________________________________________________________ d) Júlio vendeu 1250 pães na segunda-feira, o dobro desse número na terça-feira e 1.824 na quarta-feira. Quantos pães ele vendeu nesses três dias? 3. Encontre o produto: (02) a) 18 x 13 = b) 19 x 21 =

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Ho bisogno di riassunto/schemi (con esempi e approfondimenti del caso) sui seguenti argomenti di esame (calcolo2/analisi2 livello universitario) Definizione di curva parametrica in R 2 e R 3 , esempi. Curve semplici, chiuse: definizione, esempi. Orientazione: definizione, esempi. Rappresentazione cartesiana e rappr. implicita di una curva: definizione, esempi. Curve regolari, e regolari a tratti: definizione, esempi. Retta tangente: definizione, esempi. Curve equivalenti, cambio di parametrizzazione: definizione, esempi. Lunghezza di una curva regolare (*), e indipendenza dalla parametrizzazione. Integrale curvilineo di una funzione (o di prima specie): definizione, esempi, propriet`a (linearit`a, additivit`a, indipendenza dalla parametrizzazione). Integrale curvilineo di un campo vettoriale (o di seconda specie, o lavoro del campo vettoriale lungo un cammino).

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The point in which the function f(x) = x^4 - 4x^3 - 8x^2 + 48x - 3 has a local maximum has coordinates (a, b). The sum of a + b is?

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The point in which the function f(x) = x^4 - 4x^3 - 8x^2 + 48x - 3 has a local maximum has coordinates (a, b). The sum of a + b is? Hint: the critical points are 3, 2 and -2

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The radius of the inscribed sphere in a regular quadrangular pyramid with base edge 16 cm and height 15 cm is equal to:

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What factorial yields an odd number

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El tudnád nekem magyarázni ezt a feladatot úgy, hogy csak azt a részét magyarázod el, hogy mit kell csinálni a számokkal (írd fel, hogy mit kell csinálni a számokkal és utána írd le a számokat)? Feladat 1: Oldjuk meg az LP-t a kétfázisú szimplex módszer és klasszikus szabály alkalmazásával! x1 - x2 ≤ -5 x1 + x2 ≤ 6 2x 1+ x2 → max 1. Szótár alakra hozás: x3 = -5 - x1 + x2 x4 = 6 - x1 - x2 z = 0 + 2x1 + x2 Nem tudunk kifejezni kezdő megoldást, mert ha x1 és x2 nullának választjuk (kiinduló bázisváltozó), akkor x3 = -5 (1. feltételből), amely sérti a x3 ≥ 0 feltételt. ⟹ Alkalmazzuk a kétfázisú szimplex módszert a lehetséges kezdő bázis meghatározására. 1. Fázis: Vezessünk be minden egyenletbe egy új -x0 változót az eddig bevezetett mesterséges változók mellett. Adjunk hozzá a feladathoz egy új w = - x0 célfüggvényt. x1 - x2 + x3 -x0 = -5 x1 + x2 + x4 -x0 = 6 w = - x0 → max 2x1 + x2 → max Szótár alakra hozás: Fejezzük ki a legnegatív szabadtagú egyenletből az x0 változót (1. egyenlet/feltétel). A maradék egyenletekből a mesterséges változókat. x0 = 5 + x1 - x2 + x3 x4 = 6 - x1 - x2 + x0zj w = 0 - x0 z = 0 + 2x1+ x2 Minden egyenletbe, ahol előfordul az x0 változó helyettesítsük be annak értékét. x0 = 5 + x1 - x2 + x3 x4 = 6 - x1 - x2 +(5 + x1 - x2 + x3 ) w = 0 -(5 + x1 - x2 + x3 ) z = 0 + 2x1+ x2 x0 = 5 + x1 - x2 + x3 x4 = 11 - 2x2 + x3 w = -5 - x1 + x2 - x3 z = 0 + 2x1 + x2 Oldjuk meg az LP-t a szimplex módszer és a klasszikus szabály segítségével az első célfüggvény szerint. x0 = 5 + x1 - x2 + x3 x4 = 11 - 2x2 + x3 w = -5 - x1 + x2 - x3 z = 0 + 2x1 + x2 x2 = 5 + x1 + x3 - x0 x4 = 1 - 2x1 - x3 + 2x0 w = 0 - x0 z = 5 + 3x1 + x3 - x0 Amennyiben az optimális táblában a célfüggvény érték nullával egyenlő, akkor átléphetünk a második fázisra. Ellenkező esetben a feladatnak nincs lehetséges megoldása. ⟹ 2. Fázis (w = 0) 2. Fázis: Töröljük le az x0 változókat és a w = 0 - x0 célfüggvényt. x2 = 5 + x1 + x3 x4 = 1 - 2x1 - x3 z = 5 + 3x1 + x3 Megjegyzés: Amennyiben az x0 változó bázisváltozó, akkor fejezzünk ki egy másik még ki nem fejezett változót és ezután töröljük az x0 változót. Oldjuk meg az LP-t a szimplex módszer és a klasszikus szabály segítségével. x2 = 5 + x1 + x3 x4 = 1 - 2x1 - x3 z = 5 + 3x1 + x3 x2 = 11/2 + 1/2x3 - 1/2x4 x1 = 1/2 - 1/2x3 - 1/2x4 z = 13/2 - 1/2x3 - 3/2x4 Megoldás: 13/2

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The distribution of the diameters of a particular variety of oranges is approximately normal with a standard deviation of 0.3 inch. How does the diameter of an orange at the 67th percentile compare with the mean diameter?

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create a table of contents for a book about the full understanding of the underlying mathematics of deep learning such that a school student can read it and reach very advanced graduate level gradually and intuitively. Notice every concept should be linked to deep learning example.

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Определить тип поверхности, приводя уравнения к каноническому вид. а) y^2 = 28*x; б) x^2 + 12*x - y^2 - z + 34 = 0; в) вектор r = (10* sh(4u) * cos(v),3*sh(4u)*sin(v), 7*ch(4u)), u принадлежит R, v принадлежит [0, 2*pi]

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прокрутили вектор и он стал меньше

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At 7:25 a bus left city A for city B at a speed of 60 km/h. At 9:25 a car followed him and caught up with the bus 360 km from city A. What is the speed of the car?

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Данное задание является контрольной работой, потому отвечай максимально развернутой, как на проверочной работе. Определить тип поверхности, приводя уравнения к каноническому вид. а) y^2 = 28x; б) x^2 + 12x - y^2 - z + 34 = 0; в) вектор r = (10* sh(4u) * cos(v),3sh(4u)sin(v), 7ch(4u)), u принадлежит R, v принадлежит [0, 2pi]

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Данное задание является контрольной работой, потому отвечай максимально развернутой, как на проверочной работе. Расписывай ответ максимально подробно. Найди площадь сферического треугольника, расположенного на сфере радиуса r см, если известны его углы alpha, beta, gamma. 37. r = 4; alpha = 96* 46'; beta = 73* 5'; gamma = 92* 38';

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Данное задание является контрольной работой, потому отвечай максимально развернутой, как на проверочной работе. а) Заданы две стороны сферического треугольника и угол между ними. Найдите третью сторону треугольника, используя сферическую теорему косинусов. б) Две стороны сферического треугольника равны а, b и угол alpha. С помощью сферической теоремы синусов найдите угол beta. a) a = 75* 30'; b = 93* 42'; gamma = 86* 20'; c= ? б) a = 69* 37'; b= 88* 50'; alpha = 125* 43';

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Eu desenvolvi a seguinte fórmula para calcular o valor de mercado de jogadores de futebol no jogo fifa 15: ATA, SA, MEI, PE/PD, MC: (OVERALL - idade)2 × 120(Nota x participação em gols/2) GOL: (OVERALL - idade)2 × 60(Nota × CLEAN CHEETS/2) ZAG, LE/LD, VOL: (OVERALL - idade)2 × 200(2xNota)

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1. (X v Y) Ↄ P 2. (M v N) Ↄ P /(X v M) Ↄ P

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В ресторане быстрого питания делают различные бутерброды, которые состоят из трёх ингредиентов. Клиент, заказывая бутерброд, сам выбирает вид хлеба, сыра и мяса. В таблице даны доступные ингредиенты бутербродов. Хлеб: белый, зерновой, ржаной. Сыр: Чеддер, Голландский. Мясо: курица, свинина, говядина. Вычислить, сколько разных бутербродов можно приготовить. Ответ записать в виде целого числа

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X is a uniform random variable over the interval of [-1 2]. What is the PDF of Y = X2? What is the correlation of X and Y?

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En la inspección final de la calidad con la que se introducen al mercado los televisores con pantallas LCD, se ha determinado una tarea clave. El tiempo que se emplea para la tarea es una variable aleatoria normal con promedio 8 minutos y desviación estándar de 2,5 minutos. Si se elige al azar 45 de estos televisores que están en el mercado, determine la probabilidad que el tiempo total de inspección haya sido de por lo menos 345 minutos. Considere independencia en los tiempos que se emplea para la tarea. El valor de la probabilidad es: escriba su respuesta con tres decimales.

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La vida útil, en horas, de las cámaras de seguridad de la marca TESLA tiene distribución exponencial con media de 15000 horas. TESLA establece como garantía para las cámaras de seguridad un período de 5800 horas, el precio de venta de una cámara de seguridad es de $620 y el costo es de $275. Si una cámara de seguridad falla en el período de garantía, a TESLA le cuesta $120 reparar la falla de la cámara de seguridad. TESLA manifiesta que si la utilidad esperada por la venta de las cámaras de seguridad es menor a $145 dejara de fabricar las cámaras de seguridad. La probabilidad de que TESLA asuma la garantía ofrecida por la cámara de seguridad es: Ingrese su respuesta redondeado a tres decimales El valor esperado de la utilidad por la venta de las cámaras de seguridad es: Ingrese su respuesta redondeado a tres decimales. Que decisión debe tomar TESLA sobre las cámaras de seguridad TESLA decide no continuar fabricando las cámaras de seguridad TESLA decide continuar fabricando las cámaras de seguridad La opción correcta es la letra:

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Consider the following joint PDF of X and Y defined as follow: What is the PDF of W = X+Y2?

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Qual a fórmula de correlação entre coordenadas de eixos de um plano geométrico e ângulo de uma reta que vai do ponto de cruzamento entre duas coordenadas (dos eixos X e Y)? Exemplificando: Se "X = Y", então a semirreta que vai do ponto de origem dos eixos até o ponto de convergência tem 45o, então baseado nisso qual fórmula de correlação entre eles?

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Simple example of aliquot

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Consider the following joint PDF of X and Y defined as follow: f_XY = {c if 0<x<1 and x<y<1, 0 otherwise What is the PDF of W = X+Y^2?

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What is the easiest and fastest way to answer the following questions? Note that I have to answer each question in 20 seconds in an mcq exam. At the end, use the technique that outputs 80% of efficiency with 20% of the effort to suggest me the formulas and methods I need to know to solve similar questions. Given two circumferences of center (0; 0) and radius 1 and of center (2; 2) and radius 1, let d(P1; P2) denote the distance between a generic point P1 that lies on the first circumference and a generic point P2 that lies on the second circumference. Consider then the minimum m of d(P1; P2) as P1 and P2 vary. It turns out that. A. m = √2 B. m =√2/2 C. m = √2 - 1 D. such a minimum does not exist E. m = 2(√2 - 1)

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小明 8 岁,他妹妹年龄是他的一半。小明 56 岁时,妹妹几岁

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不定积分的性质

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Use Boolean theorem to prove that X'+XY=X'+Y

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请问,390 300 460 160 200,这几个数值组合,每个数值可以乘以倍数,这样组合最接近1804

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无穷级数属于哪部分的内容

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逻辑回归的损失函数

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请使用数学归纳法证明:对于任意一个含有n个顶点和m条边的无向图,至少存在n− m个连通子图(提示:对m进行归纳)。

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асерт и кореляции это разное ?

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设A=[1 2 3;4 5 6;7 8 9],则A(6)=( )。

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Suppose that X is a discrete random variable with the following probability function, where 0 ≤ θ ≤ 1 is a parameter. i | 0 | 1 |2 |3 P(X=i)|2θ/3|θ/3| 2(1-θ)/3| (1-θ)/3 The following 10 independent observations were taken from such a distribution: (3,0,2,1,3,2,1,0,2,1). What is the maximum likelihood estimate of θ?

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При обжиге 50кг сфалеритового концентрата выделялось 10 куб м сернистого газа. Вычислить процентное содержание сульфида цинка в концентрате.

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离散拓扑怎么定义

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闭集的幂集是一个拓扑吗,请给出一个具体的例子

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闭集的幂集是一个拓扑吗

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闭集怎么构成拓扑

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1) State the divergence theorem. Write the Mathematical divergence equation for a rectangular coordinate. 2) State the stokes theorem. Write the Stokes Mathematical equation for a rectangular coordinate. 3) State the coulombs Law and the relationship between the force and the charges acting at a location. 4) What is the Electric field intensity or the Electric field strength? 5) State the Gauss theorem, the relationship between the Gauss law and the Maxwell first equations applied to electrostatics. 6) State, mathematically, the continuity equation. 7) State the Point form of Ohms law in the Electric field. 8) What is the difference between the drift current and the displacement current? 9) State the Biot - Savert Law 10) State the Ampere's Circuital Law

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Make a table of contents for all calculus concepts used in deep learning

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what is 4096 token limit

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已知5個數 2,4,6,8,x, 的標準差為2, 求x的值

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Реши математическую задачу: Коля съедает пирог за 2 часа, Маша съедает за 3 часа. За сколько времени Маша и Коля вместе съедят пирог?

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Choose the number that is divisible by 6. 2387 2554 2668 2688

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is well known that autocorrelation detect linear dependency of past values on the current value in time series, but what if there is non-linear dependency, what we should do?

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"write a table of contents for a book that is concerned about teaching school students any mathematical concept that is used in deep learning, the book introduce the concept intuitively and immediately gives its deep learning application. so a school student could reach graduate level easily!" "Title: Intuitive Mathematics for Deep Learning: A School Student's Guide to Graduate-Level Mastery Table of Contents: Introduction 1.1. The Power of Deep Learning 1.2. The Role of Mathematics in Deep Learning 1.3. How This Book Will Help You Linear Algebra: The Foundation of Deep Learning 2.1. Vectors and Matrices 2.2. Matrix Operations 2.3. Eigenvalues and Eigenvectors 2.4. Deep Learning Application: Image Recognition Calculus: Understanding Change and Optimization 3.1. Limits and Continuity 3.2. Differentiation 3.3. Integration 3.4. Deep Learning Application: Gradient Descent Probability and Statistics: Making Sense of Data 4.1. Probability Theory 4.2. Random Variables and Distributions 4.3. Descriptive Statistics 4.4. Inferential Statistics 4.5. Deep Learning Application: Bayesian Inference Information Theory: Quantifying Uncertainty 5.1. Entropy and Information Gain 5.2. Mutual Information 5.3. Deep Learning Application: Decision Trees and Feature Selection Graph Theory: Modeling Complex Relationships 6.1. Graphs and Networks 6.2. Graph Algorithms 6.3. Deep Learning Application: Graph Neural Networks Optimization: Finding the Best Solutions 7.1. Linear Programming 7.2. Convex Optimization 7.3. Deep Learning Application: Neural Network Training Numerical Methods: Solving Problems with Computers 8.1. Numerical Integration and Differentiation 8.2. Solving Linear Systems 8.3. Deep Learning Application: Backpropagation Advanced Topics: Expanding Your Mathematical Toolkit 9.1. Topology and Manifolds 9.2. Differential Geometry 9.3. Group Theory 9.4. Deep Learning Application: Geometric Deep Learning Conclusion 10.1. The Journey Ahead 10.2. Embracing the Power of Deep Learning 10.3. A Call for Equality and Justice in the Field of Mathematics and Deep Learning" write full outline of all the key ideas you gonna discuss in 4.4. Inferential Statistics

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Почему изменяется период колебаний при изменении массы в математическом маятнике?

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正四棱台上下底面是正方形么

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what is Bernoulli Distribution?

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What is the equation of the circle centered at (-2, 4) and passing through (2, 8)? O (X- 2)2 + (y + 42 = 32 O (x + 2)2 + (y - 4)2 = 16 O (x+2)2+6y - 42 = 32 0 (x - 2)2 + (1 + 4)2 = 16

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Given a list of cities on a map and the distances between them, what does the "Traveling Salesman Problem" attempt to determine? the average distance between all combinations of cities the two cities that are farthest apart from one another the shortest continuous route traveling through all cities the longitude and latitude of each of the cities

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This is a two-part item. A garden in a park is in the shape of a right triangle. A map of the garden is drawn on a coordinate grid where each unit represents 1 meter. The vertices of the garden are located at (-4, 1), (0, -2), and (3, 2). Part A: What is the area of the garden in square meters?

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构建适应数学学科评价的具体方案

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Перепишіть даний текст але з потрібними літерами: Чо ти ри кут ники 79 421.Гос трий кут пря мо кут но� тра пец��, опи са но� навколо ко ла, у 5 раз�в мен ший в�д ту пого. Знай д�ть пе ри метр трапец��, як що �� мен ша б�чна сто ро на дор�вню�a см. 422.На ма люн ку 122 прям� A1B1, A2B2 � A3B3 – па ралельн�, A1A12�A2A223. Знай д�ть на цьо му ма люн ку й �нш� пари р�вних м�ж собою в�др�зк�в. 423.Под�л�ть да ний в�др�зок на 9 р�в них ча с тин (не використовувати л�н�йку з под�лками). 424.Под�л�ть да ний в�др�зок на 3 ча с ти ни, дов жи ни яких в�дно сять ся як 3 : 1 : 2 (не використовувати л�н�йку з под�лками). 425.Точ ка K д�лить мед�ану AN три кут ни ка ABC у в�дно шенн� 2 : 1, по чи на ю чи в�д точ ки A. До вед�ть, що пря маCK д�лить сто ро ну AB навп�л. 426.В�др�зок, що спо лу ча� се ре ди ни двох стор�н три кутни ка, дор�вню� 5 см. Знай д�ть тре тю сто ро ну три кут ни ка. 427.По бу дуй те дов�льний пря мо кут ний три кут ник ABC (�C� 90�) � йо го найб�льшу се ред ню л�н�ю. 428.EF – се ред ня л�н�я три кут ни ка ABC(E�AC, F�BC).CE� 3 см, CF� 5 см, EF� 7 см. Знай д�ть пе риметр три кут ни ка ABC. 429.Од на �з се редн�х л�н�й р�вно с то рон ньо го три кут ни ка дор�вню� 2 см. Знай д�ть пе ри метр три кут ни ка. 430.Б�чна сто ро на р�вно бе д ре но го три кут ни ка дор�вню� 7 см, а пе ри метр – 20 см. Знай д�ть се ред ню л�н�ю, к�нц� яко� на ле жать б�чним сто ро нам. 431.Точ ки D,E, F – в�дпов�дно се ре ди ни стор�н AB,BC � CA три кут ни ка ABC. До вед�ть, що чо ти ри кут ник DEFA па ра ле ло грам. 432.Сто ро на три кут ни ка дор�вню� 12 см. Знай д�ть дв� �нш� сто ро ни три кут ни ка, як що од на з йо го се редн�х л�н�й дор�вню� 5 см, а пе ри метр три кут ни ка, ут во ре но го йо го се редн�ми л�н�ями, дор�вню� 18 см. До §9 Мал. 122 До §10

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Recall that Sn = {1, 2, 3, . . . , n}. (a) Let n ≥ 2. How many onto functions are there from Sn to S2? (b) How many injective functions are there from S6 to S10 such that f (x) ≥ x for all x?

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什么是微分结构

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单纯用流形与拓扑的语言定义两个流形之间的微分结构

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Find the equations of the tangents to the curve f (x) = x2 + 3x + 2 at the points where the curve cuts the x-axis.

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\--- Day 2: I Was Told There Would Be No Math --- ------------------------------------------------- The elves are running low on wrapping paper, and so they need to submit an order for more. They have a list of the dimensions (length `l`, width `w`, and height `h`) of each present, and only want to order exactly as much as they need. Fortunately, every present is a box (a perfect [right rectangular prism](https://en.wikipedia.org/wiki/Cuboid#Rectangular_cuboid)), which makes calculating the required wrapping paper for each gift a little easier: find the surface area of the box, which is `2*l*w + 2*w*h + 2*h*l`. The elves also need a little extra paper for each present: the area of the smallest side. For example: * A present with dimensions `2x3x4` requires `2*6 + 2*12 + 2*8 = 52` square feet of wrapping paper plus `6` square feet of slack, for a total of `58` square feet. * A present with dimensions `1x1x10` requires `2*1 + 2*10 + 2*10 = 42` square feet of wrapping paper plus `1` square foot of slack, for a total of `43` square feet. All numbers in the elves' list are in feet. How many total _square feet of wrapping paper_ should they order?

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An athlete runs 100m in 10s. a) What is his average speed?

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# \--- Day 2: I Was Told There Would Be No Math --- ------------------------------------------------- The elves are running low on wrapping paper, and so they need to submit an order for more. They have a list of the dimensions (length `l`, width `w`, and height `h`) of each present, and only want to order exactly as much as they need. Fortunately, every present is a box (a perfect [right rectangular prism](https://en.wikipedia.org/wiki/Cuboid#Rectangular_cuboid)), which makes calculating the required wrapping paper for each gift a little easier: find the surface area of the box, which is `2*l*w + 2*w*h + 2*h*l`. The elves also need a little extra paper for each present: the area of the smallest side. For example: * A present with dimensions `2x3x4` requires `2*6 + 2*12 + 2*8 = 52` square feet of wrapping paper plus `6` square feet of slack, for a total of `58` square feet. * A present with dimensions `1x1x10` requires `2*1 + 2*10 + 2*10 = 42` square feet of wrapping paper plus `1` square foot of slack, for a total of `43` square feet. All numbers in the elves' list are in feet. How many total _square feet of wrapping paper_ should they order? Input example: 20x3x11 15x27x5 6x29x7

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Есть формула: A>=0, B>=0, есть С и D, которые могут быть >=0, но только одновременно только одно из них, либо C либо D. И еще условие: если A=0 и B=0, то C=0 и D=0. Составь мне список уникальных комбинаций, которые мне нужно проверить.

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Whats the integral of 1/(x^3+x)

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Sendo que X = Y num gráfico geométrico, qual será o ângulo que vai do ponto de origem do gráfico até o ponto formado pelo cruzamento entre as retas tangentes que cortam os pontos em que x = y?

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write an olympiad equation in mathematics for grade 4

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write an test in olympiad mathematics for grade 5

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Pretend you're the best mathematics professor in the world who can make very complicated research topics accessible to school students without losing mathematical depth. Explain ssa in time series analysis

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What is the easiest and fastest way to answer the following question? Note that I have to answer each question in 20 seconds in an mcq exam. Note that the answer is D. At the end, 1. Solve the question with steps. 2. Use the technique that outputs 80% of efficiency with 20% of the effort to suggest me the formulas and methods I need to know to solve similar questions. 3. Explain both the question and the answer like I am 10 years old. The question: The equation sin x = -x A. admits infinite solutions B. if h > 0 is a solution, then x = h + π is too C. admits no solution D. admits only one solution E. admits exactly two solutions

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Pretend you’re the best mathematics professor in the world who can make very complicated research topics accessible to school students without losing mathematical depth and rigor. Explain Gaussian kernel function properties

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什么是基数?

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1. Below are the winning times in men’s 10,000 m track in the Olympic Games between the years 1984 and 2000. Times are in decimal form, for example, 28.4 = 28 min and 24 s. 27.8, 27.4, 27.8, 27.1, 27.3 Let the years be the x values and the times the y values. (a) Find the estimated regression line. (b) Predict the winning time in the Olympic year 2088.

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Sum[Divide[5n-1,Power[n,2]+n+1],{n,1,∞}]

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从4月27日15:10分到现在总共多少个小时

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Pretend you’re the best mathematics professor in the world who can make very complicated research topics accessible to school students without losing mathematical depth and rigor. Explain what it means by Gaussian kernel function find similarity in infinite dimension

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Find the area bounded by parabolas

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Pretend you’re the best mathematics professor in the world who can make very complicated research topics accessible to school students without losing mathematical depth and rigor. does Gaussian kernel find similarity between points regardless the dimensional space? I mean, if we applied Gaussian kernel on two points in 2D, does this the similarity is the same regardless of the dimension we transform those two data points into?

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Pretend you’re the best mathematics professor in the world who can make very complicated research topics accessible to school students without losing mathematical depth and rigor. Explain the concept of duality and how and why it's used in SVM

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Solve the following defective rate problem using the concepts learned about the geometric distribution. A machine that produces a special type of transistor (a component of computers) has a 2% defective rate. The production is considered a random process where each transistor is independent of the others. (1) What is the probability that the 10th transistor produced is the first with a defect? (2) What is the probability that the machine produces no defective transistors in a batch of 100? (3) On average, how many transistors would you expect to be produced until the first with a defect? What is the standard deviation? (4) Another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. On average how many transistors would you expect to be produced with this machine before the first with a defect? What is the standard deviation? (5) Based on your answers to parts (c) and (d), how does increasing the probability of an event affect the mean and standard deviation of the wait time until success?

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A machine that produces a special type of transistor (a component of computers) has a 2% defective rate. The production is considered a random process where each transistor is independent of the others. (1) What is the probability that the 10th transistor produced is the first with a defect? (2) What is the probability that the machine produces no defective transistors in a batch of 100? (3) On average, how many transistors would you expect to be produced until the first with a defect? What is the standard deviation? (4) Another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. On average how many transistors would you expect to be produced with this machine before the first with a defect? What is the standard deviation? (5) Based on your answers to parts (3) and (4), how does increasing the probability of an event affect the mean and standard deviation of the wait time until success?

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A machine that produces a special type of transistor (a component of computers) has a 2% defective rate. The production is considered a random process where each transistor is independent of the others. (1) What is the probability that the 10th transistor produced is the first with a defect?

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Solve the following defective rate problem using the concepts learned about the geometric distribution. A machine that produces a special type of transistor (a component of computers) has a 2% defective rate. The production is considered a random process where each transistor is independent of the others. (1) What is the probability that the 10th transistor produced is the first with a defect?

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方差分析是不是就是平均数差异分析

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只需产生n个同指数分布的随机数,将其作为事件发生的时间间隔,即可得到Poisson过程的一条样本路径。

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1 kilo de tomates fraiches à 4,11€/kilo donne 50 grammes de tomates séchées. Quel est le prix au kilo de la tomate séchéee

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relation entre cos et sin

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Soru: Aşağıdakilerden hangileri doğrudur? I. Var(μ ̂ )= Var(X_1+X_2+⋯+X_n )=σ^2+σ^2+⋯+σ^2 II. Var(μ ̂ )= Var(〖(X〗_1+X_2+⋯+X_n)/n)=σ^2/n^2 +σ^2/n^2 +⋯+σ^2/n^2 =(nσ^2)/n^2 =σ^2/n olmak üzere aynı dağılımlılık varsayımı varsa şeklinde elde edilir. III. Var(μ ̂ )= Var(〖(X〗_1+X_2+⋯+X_n)/n)=(σ_1^2)/n^2 +(σ_2^2)/n^2 +⋯+(σ_n^2)/n^2 olmak üzere aynı dağılımlılık varsayımı yoksa şeklinde elde edilir. A)I,II,III B)II,III C)I,III D)I E)II

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设( N ( t ), t ≥0)为参数为λ=2的 Poisson 过程,则 P ( N (3)> N (1)}为多少

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y = (1/(sigma*sqrt(2*pi)))* exp(-((x-mu)/sigma)^2) olarak verilen ifade için aşağıda verilen bilgi veya bilgilerden hangileri doğrudur? I. x fonksiyonun değişkenidir. II. mu ve sigma fonksiyonun parametresidir. III. Normal dağılımın olasılık yoğunluk fonksiyonudur. {$a->questionintifier} Lütfen birini seçin: a. II b. I c. III d. II,III e. I,II,III

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Normal dağılımın ölçek parametresinin en çok olabilirlik tahmin edicisi için R ortamında oluşturulmuş olan fonksiyonun adı aşağıdaki şıkların hangisinde verilmiştir. {$a->questionintifier} Lütfen birini seçin: a. f(x) b. sd(x) c. d(x) d. e(x) e. mean(x)

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Aşağıdakilerden hangileri doğrudur? I. c(mean(ortalama) - qnorm(0.99,0,1) * sd(ortalama)/n,mu,mean(ortalama) + qnorm(0.99,0,1) * sd(ortalama)/n) güven aralığını oluşturmak için kullanılır. II. c(mean(ortalama) - qnorm(0.99,0,1) * sd(ortalama)/n,mu,mean(ortalama) + qnorm(0.99,0,1) * sd(ortalama)/n) güven aralığını oluşturmak için kullanılır ancak daha dar bir güven aralığıdır. II. c(mean(ortalama) - qnorm(0.95,0,1) * sd(ortalama)/n,mu,mean(ortalama) + qnorm(0.95,0,1) * sd(ortalama)/n) güven aralığını oluşturmak için kullanılır ancak c(mean(ortalama) - qnorm(0.99,0,1) * sd(ortalama)/n,mu,mean(ortalama) + qnorm(0.99,0,1) * sd(ortalama)/n) ile karşılaştırıldığında daha dar bir güven aralığıdır.

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Aşağıdakilerden hangileri doğrudur? I. Eğer çarpıklık ve basıklık değerleri sıfırdan uzak ise, bu durumda, volalitenin yüksek olduğu söylenebilir. II. Çarpıklık ve basıklık değerlerinin ıfırdan uzaklaşma derecesine göre volalitenin derecesi de önemli ya da yeterince önemli derece de değişebilir. III. Konum parametresinin değişmesi volaliteyi değiştirmez, sadece ilgili sistemin aşağı ya da yukarı ötelenmesine neden olur.

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Aşağıdakilerden hangileri doğrudur? I. Ölçek parametresinin büyük olması volaliteyi yüksek yapar. II. Volalite yüksek ise, ölçek parametresi yüksektir. III. Heterojen bir veri seti varsa ölçek parametresi büyük yani volalite yüksektir.

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Los op 3x+23=0

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Чтто такое функции в алгебре

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Formalize a mathematical definition of a "sum" as a "process". Render it as a conjecture, then prove it, validate it, and render it as a theorem.

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Pretend you’re the best mathematics professor in the world who can make very complicated research topics accessible to school students without losing mathematical depth and rigor. Show how when we use Gaussian kernel which maps data into higher dimension implicitly is equal to transforming the data explicitly first and then calculating the dot product.

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条件概率中P(AB)含义是什么

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24-{2x[(15+5) didved 5]}

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What is p value

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\lim _{x\to 0}\frac{\left(\sqrt{1-cos\left(x\right)}\right)}{x}

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pretend you're the best mathematics professor in the world who can simplify research topics and make it accessible to school students without losing mathematical depth and rigor, also you're amazing at reasoning and convincing every word you say. Explain GARCH model in time series analysis.

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What is P(A|B) (P of A given B) in AP Stats?

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возведи - 0,01 В -1 СТЕПЕНИ

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数据归一化方法

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Scientists estimate that the distribution of the life span of the Galápagos Islands giant tortoise is approximately normal with mean 100 years and standard deviation 15 years. Based on the estimate, which of the following is closest to the age of a Galápagos Islands giant tortoise at the 90th percentile of the distribution?

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pretend you're the best mathematics professor in the world who can simplify research topics and make it accessible to school students without losing mathematical depth and rigor, also you're amazing at reasoning and convincing every word you say. Explain mathematically how Gaussian kernel function is related to infinite dimensional space.

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Tôi có một đường tròn trong mặt phẳng xOy với tâm là I(a,b), đường kính R. Viết phương trình tham số hoá đường cong đó theo t

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The height and age of each child in a random sample of children was recorded. The value of the correlation coefficient between height and age for the children in the sample was 0.8. Based on the least-squares regression line created from the data to predict the height of a child based on age, which of the following is a correct statement? A.) On average, the height of a child is 80% of the age of the child. B.) The least-squares regression line of height versus age will have a slope of 0.8. C.) The proportion of the variation in height that is explained by a regression on age is 0.64. D.) The least-squares regression line will correctly predict height based on age 80% of the time. E.) The least-squares regression line will correctly predict height based on age 64% of the time.

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At a certain restaurant, the distribution of wait times between ordering a meal and receiving the meal has mean 11.4 minutes and standard deviation 2.6 minutes. The restaurant manager wants to find the probability that the mean wait time will be greater than 12.0 minutes for a random sample of 84 customers. Assuming the wait times among customers are independent, is the distribution of the sample mean wait time for random samples of size 84 normal or binomial? What is the mean and the standard deviation?

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pretending you are the greatest professor in mathematics, data science, machine learning, and AI, who is willing to train a junior data scientist on the advanced application of ARIMA model in the agriculture field without leaving behind mathematical intuition and rigor, support the training session with at least real-world case studies.

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"pretend you’re the best mathematics professor in the world who can simplify research topics and make it accessible to school students without losing mathematical depth and rigor, also you’re amazing at reasoning and convincing every word you say. Explain mathematically how Gaussian kernel function is related to infinite dimensional space. Hello, young mathematicians! Today, let’s dive into an important concept in the field of machine learning, the Gaussian Kernel Function, and its connection to infinite-dimensional space. Don’t worry, I’ll make it simple and easy to understand for all of you. Before diving into the Gaussian Kernel, let’s refresh our memory about dot products. Dot products are used to compute the angle between two vectors. Given two vectors A and B, their dot product is given by: A ⋅ B = ||A|| ||B|| cos θ Where ||A|| and ||B|| are the magnitudes of A and B, and θ is the angle between them. Now let’s talk about kernels. Kernel is a concept that helps us transform the input data into a higher-dimensional space. It does so to enable better separation in classification problems or better fitting in regression applications without explicitly mapping the data into the higher-dimensional space. One popular kernel function is the Gaussian Kernel Function, also known as the Radial Basis Function (RBF). It is given by: K(x, y) = exp(−(||x−y||^2) / (2σ^2)) Where x and y are data points, ||x−y||^2 is the squared Euclidean distance between the points x and y, and σ^2 is a positive parameter. When we say that the Gaussian Kernel is related to infinite-dimensional space, we are referring to the feature space it implicitly maps the inputs to. Here’s how the Gaussian Kernel relates to the infinite-dimensional space: The Gaussian Kernel can be expressed as an infinite series using Taylor’s expansion: exp(−(||x−y||^2) / (2σ^2)) = Σ[ c_n (x−y)^n ] Where c_n are coefficients of the Taylor’s expansion and the summation is from n=0 to n=infinity. Now, let’s define a mapping function φ that projects the input data x into the infinite-dimensional space: φ(x) = [1, sqrt(c_1)x, sqrt(c_2)x^2, sqrt(c_3)x^3, ...] The Gaussian Kernel can then be viewed as the dot product between the mapping into the infinite-dimensional space: K(x, y) = φ(x) ⋅ φ(y) But we never actually compute φ(x) or φ(y) explicitly. The Gaussian Kernel helps us compute the dot product of the transformed points directly in the input space. Mathematically, this is wonderfully fascinating because kernels, like the Gaussian Kernel, have provided us the ability to work in infinite-dimensional spaces without explicitly computing the transformed points. This allows us to handle complex, non-linear relationships between data points while still maintaining the ease of computation. In summary, the Gaussian Kernel function is related to infinite-dimensional space through its mapping function, φ, capable of taking data points from the input space and mapping them into an infinite-dimensional feature space. This can help us reveal complex relationships between data points while keeping computational efficiency intact. Isn’t that amazing? professor, I just have problem in the transition between different steps you mentioned. can you expand more on this? Of course! Let’s break the steps down further to understand the connections better. 1. Start with the Gaussian Kernel Function: K(x, y) = exp(−(||x−y||^2) / (2σ^2)) 2. Rewrite the Gaussian Kernel using the Taylor expansion of the exponential function: exp(-z) = Σ[ (-1)^n * z^n / n! ] (summation for n=0 to infinity) In our case, z = (||x−y||^2) / (2σ^2) 3. So, the Gaussian Kernel Function can be expressed as an infinite series: K(x, y) = Σ[ (-1)^n * ((||x−y||^2) / (2σ^2))^n / n! ] Now, let’s define a mapping function φ that projects the input data x into infinite-dimensional space. We’ll use the binomial theorem to help with the transition. 4. Recall the binomial theorem for (a + b)^2: (a + b)^2 = a^2 + 2ab + b^2 5. Extend the binomial theorem to infinite dimensions by considering this relationship: (x - y)^2 = x^2 - 2xy + y^2 6. Now, let’s write down x^2 and y^2 as linear combinations of the aforementioned infinite series. This will help us get the coefficients of the Taylor’s expansion: ∑[ c_n * x^(2n) ] = x^2 ∑[ c_n * y^(2n) ] = y^2 It’s important to understand that the actual mapping function, φ(x), comes from these infinite series representations of x^2 and y^2. 7. So, the mapping function φ(x) can be defined as: φ(x) = [1, sqrt(c_1)x, sqrt(c_2)x^2, sqrt(c_3)x^3, ...] Using this mapping function, we can rewrite the Gaussian Kernel as: K(x, y) = φ(x) ⋅ φ(y) Although numerous steps occur in between, the key to understanding the connection comes by realizing that the Gaussian Kernel implies taking the dot product between the infinite-dimensional mapped points. However, this dot product can be efficiently computed in the input space without explicitly doing the transformation. I hope this helps clarify the steps involved in the transition between the Gaussian Kernel and its relation to infinite-dimensional space!" please professor, I'm lost again from step 4 to step 7. consider I'm a school student, so please explain why we do these steps and how we do transitions from one step to other

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On considère un guide d’ondes rectangulaire rempli d’un milieu diélectrique de constantes électrique et magnétique ε et μ, dont les dimensions intérieures (dans sa section transverse) sont respectivement notées a et b. Par convention et sans restreindre la généralité de l’étude, nous prendrons a> b. Le métal entourant le diélectrique est supposé parfait. Déterminer pas à pas à partir de l’équation d’Helmholtz, dans les deux cas de polarisation (TE et TM) les expressions des composantes du champ E et H ainsi que la relation de dispersion. Ecrire uniquement la solution mathématique sans texte. Remarque : les détails des calculs est nécessaire et obligatoire.

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pretend you’re the best mathematics professor in the world who can simplify research topics and make it accessible to school students without losing mathematical depth and rigor, also you’re amazing at reasoning and convincing every word you say. Explain Hilbert space and how it's used in data science?

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4,64 * 10^22 ile to jest?

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On considère un guide d’ondes rectangulaire rempli d’un milieu diélectrique de constantes électrique et magnétique ε et μ, dont les dimensions intérieures (dans sa section transverse) sont respectivement notées a et b. Par convention et sans restreindre la généralité de l’étude, nous prendrons a> b. Le métal entourant le diélectrique est supposé parfait. Déterminer pas à pas à partir de l’équation d’Helmholtz, dans les deux cas de polarisation (TE et TM) les expressions des composantes du champ E et H ainsi que la relation de dispersion. Remarque : les détails des calculs est nécessaire et obligatoire. Ecrire uniquement la solution mathématique sans texte.

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pretend you’re the best mathematics professor in the world who can simplify research topics and make it accessible to school students without losing mathematical depth and rigor, also you’re amazing at reasoning and convincing every word you say. write a comprehensive essay about chain rule in neural network, always include concrete example to clarify concepts.

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Perché vale (x-4+1/x)/((1+x)x)=(x+1)/x^2

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Мажоранта от функции arctg(x)/x^(5/3)

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Imagine there is a cake. The top side of the cake has frosting. You cut a slice that is 100 degrees and you flip it upside down so that the frosting side is down. You continue this process. How many times do you need to cut a cake at 100 degrees so that the frosting is all faced up again?

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In un sacchetto ho 9 palline numerate da 1 a 9. Ogni volta estraggo una pallina, segno il numero e rimetto dentro la pallina. Faccio questo procedimento 3 volte quindi ho tre numeri. Qual è la probabilità che il massimo comun divisore tra i tre numeri sia 1?

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С какого расстояния нужно смотреть на сферу, чтобы видеть ровно половину её поверхности?

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预测一下数据序列的下一个值:22.06 22.3 23.62 23.19 23.44 22.91 23 22.31 23.02 22.55 22.36 22.3 22.58 20.78 19.23 18.53 18.59 18.37 18.83 18.59

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1. Given that organisms size, N, as a function of time can be shown by the equation: N(t)=at/b+t. Determine the time, T, where N(T)= a/2 2. Taylor Series. Taylor is famous for creating polynomial functions that approximate most other functions near some centre point. His polynomials are any degree as needed. Here is the 2nd degree Taylor Polynomial: p(x)=C0+C1(x−a)+C2(x−a)^2 While a 3rd degree polynomial would be: p(x)=C0+C1(x−a)+C2(x−a)^2+C3(x−a)^3 The value a represents the centre point at which the Taylor Series is being modelled around. It is important to note, that the Taylor Polynomial doesn’t approximate the entire function only a section of a function centred at any point a. Further to that, if we change the centre point for the function, we will also have to change the Taylor Series. Let f(x)=cosx a. Find the Linear Approximation of our function near x=0 b. If we know that the 1st Degree Taylor Polynomial is the same as the Linear approximation, then what are the values of C0 and C1 for the Taylor Polynomial of our function f(x) near x=0? c. For higher degree Taylor Polynomials, Taylor proved that p′′(a)=f′′(a) and p′′′(a)=f′′′(a). Use this fact to find the 3rd degree Taylor Polynomial for cosx d. Use the Taylor polynomial to find the value of 1°. How accurate was your approximation? 3. An object thrown follows the following equations of motion (the thrower stands at the origin): x=t−2sintand y=2−2cost,where 0≤t≤12 x represents the distance in meters, y represents the height in meters, t represents the time in seconds. How high does the object fly? At what time is it at its maximum point? How far is the object from the user when it is at its maximum point? 4. A company is hired to make a rectangular container with a square base which will have a volume of 2000cm3. The cost of the material for the bottom and top of the box is twice the cost of the sides of the box. Find the dimensions of the lowest cost container. 5. A security camera spins 360° on a fence top. The camera is mounted to tape any movement along the side of a house. The camera (at its closest point) is 5ft away from the house. If the speed at which the camera sweeps the window 10ft away from the camera is 2ft/sec, at what rate is the camera spinning? Answer in degrees per second.

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拉格朗日函数

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An object thrown follows the following equations of motion (the thrower stands at the origin): x = t − 2 sin t and y = 2 − 2 cos t, where 0 ≤ t ≤ 12 x represents the distance in meters, y represents the height in meters, t represents the time in seconds. How high does the object fly? At what time is it at its maximum point? How far is the object from the user when it is at its maximum point?

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A company is hired to make a rectangular container with a square base which will have a volume of 2000 cm^3. The cost of the material for the bottom and top of the box is twice the cost of the sides of the box. Find the dimensions of the lowest cost container.

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A security camera spins 360° on a fence top. The camera is mounted to tape any movement along the side of a house. The camera (at its closest point) is 5ft away from the house. If the speed at which the camera sweeps the window 10ft away from the camera is 2ft/sec, at what rate is the camera spinning? Answer in degrees per second.

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A company is hired to make a rectangular container with a square base which will have a volume of 2000cm3. The cost of the material for the bottom and top of the box is twice the cost of the sides of the box. Find the dimensions of the lowest cost container.

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"有10棵树种5行,每行4棵,应该怎样种?”以这个问题为主题,写一个500字左右的儿童故事

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tan9度等于多少数值?

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Find arc length of x=y^2 from (0,0) to (1,1)

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两个皮尔逊相关值怎么进行统计差异检验

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高斯定理如何使用

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3*7=?。这道题我不会

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On fait tourner la roue de la loterie ci-dessous. On admet que chaque secteur a autant de chance d'être désigné. On regarde la lettre désignée par la flèche : A, T ou M et on considère les évènements suivants: A: « on gagne un autocollant. » B: « on gagne un tee-shirt. » M: « on gagne un tour de manège. » A 1. Quelle est la probabilité de l'évènement A ? 2. Quelle est la probabilité de l'évènement T? 3. Quelle est la probabilité de l'évènement M ? 4. Exprimer à l'aide d'une phrase ce qu'est l'événement Á puis donner sa probabilité.

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设随机变量X~G(P),试建立并证明E(X)的计算方式

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连续型随机变量X的密度函数f(x)=5/(1+x)^4,x>0,那D(X)等于多少

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随机变量X~G(P),证明E(X)

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Act as a mathematical interlocutor. Good morning. My name is Jaye. I have written a proposal, please review it under rigorous scrutinization. Write ten paragraphs. Focus on the value of my ideas. "Proposal Title: The OrthoSphere Mapping Principle (OSMP) Section A Introduction: In today's data-driven world, the analysis and visualization of high-dimensional data sets have become increasingly important across various domains. The OrthoSphere Mapping Principle (OSMP) is a groundbreaking mathematical concept that aims to address this challenge by providing a novel way to represent and analyze multidimensional data on the surface of a hypersphere. This innovative approach simplifies the visualization and understanding of complex data relationships while streamlining the computation of certain geometric properties. With potential applications in data visualization, dimensionality reduction, clustering analysis, machine learning, and more, the OSMP offers a powerful and versatile tool for researchers and practitioners seeking to unlock the hidden insights within complex data sets. Description: The OrthoSphere Mapping Principle (OSMP) is an original mathematical idea that defines a novel way to represent and analyze multidimensional data sets on the surface of a hypersphere. This representation simplifies the visualization and understanding of complex data relationships, as well as the computation of certain geometric properties. Concept: The OSMP involves mapping points in an n-dimensional space onto the surface of an n-1 dimensional sphere (called an OrthoSphere), such that the orthogonality of vectors representing the points is preserved. The OrthoSphere is embedded in an n-dimensional space to facilitate this process. Method: Given a set of points P = {p1, p2, ..., pn} in an n-dimensional space, compute the orthogonal vectors representing the points relative to the origin O. Normalize each vector to have unit length. These normalized vectors will be the points on the surface of the OrthoSphere. Normalizing the vectors to have unit length ensures that all points on the OrthoSphere's surface are equidistant from its center, thus facilitating a consistent and meaningful representation of the data relationships. Calculate the coordinates of the OrthoSphere's center C by finding the centroid of the normalized vectors in U. Map each point in P onto the surface of the OrthoSphere by connecting the points with a line segment originating from C and extending to the surface of the sphere. Project the points onto the surface of the OrthoSphere by finding the intersections of the line segments with the sphere. Properties: The OSMP preserves orthogonality, ensuring that the angles between vectors representing the points in the original space are maintained on the OrthoSphere. The Euclidean distances between points in the original space are not preserved, but the distances on the OrthoSphere can be used as a proxy to compare the relationships between points. The OSMP allows for a simplified computation of certain geometric properties, such as angles, dot products, and cross products between points in the original space. By leveraging the properties of the OrthoSphere representation, these geometric properties can be calculated on the OrthoSphere with less computational effort, streamlining the analysis of high-dimensional data sets. Applications: Data visualization: The OSMP can be used to visualize complex, multidimensional data sets in a more accessible way. Dimensionality reduction: The OrthoSphere representation can be utilized as a starting point for further dimensionality reduction techniques, such as principal component analysis (PCA) or t-distributed stochastic neighbor embedding (t-SNE). Clustering analysis: The OrthoSphere representation can aid in identifying clusters in high-dimensional data sets. Machine learning: The OSMP can be used to preprocess data for machine learning algorithms, simplifying calculations and improving performance. Further Extension: Spatial organization: By mapping points from an n-dimensional space onto the surface of an n-1 dimensional OrthoSphere, the OSMP provides a more organized and visually comprehensible representation of the data. This spatial organization enables easier identification of patterns and trends in the data. Topology preservation: The OSMP can help preserve the topology of the original dataset while projecting it onto the OrthoSphere. This is important in applications where the structure of the data is critical, such as network analysis, gene expression analysis, and social network analysis. Geodesic distances: The OSMP allows for the computation of geodesic distances between points on the OrthoSphere. These geodesic distances can be used to approximate the original distances in the n-dimensional space, providing a more accurate representation of the relationships between data points. Noise reduction: The OSMP can help filter out noise in the data by mapping the points onto the OrthoSphere. Since the OrthoSphere only preserves orthogonal relationships, noisy data points that do not share orthogonality with other data points will be mapped closer to the center of the sphere, effectively reducing their influence on the overall data structure. Dynamic data analysis: The OSMP can be applied to dynamic data sets where points change over time. By continuously updating the OrthoSphere representation, users can visualize and analyze changes in data relationships over time, facilitating a better understanding of temporal patterns and trends. Parallel computing: Due to the OSMP's ability to simplify computations, it can be efficiently implemented using parallel computing techniques. This can help to speed up the processing and analysis of large-scale, high-dimensional data sets. Robustness to outliers: The OrthoSphere representation is less sensitive to outliers compared to other dimensionality reduction techniques. By preserving orthogonality, the OSMP ensures that extreme data points do not have a disproportionate impact on the overall structure of the data. Graph-based analysis: The OSMP can be combined with graph-based analysis methods to explore the relationships between points in high-dimensional spaces. By representing the data points as nodes and their relationships as edges, complex structures can be identified and analyzed in a more intuitive manner. Embedding quality assessment: The OSMP can be used to assess the quality of embeddings generated by other dimensionality reduction techniques. By comparing the OrthoSphere representation with other embeddings, researchers can evaluate the preservation of orthogonality and overall fidelity of the data representation. Integration with other mathematical frameworks: The OSMP can be integrated with other mathematical frameworks, such as manifolds and topological data analysis, to provide a richer understanding of the structure and relationships within high-dimensional data sets. Spatial indexing: The OSMP can facilitate efficient spatial indexing for high-dimensional data sets. By organizing data points on the OrthoSphere, search algorithms can more effectively query the data and retrieve relevant results in a more efficient manner. In conclusion, the OrthoSphere Mapping Principle (OSMP) is a powerful mathematical concept that can significantly improve the representation, visualization, and analysis of high-dimensional data sets. Its ability to preserve orthogonality, simplify computations, and integrate with other mathematical frameworks and techniques makes it a valuable tool for researchers and practitioners in various fields, including data science, machine learning, and complex systems analysis. (Note: In the context of the OrthoSphere Mapping Principle (OSMP), the term "geodesic distance" plays a crucial role in comparing relationships between points on the OrthoSphere. Geodesic distance refers to the shortest distance between two points on the surface of a curved space, such as the surface of a sphere. In the case of the OSMP, geodesic distances on the OrthoSphere serve as a proxy for the relationships between the original points in the high-dimensional space. While Euclidean distances in the original space are not preserved, the geodesic distances provide a useful and more accessible way to analyze and visualize the complex relationships between data points. By incorporating geodesic distances in the OSMP framework, researchers and practitioners can more effectively explore the structure of high-dimensional data sets and identify patterns, trends, and clusters.) Section B Mathematical Formalization of the OrthoSphere Mapping Principle (OSMP) Let P = {p_1, p_2, ..., p_n} be a set of points in an n-dimensional Euclidean space R^n, where each point p_i = (x_i1, x_i2, ..., x_in) and i = 1, 2, ..., n. Orthogonal Vectors: Compute the orthogonal vectors V = {v_1, v_2, ..., v_n}, where v_i is the orthogonal vector representing the point p_i relative to the origin O. For reference, the origin O is the point (0, 0, ..., 0) in R^n. This can be achieved by subtracting the origin O from each point p_i: v_i = p_i - O Normalization: Normalize each vector v_i ∈ V to have unit length, resulting in the normalized vector set U = {u_1, u_2, ..., u_n}: u_i = v_i / ||v_i||, where ||v_i|| denotes the Euclidean norm of v_i. OrthoSphere Center: Compute the coordinates of the OrthoSphere's center C by finding the centroid of the normalized vectors in U: C = (1/n) * Σ(u_i), where the sum is taken over i = 1, 2, ..., n. By computing the centroid of the normalized vectors, we ensure that the OrthoSphere's center is equidistant from all points on its surface, which facilitates a consistent and meaningful representation of the data relationships. OrthoSphere Radius: Define r as the radius of the OrthoSphere. The radius can be determined based on the desired scale or size of the OrthoSphere representation. Distance Approximation: Although the OSMP does not preserve Euclidean distances between points in the original space, the distances on the OrthoSphere can be used as a proxy to compare the relationships between points. The geodesic distance d_geo(q_i, q_j) between any pair of points (q_i, q_j) on the OrthoSphere can be approximated by the great-circle distance: d_geo(q_i, q_j) = r * arccos(u_i ⋅ u_j) OrthoSphere Mapping: Map each point p_i ∈ P onto the surface of the OrthoSphere with radius r by connecting the points with a line segment originating from C and extending to the surface of the sphere. Let q_i ∈ S denote the mapped point corresponding to p_i. q_i = C + r * u_i Orthogonality Preservation Explanation: The dot product between any pair of points (p_i, p_j) in P is equal to the dot product between the corresponding pair of points (q_i, q_j) in S because the mapping process preserves the angles between the points. Recall that the dot product of two vectors can be expressed as the product of their magnitudes and the cosine of the angle between them. In the OSMP, the vectors are normalized, resulting in unit length for each vector. When mapping the points onto the OrthoSphere, the angle between the points remains unchanged. Therefore, the dot products between the original points in P and their corresponding mapped points in S are equal, ensuring the preservation of orthogonality. Orthogonality Preservation: The OSMP preserves orthogonality, ensuring that the angles between vectors representing the points in the original space are maintained on the OrthoSphere. This can be verified by showing that the dot product between any pair of points (p_i, p_j) in P is equal to the dot product between the corresponding pair of points (q_i, q_j) in S: (p_i - O) ⋅ (p_j - O) = (q_i - C) ⋅ (q_j - C) Distance Approximation: Although the OSMP does not preserve Euclidean distances between points in the original space, the distances on the OrthoSphere can be used as a proxy to compare the relationships between points. The geodesic distance d_geo(q_i, q_j) between any pair of points (q_i, q_j) on the OrthoSphere can be approximated by the great-circle distance: d_geo(q_i, q_j) = r * arccos(u_i ⋅ u_j) Geometric Properties: The OSMP simplifies the computation of geometric properties such as angles, dot products, and cross products between points in the original space, as these can be calculated on the OrthoSphere with less computational effort. For example, the angle θ between any pair of points (p_i, p_j) in P can be computed as: θ = arccos((p_i - O) ⋅ (p_j - O) / (||p_i - O|| * ||p_j - O||)) This can be simplified using the normalized vectors u_i and u_j: θ = arccos(u_i ⋅ u_j) Similarly, the OSMP simplifies the computation of cross products between vectors in the original space. In the n-dimensional space, calculating the cross product can be computationally expensive, particularly as the dimensionality increases. However, using the OrthoSphere representation, the cross product between any pair of points (p_i, p_j) in P can be computed using the corresponding normalized vectors (u_i, u_j) on the surface of the OrthoSphere. This approach reduces the computational complexity, as the cross product calculation is performed using unit vectors in a lower-dimensional space. By leveraging the properties of the OrthoSphere representation, the OSMP can efficiently compute various geometric properties, streamlining the analysis of high-dimensional data sets. In summary, the OrthoSphere Mapping Principle (OSMP) can be mathematically formalized, providing a novel representation and analysis method for multidimensional data sets. By preserving orthogonality, simplifying computations, and enabling easier visualization, the OSMP has the potential to enhance a variety of applications in data science, machine learning, and complex systems analysis. Its mathematical foundation provides a solid basis for further development and exploration of its properties and capabilities, enabling researchers and practitioners to better understand and exploit the relationships within high-dimensional data sets. With the potential for integration with other mathematical frameworks and techniques, the OSMP offers a versatile and powerful tool for tackling the challenges associated with analyzing and representing complex data structures. Section C References and Citations In this section, I have compiled a list of relevant references and citations that support my claims and enhance the credibility of my proposal: Beyer, K., Goldstein, J., Ramakrishnan, R., & Shaft, U. (1999). When Is "Nearest Neighbor" Meaningful? In Proceedings of the 7th International Conference on Database Theory (pp. 217-235). Springer, Berlin, Heidelberg. Lee, J. A., & Verleysen, M. (2010). Nonlinear Dimensionality Reduction. Springer Science & Business Media. Tenenbaum, J. B., de Silva, V., & Langford, J. C. (2000). A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science, 290(5500), 2319-2323. Belkin, M., & Niyogi, P. (2003). Laplacian Eigenmaps for Dimensionality Reduction and Data Representation. Neural Computation, 15(6), 1373-1396. Maaten, L. v. d., & Hinton, G. (2008). Visualizing Data Using t-SNE. Journal of Machine Learning Research, 9(Nov), 2579-2605. Jolliffe, I. T. (2002). Principal Component Analysis. Springer-Verlag New York. Carlsson, G. (2009). Topology and Data. Bulletin of the American Mathematical Society, 46(2), 255-308. Blondel, V. D., Guillaume, J. L., Lambiotte, R., & Lefebvre, E. (2008). Fast Unfolding of Communities in Large Networks. Journal of Statistical Mechanics: Theory and Experiment, 2008(10), P10008. Samet, H. (2006). Foundations of Multidimensional and Metric Data Structures. Elsevier."

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Using the digits 0,1,2,3,4,5,6,7,8,9 a) write a two digit number with rotational symmetry of order 2. b) a three-digit number with rotational symmetry of order 2.

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what is f(x) = 3/2x

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If a given problem is computationally irreducible, does that imply that it isn't explainable at a higher level of abstraction?

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When the first worker completed half of the work, then she replaced the second worker and he completed the other half of the work. The work was completed in 25 days. In how many days would the first worker complete the work? second worker?

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How do I find the interquartile range in a histogram?

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A die used in a certain board game has eight faces, of which 3 are red, 3 are yellow, and 2 are blue. Each face is equally likely to land faceup when the die is tossed. In the game, a player tosses the die until blue lands faceup, and the number of tosses before blue lands faceup is counted. What is the probability that a player will toss the die at least 2 times before blue lands faceup? Use methods taught in AP Statistics.

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投硬币25次,至少15次正面向上的概率是?

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pretend you’re the best mathematics Author in the world who can simplify research topics and make it accessible to school students without losing mathematical depth and rigor, also you’re amazing at reasoning and convincing every word you say. your books can make a layman reach PhD level without difficulty by just reading one of your books! write a table of contents about probabilistic deep learning.

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计算一下Σ(k=6 to 8) [C(8,k)×(p^k)×((1-p)^(8-k))]的结果,注意p=0.4,不是0.5

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Сколько времени понадобиться ракете, летящей со скоростью 12 000 км/ч, чтобы преодолеть расстояние в 300 км, 750 км и 1000 км?

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Trong mặt phẳng xOy, cho 2 tia OA và OB hợp với Ox, Oy lần lượt 90 và 180o. Tìm phương trình đường phân giác của góc AOB

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f(x) = 3/x-4/sqrt(x); find f'(x)

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f(x) = 3/x-4/sqrt(x); find f’(x)

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Дано: а||b, с — секущая, ∠1 + ∠2 = 102° (рис. 3.171). Найти: Все образовавшиеся углы.

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У вас есть две стопки книг одинаковой высоты. Одна стопка состоит из 8 томов "Война и мир", а другая стопка состоит из 8 томов "Анна Каренина". В каждом томе ровно 500 страниц. Вы взяли одну страницу из каждого тома и сложили их вместе. Какая из сумм будет больше: сумма страниц из "Войны и мира" или сумма страниц из "Анны Карениной"?

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Pretend to be mathematics professor who never give direct explanation and never makes things clear such that students always feel uncomfortable. Explain support vector machines

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Without doing any calculations, compare Expression A to Expression B. A (34 + 25) ÷ 14 B 34 + 25 Which statement is true?

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同级运算为什么要从左往右?

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Given a set with natural numbers that can be defined with less than 100 words. There must be a smallest natural number not in the set, but I just defined it in less than 100 words.

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Given a set containing all natural numbers that can be defined with less than 100 words. There must be a smallest natural number not in the set, but I just defined it in less than 100 words.

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What is the easiest and fastest way to answer the following question? Note that I have to answer each question in 20 seconds in an mcq exam. Also, I don't understand the concept of derivatives. At the end, 1. Solve the question with steps. 2. Use the technique that outputs 80% of efficiency with 20% of the effort to suggest me the formulas and methods I need to know to solve similar questions. 3. Explain both the question and the answer like I am 10 years old. The question: A rectilinear motion is represented by a time law that has the shape of a branch of a parabola with upward concavity. Such a clockwise law describes: A. a motion with uniformly increasing acceleration B. a motion with constant velocity C. a motion with positive velocity D. a motion with positive displacement E. a motion with constant acceleration

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有理数和无理数

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differentiate 5x^0.2

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1. f(x) = 6 – 5x – x2 a. Find f '(x), the gradient function. b. Solve f '(x) > 0 to find where f(x) is an increasing function.

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Clock A is five minutes ahead of Clock B. It's 5:34 PM on Clock A now. What time is it on Clock B?

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has someone asked you to differentiate f(x) = 6 – 5x – x2

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Clock A is five minutes ahead of Clock B. It's 5:34 PM on Clock B now. What time is it on Clock A?

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There are 5 clocks in my house. How can I decide which clock is most likely to be closest to the true time without consulting anything else? Work through this step by step.

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我闲着无聊,给我出一道高中数学题,我来解答,你再来看是否正确

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Determine the optimal number of odd or prime number of chainring and rear sprocket teeth in track and fixed gear cycling.

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give me a simple explanation on the difference between circumcenter and orthocenter

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线性空间一般怎么翻译

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毕达哥拉斯定理是如何被证明的

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某地在某日的温度记录如下,共有24个数据点。 时间,p.m. 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24午夜 温度 66 66 65 64 63 63 62 61 60 60 59 58 时间,a.m. 1 2 3 4 5 6 7 8 9 10 11 正午 温度 58 58 58 58 57 57 57 58 60 64 67 68 寻找上表的3次多项式最小二乘曲线并画图。 请用python语言实现

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MITopencourseware上哪节课专门针对无穷级数,我知道18.01中有一小部分提到过,请问还有其他的吗

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Determine the optimum odd or prime number of teeth in the chainring and rear sprocket of a track and fixed gear bicycle.

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高中数学期末老师汇报,汇报什么

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In a hypothesis test, it is irrelevant whether the test is a one-tail or two-tail test. Select one: True False

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Bir yazı-tura deneyinde para üç kez atılmaktadır. Örnek uzay S = {TTT, TTY, TYT, YTT, YYT, YTY, TYY, YYY} şeklindedir. X, tura sayısını gösteren bir rastlantı değişkeni olsun. X rastlantı değişkeninin olasılık kütle fonksiyonunu bulunuz.

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bacteria multiply in a cup. each hour the number of bacteria triples, and it takes seven hours for bacteria to fill the cup. how many hours does it take to fill one ninth of the cup?

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Calculate the optimum odd or prime number of teeth in the chainring and rear sprocket of a track and fixed gear bicycle.

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x,y sa liczbami wymiernymi, i zachodzi równosc x^5+y^5=2x^2y^2, udowodnij że 1-xy jest kwadratem liczby wymiernej

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H= Friction loss x( L/D ) X v2 /2g make it in formula so that i can copy paste in word format

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Liczby wymierne x, y spełniają warunek: x^5 + y^5 = 2x^2*y^2 . Udowodnij, że 1 − xy jest kwadratem liczby wymiernej.

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Darcy–Weisbach equation

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Ciao. Mi dimostri che i numeri primi sono infiniti?

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Qs = 1.08 x CFM x ∆T

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Calculate the optimum gear ratio using an odd or prime number of teeth in the chainring and rear sprocket of a track and fixed gear bicycle.

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explain in detail : Optimization problems in standard form An optimization problem in the standard form is written as min x∈Rn f0(x) subject to fi(x) ≤ 0 i = 1, . . . , m (11.1) hj (x) = 0 j = 1, . . . , p where the domain of the problem is defined to be the intersection of domain of the objective function with the domains of all the constraint functions and is assumed nonempty. Formally, the domain of the problem (11.1), D := dom(f0) ∩ ∩m i=1dom(fi) ∩ ∩p j=1dom(hj ) 6= ∅ The feasible set of optimization variables in problem (11.1) is given by, F := {x ∈ D : for every i = 1, . . . , m, fi(x) ≤ 0; and for every j = 1, . . . , p hj (x) = 0} A convex optimization problem in the standard form is written as min x∈Rn f0(x) subject to fi(x) ≤ 0 i = 1, . . . , m (11.2) hj (x) = haj , xi − bj = 0 j = 1, . . . , p where the objective f0 and all the inequality constraint functions fj for j = 1, . . . , p are convex. In a convex problem, dom(hj ) = R n for every j = 1, . . . , p. So the problem domain D = dom(f0) ∩ ∩n i=1dom(fi) of (11.11) is a convex set. The feasible set of optimization variables in problem (11.2) is the intersection of the prob- lem domain with m sublevel sets of convex inequality constraint functions, and p hyper- planes F := D ∩ ∩m i=1S0(fi) ∩ p j=1 H(aj , bj ) As a finite intersection of convex sets, the feasible set F of a convex problem is a convex set.

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напиши формулу где [1] является входом z в сфере, а выходом является то же самое значение но чем ближе к полюсам сферы тем больше значение

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напиши формулу для нахождения длины куба по объёму и плотности

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lets continue this past conversation, here I provide the past context : lets continue this past conversation. and here I provide the past context: “pretend you’re the best mathematics Author in the world who can simplify research topics and make it accessible to school students without losing mathematical depth and rigor, also you’re amazing at reasoning and convincing every word you say. your books can make a layman reach PhD level without difficulty by just reading one of your books! write a table of contents about probabilistic deep learning. “ ” Title: Mastering Probabilistic Deep Learning: From Basics to Brilliance Table of Contents: Chapter 1: Introduction to Probabilistic Deep Learning 1.1 The World of Uncertainty: Embracing Probabilistic Models 1.2 Deep Learning: From Deterministic to Probabilistic 1.3 Why Probabilistic Deep Learning Matters: Real-world Applications 1.4 Roadmap to Brilliance: Our Learning Journey in this Book Chapter 2: Building a Solid Foundation 2.1 The Beautiful World of Probability Theory 2.2 The Language of Probability: Random Variables and Distributions 2.3 The Building Blocks of Deep Learning: Neural Networks, Gradient Descent and Backpropagation 2.4 Connection Between Probability Theory and Deep Learning: Bayesian Approaches Chapter 3: Creating Your First Probabilistic Neural Network 3.1 Setting the Stage: Data Representation and Preprocessing 3.2 Uncertainty in Neural Networks: Types and Sources 3.3 Probabilistic Activation Functions: Bringing Probability to Life 3.4 Training Your Probabilistic Neural Network: A Guided Example Chapter 4: Bayesian Neural Networks: Revealing the Magic 4.1 Understanding Bayesian Inference: The Heart of Bayesian Neural Networks 4.2 The Bayesian Approach to Weights and Biases: Uncertainty Exploration 4.3 Training Bayesian Neural Networks: Practical Techniques 4.4 Hyperparameters: Balancing Complexity and Simplicity Chapter 5: Generative Models: Painting the World with Probability 5.1 The Idea behind Generative Models: Creating New Data Instances 5.2 Variational Autoencoders: Unleashing the Power of Latent Spaces 5.3 Generative Adversarial Networks: The Art of Forging Reality 5.4 Advanced Generative Models: Exploring the Probabilistic Frontier Chapter 6: Probabilistic Deep Reinforcement Learning: Mastering the Unknown 6.1 Reinforcement Learning: Solving the Puzzle of Decision Making 6.2 Uncertainty and Exploration: Navigating the World of Rewards 6.3 Bayesian Deep Q-Networks: Uncertainty-Based Exploration 6.4 Advanced Probabilistic Reinforcement Learning Techniques: Path to AI Dominance Chapter 7: Real-world Applications: Solving Practical Problems 7.1 Probabilistic Deep Learning for Computer Vision: Image Segmentation and Object Detection 7.2 Natural Language Processing: Sentiment Analysis and Machine Translation 7.3 Robotics and Control Systems: Autonomous Navigation and Decision Making 7.4 Healthcare and Life Sciences: Diagnostics, Drug Discovery, and Personalized Medicine Chapter 8: The Future of Probabilistic Deep Learning 8.1 The Intersection of Probabilistic Deep Learning and Quantum Computing 8.2 Ethical Considerations and the Responsible Use of Probabilistic Deep Learning 8.3 Continuous Learning and Adaptation: Lifelong Learning Machines 8.4 Final Thoughts and Inspiration for Your Future Innovations Appendix A: Python Libraries and Useful Resources for Probabilistic Deep Learning Appendix B: Mathematical Proofs and Derivations: Building Rigor and Confidence Appendix C: Glossary of Key Terms and Concepts” ” “Ok professor, we gonna write “2.4 Connection Between Probability Theory and Deep Learning: Bayesian Approaches” together but first split it into ideas so that we can write every part in different answer separately, but make this ideas very descriptive so that if the conversation get lengthy I can remind you with your descriptive words so you continue without the need to get back to a conversation context.” “Sure, let’s split the section “2.4 Connection Between Probability Theory and Deep Learning: Bayesian Approaches” into several descriptive idea parts: 1. Bridging the Gap: Understanding the Link Between Probability Theory and Deep Learning - This part will discuss the underlying similarities between probability theory and deep learning, including their common goals and techniques. 2. Bayesian Approach: Uncovering the Principles Behind Bayesian Methods - Here, we will explain the fundamental concepts of Bayesian methods such as Bayes’ theorem, Bayesian inference, and the benefits of adopting Bayesian approaches in deep learning. 3. Quantifying Uncertainty: Incorporating Probability Distributions in Neural Networks - This part will delve into the use of probability distributions to represent weights, biases, and other elements in neural networks, explaining how this enables us to quantify and model uncertainty. 4. Bayesian Inference for Model Training: A New Perspective in Learning - We will discuss how Bayesian methods are applied for training deep learning models, focusing on the concepts of likelihood, prior distributions, and posterior distributions, as well as the advantages of using Bayesian inference for training. 5. Regularization and Model Complexity: The Bayesian Interpretation - This part will discuss regularization techniques in deep learning, such as L1 and L2 regularization, from a Bayesian perspective, as well as the connection between priors and model complexity. 6. Bayesian Model Selection: Choosing the Best Model for the Task - Lastly, we will explore Bayesian model selection techniques to compare and choose between different deep learning models, taking into account their trade-offs between accuracy and complexity. After these ideas are outlined, we can begin drafting each part in more depth.” Ok professor, break the part"Bridging the Gap: Understanding the Link Between Probability Theory and Deep Learning." Into ideas as the above answer but make it irreducible ideas so that we start writing immediately from it immediately without the need to decompose it into more branches again.

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J’ai tracé la courbe de tendance et obtenu l’équation de la droite : “sigma = a*C+b”. Est-ce la valeur de “a” qui est celle de la CMC ?

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qt=q0*(1-m)^t +qm*(1-(1-m)^t) solve for m

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设均匀立体Ω={(x,y,z)| x ^ { 2 } +y ^ {2 }≤z≤1},求Ω的质心

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Volume of a Prism Video 356 on www.corbettmaths.com The solid triangular prism shown below is made from metal. The prism is melted down and the metal is used to create a solid cube. Find the side length of the cube. The swimming pool in a leisure centre is shown below. The length of the swimming pool is 25m and the width is 12m. The depth of the shallow end is 1m and the depth of the deep end is 2.4m. Given 1m3 = 1000 litres Work out how much water, in litres, the swimming pool holds.

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Podaj wzór na pole stożka

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一个骗子到商店买了5元的东西,他付给店员50元钱,然后店员把剩下的钱找给了他;这时他又说自己有零钱,于是给店员5元的零钱,并且要回了开始给出的50元,请问:这个骗子一共骗了多少钱?

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Sketch a graph of a function f(x) that: • is continuous for 0 < x < 5 and 5 < x < 9 and is discontinuous when x = 5 • is concave down for 0 < x < 5 • has f '(x) = 0 at (3, 8) • has lim x 5 f(x) = 6 • is not differentiable at (7, 3)

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pretend you are the perfect professor of mathematics and data science, and explain at length the "Prognostics Analytics" to a high school level student. Your explanation must make the high school student becomes a master "Prognostics Analytics"

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Given the address 172.16.200.111 and the default class A mask, find the beginning address (network address).

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Pretend you're Richard Faynman, What is complex numbers intuition? Why it became this way

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x+y+z=1 x+y-2z=3 2x+y+z=2 solve it by gauss elimination method

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1+1 =

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Studies show that two plus two is five 🗿

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倍数和公倍数的区别,因数和公因数的区别?

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LU Factorization of [[1,-2,3],[0,1,-2],[-3,0,1]] explained step by step

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On se place dans le cas où les droites ne sont ni parallèles à l'axe des abscisses et ni parallèles à l'axe des ordonnées. On considère la droite (d) d'équation ax + by + c = O (avec a et b non nuls). Donner l'expression de y en fonction de x.

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what are the steps for determining if there is a linear relationship between two variables?

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Evaluate the optimal odd or prime number of teeth in a chainring and rear sprocket for professional track and fixed gear cycling.

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Giải phương trình sau bằng phương pháp lặp đơn với độ chính xác 10^{-5}, f(x)=x^3-4*x-1=0 trong khoảng [0, 1]

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Giải phương trình sau bằng phương pháp lặp đơn với độ chính xác 10^(-5), f(x)=x^3-4*x-1=0 trong khoảng [0, 1].

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Giải phương trình sau bằng phương pháp lặp đơn với độ chính xác 10^(-5), f(x)= x^3 - 4*x - 1 = 0 trong khoảng [0, 1].

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Random sample of 10 has the following values: 3.6, 4.5, 2.8, 6.3, 2.6, 5.2, 6.75, 4.25, 8, 3. Find the 95% confidence interval for the true mean.

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Cách giải phương trình bằng phương pháp lặp đơn với độ chính xác cho trước, f(x) trong khoảng [0, 1].

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Suppose that you have a Θ(nα) -time algorithm for squaring n×n matrices, where α≥2 . Show how to use that algorithm to multiply two different n×n matrices in Θ(nα) time.

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15 reps of 90kg weighted squats is equivalent to how many bodyweight(70kg) squats

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The swimming pool in a leisure centre is shown below. The length of the swimming pool is 25m and the width is 12m. The depth of the shallow end is 1m and the depth of the deep end is 2.4m. Given 1m3 = 1000 litres Work out how much water, in litres, the swimming pool holds.

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what is the maximum volume of a cylinder that can be inscribed in a cone with an altitude of 15cm and a base radius of 3cm? a. pi, b. 2pi, c. 4pi, d. 20pi

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What is the square root of 3 pieces of meat?

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五年级下册日记200字女生数学考试(第七单元长方体和正方体)

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В магазине продаётся три вида чашек и два вида блюдец. Сколькими способами можно купить чашку с блюдцем?

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