Ex: The average daytime temperature of a city is given by function D(t) = 5cos(301) 20⁰ where t is the time in months after January. a) Sketch the graph of D against t for Osts24 b) Find the average daytime temperature during May. c) Find the minimum average daytime temperature, and the month in which it occurs.

Q: Find a unit normal vector of the surface at the given point P. x² + y² = 25, P: (4, 3,6)

A: The equation is x2+y2=25 and the point is P4, 3, 6. Now, the unit normal vector is n^=∇ϕ∇ϕ. Now, for…

Q: Using Reduction of Order: (D2-1)y = 2e2x

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Q: Compute the integral $12)=3/2 (2¹0 + 1)(2+2+1) (z¹2 i) dz

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Q: F.3

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Q: 1) Definitions. The graph below shows 5 cities. The weights on the edges represent the airfare for a…

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Q: Consider the first order separable equation y = y(y - 1) An implicit general solution can be written…

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Q: A mathematical model is a simplified description of a system or a process. In your opinion, how are…

A: The advantages of using a model are familiar objects to represent unfamiliar things, can help you…

Q: ∑ sin2(3n+2) / (2n2-3) ii. ∑ 1 / (n - 2π) iii. ∑ (n + 1) / (n3 + 2)

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Q: 2. Draw the complete shear and bending moment diagrams. A -1 m- 800 N 1200 N·m -1 m. -1 m- 600 N -1…

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Q: From the list below select ALL properties of the given function f. f: Z→Z, f(n) = [n+1] f is not a…

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Q: 1) A particle moves in a velocity field (²xy + 10, x²) starting from point (0, 1) at t = 1. Where…

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Q: + tany)dx + xsec³ydy 4) Evaluate (¹ Y=X²-1 from (1,0) to (2, 3) where C is the curve

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Q: Use Adams predictor-corrector system with h-0.25 to solve the initial value problem y'=(x+y)²,…

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Q: ' // F F. ds for the given vector field F and the oriented surface S. In other words, find the flux…

A: The given problem is to evaluate the given surface integral over the surface S is the part of the…

Q: Let R be the relation defined on P({1,..., 100}) by ARB if and only if An B is even. Is R reflexive?…

A: Given: R is the relation defined on P1,....,100 by A R B.           A∩B is even.We need to check…

Q: Minimize z = 3x + 4y subject to the constraints   3x - 4y ≤ 12, x + 2y ≥ 4   x ≥ 1, y ≥ 0.

A: Solution :- While solving problems , it is considered as x=x1 & y = x2 Problem is Max Z =…

Q: For each of the following series, determine whether the series converges or diverges. (Sum from 1 to…

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Q: Consider the fitness function: w = 7a + 3bc-d a 1 1 1 1 1 1 1 • b 1 0 0 0 1 0 1 C d 0 1 1 0 0 0 1 1…

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Q: Evaluate the surface integral x² + z² JJs S Y where S is the surface represented by r(u, v) = (2 cos…

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Q: Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed, and…

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Q: Let F = te [₁ Use Stokes' Theorem to evaluate F.dr, where C is the curve of intersection of the…

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Q: Find an orthogonal basis for the column space of the matrix to the right. An orthogonal basis for…

A: The given problem is to find the orthogonal basis for the column space of the given matrix.

Q: Find the solution of the given Differential Equation: y" - y - 2y = sin 2x

A: Given: y''-y'-2y=sin2x We have to solve the given differential equation.

Q: 13. Find the line pass through two points (1, 2, 3) and (1,0, -1). You should list three different…

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Q: Determine whether the linear transformation T is one-to-one and whether it maps as specified. Let T…

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Q: Evaluate the integral (curl F). n dA directly for = [e²z, e² sin y, e² cos y], S: z = y²(0 ≤ x ≤ 4,0…

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Q: Let T : R³ → R³ by the linear transformation that projects u onto ʊ = (−1, 3, 1, 1, 2). (a) Find the…

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Q: y (0) 2,y'(0) = 2 2. Find the general solution using VARIATION OF PARAMETERS: 3. Solve Ax = x'…

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Q: Using the hypothesis method, Solve the following equation: 2 (D²₁ (D³²-1) Y = x ²

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Q: Find formulas for the voltages x, and x2 (as functions of time t) for the following circuit…

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Q: Five different digits from the set of numbers (1,2,3,4,5, 6, 7}) are written in random order. Find…

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Q: Find the directional derivatives of the convex function f(x) = max{−5x + 3, 2x + 1}.

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Q: A professor had students keep track of their social interactions for a week. The number of social…

A: Statistics is the branch of mathematics which are dealing with the collection of data,…

Q: 8) Consider the following set of data: 13 7 19 4 46 25 45 14 b) Construct a Frequency Table. c)…

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Q: 10) Consider the following election with five candidates and 21 voters. a) Use the Hare System to…

A: Hare System: Firstly find the majority and tally the 1st place votes. The candidate is declared a…

Q: Σ1 (3)* (?)² i=1 ►Give a combinatorial proof of the following identity (3η) = (²n) HINT: Remember…

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Q: For each series, determine whether it converges absolutely, converges conditionally, or diverges. ∞…

A: Test for absolute converges

Q: y= Σ Use power series to solve the initial-value problem x + Σ Note: You can earn partial credit on…

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Q: · Let S : RCUN) = < u² Losv, u²³-4, 4²-sinv), (u₁v) & [13] x [2₁4] Evamate : do (y+4)³2 SS S

A: Note: For r→(u,v)=&lt;x(u,v), y(u,v), z(u,v)&gt; , take dσ=||ru→×rv|→|dA

Q: A linear spline is fit to the following points is (-2,2), (1,-1), (3,1), (5,-3) and (7.1). What's…

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Q: = areas and a fost de and to the ai i te S [0, 3] × [0, 2]. Evaluate

A: To Evaluate: ∬Sx2zdS, where S is the part of the plane z=3+x+2y above the rectangle 0,3×0,2.

Q: Consider the following matrix: 1 -6 -6 -6 -4 -2 -2 8 -60 0 12 -1 -3 -3 0 A = a) Find the distinct…

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Q: 6. [2] A manufacturer guarantees a product for 1 year. The lifespan of the product after it is sold…

A: Given Data: Let us consider the probability function is given by: ft=0.01e-0.012t,t≥00,otherwise (a)…

Q: Find the equation of osculating sphere and osculating circle at the point (1, 2, 3) on the curve x =…

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Q: 2. The function g is defined by g(x) = ï eªª, where a is a positive real number. (a) What is the…

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Q: Problem: Using the language of differential forms, find the value of the integral of the vector…

A: Here, we need to find the integral of the vector field          A=2+z2∂x+y2∂y+2xz∂z along the curve…

Q: If the statement is true, write a complete step-by-step proof of the state- ment. If the statement…

A: We now check whether the given statement is true or false.

Q: Let a be an element of a group G such that o(a) = r. Let m be a positive integer such that (m,r) =…

A: a∈GOa=rgcdm,r=1 We have to prove Oam=r

Q: The differential equation for which the method of undetermined coefficients can not be used to find…

A: The method of undetermined coefficients can be used only for the non-linear terms involving…

Q: (a) Use Desmos to draw the graph x(t) = cost, y(t) = sin³t for −ñ ≤ t ≤π. (b) Find the area of the…

A: To Find : a) Use desmos to draw the graph xt=cost , yt=sin3t  for -π≤t≤π. b) Area of the bounded…