Problems 5-6: Find the derivative of the function at the given point in the direction of A. ( 5) f(x, y, z) = -2x - 7y + 8z, (-9, -8,5), A = 3i - 6j - 2k

Q: (a) It is a fact that 14 is a primitive root mod 29 and that 1428 = 1 mod 29². Use this information…

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Q: A computer shop charges Php 15.00 per hour (or fraction of an hour) for the first 2 hours and an…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: (8) Let P = "(Vx ≤ R)(Jy ≤ R) (x + y > 0)”. Let Q = "(Vx € R) (Vy € R) [(xy > x) ✓ (xy < xy <y)]”.…

A: 8. (a)  P is true.   If  x &gt;=0, then for any y&gt;0, the statement P is true. If x&lt;0, then…

Q: c) What is the actual revenue of the 250 000th CD player sold? (between 250000 and 250001) d) What…

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Q: y (5) +y (4)-y'-y=0, y (0)=0, y'(0)=0, y" (0)=1, y 3) (0) =0, y (4) (0)=0

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Q: Exercise 3.3.20. Let A and B be sets. Suppose that BCA. Prove that AxA-BxB = [(A-B) XA]U[AX (A -…

A: We have B⊆A  first we prove that  AxA-BxB⊆  [Ax(A-B)]∪[(A-B)xA]   Then we prove that  AxA-BxB ⊇…

Q: The temperature at a point (x, y) on a flat metal plate is given by T(x, y) = 96/(2 + x2 + y2),…

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Q: Find the inverse of the matrix A = [1 2 1 310 1 1 2

A: To find the inverse matrix, augment it with the identity matrix and perform row operations trying to…

Q: Use the EXTENDED EUCLIDEAN ALGORITHM to compute the following mul- tiplicative inverses: (a) 17-¹…

A: The extended Euclidean algorithm is an algorithm to compute the integers x and y such that for given…

Q: What is 5/6 % of 600

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Q: Evaluate the Riemann sum for f(x) = 3x - 1,-6 ≤ x ≤ 4, with five subintervals, taking the sample…

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Q: Find the imaginary component if the complex number a + bi is raised to m if a = 4, b = 3, and m =…

A: a = 4, b = 3 =&gt; a + bi = 4 + 3i m = 9 =&gt; (a + bi)m = (4 + 3i)9                            = (4…

Q: K P n [9] card has a balance of $5400 and an annual interest rate of 12%. You decide to pay off the…

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Q: 6. In a survey of 200 students, 100 joined the Math Club, 150 joined the Tennis Club and 140 joined…

A: A Venn diagram is a pictorial representation of the data to make it easier to understand the data.…

Q: Prove that n n=1 does not converge by comparing 2-1 Σ n=2(2k-1) to 2-1 1 n

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Q: = . Find an equation of the tangent plane to the parametric surface R(u, v) 0≤u≤, at the point…

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Q: Consider the second-order differential equation d²x dx + a dt² dt + b²x = 0 (a, b positive real…

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Q: Faith observed that her product sales in a certain town is given by the function of M(u, v) = u²v²…

A: The given function is M(u,v)=u2v2 for (u,v)∈ℝ. The given region is bounded by lines passing through…

Q: a) Find the smallest positive integer a in the encryption function f(x) = (ax + 7) mod 26,0 ≤ x ≤…

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Q: Suppose ne Z. If n is odd, then n² is odd. Suppose ne Z. If n² is odd, then n is odd. Prove that 2…

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Q: Solve the equation: Solve the equation: Solve the equation: Solve the equation: Solve the equation:…

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Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

A: Using cylindrical shells method volume is 1152pi/7

Q: (b) Let Q = "There is an integer m so that for any integer n, n. m is even." Write Q using logical…

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Q: (1 point) Find the general solution, y(t), which solves the problem below, by the method of…

A: The given differential equation is 7tdydt+y=t3 It can be written as in the form of dydt+17ty=t27,…

Q: y"+y'-y = 0

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Q: .) 2xy dx + (x²-₁) dy = =0 4.) (x² + y2) dx + (x²-xx) dy

A: Separable of Variables: Let a differential equation can be written in the form:…

Q: A population of animals follows the following gompertz differential equation: dP = dt 4P(17-In P).…

A: We have given a gompertz differential equation, dpdt=4P17-lnP) , P0=100 We need to find what is the…

Q: 10. Suppose x, y, ze Z and x #0. If xyz, then xty and xtz. 11. Suppose x,y e Z. If x²(y + 3) is…

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Q: Let G = &lt;a, b | a6 = b3 = e, b-1ab = a3&gt;. How many elements doesG have? To what familiar group…

A: Given set is G = &lt;a, b | a^6 = b^3 = e, b^-1ab = a^3&gt;.

Q: D 8 rall E E El [9 Mohamed is 23, and is starting to save for retirement. They want to have…

A: Please find the answer innext step. Though it exceeds more than three  subparts, we have solved…

Q: Show that the spiral r = 1/θ² does not have any horizontal asymptotes.

A: We have to show that the spiral r=1θ2 does not have any horizontal asymptotes.

Q: 8) J+D Advertising has 750 employee. There are two large banks in the area Bank of Tobas and First…

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Q: 7.(a) Let X = {z € C: 0 < Arg(z) < π/3} and let ƒ: X → C be the function defined on X by f(z) = 2³.…

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Q: Glucose Concentration When glucose is infused into a per- son's bloodstream at a constant rate of c…

A: The amount of glucose present in the bloodstream at time t is g(t)=ca+g0-cae-at where here g0=0.08,…

Q: Find the value of an income stream after 19 years if R(t) = 7000e0.03t is the rate of flow of…

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Q: Use spherical coordinates. Evaluate III. (x² + y2) dv, where E lies between the spheres x² + y² + z²…

A: Evaluate the triple integrals conversion yo spherical co-ordinates

Q: 3. Use the method of Lagrange multipliers to find the point/s on the parabola y = 3x² that is/are…

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Q: D E F e.e/² sin(x). ¹/2 cos(x) e, e 2 If y (0)=0, y '(0) = 1, y "(0) = -1 -2 √3 then y=(-²) e (~/2)…

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Q: Hint(s) Check my work The Wall Street Journal reported that 33% of taxpayers with adjusted gross…

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Q: Let F be any field. Show that the transformation that maps (x, y, z) onto (z, -x, y) is a…

A: Given: The transformation that maps x,y,z onto z,-x,y and also the standard basis is…

Q: Find a vector x whose image under T, defined by T(x) = Ax, is b, and determine whether x is unique.…

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Q: Given the following payoff table where each payoff represents loss and that d3 is chosen and $₁…

A: From the given payoff table , we have to find the regret for choosing d3 .

Q: y' = y² - 3y + 2

A: According to the guidelines, we have to solve only the first question, rest of the question should…

Q: 2. Let x and y be vectors in R³. Prove that y=(|x +ỷ1² − |x|² − |ÿ1²): a) Using a geometric…

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Q: List the first four elements of the set { x | x = 4k + 1, and k is a natural number}  (List each…

A: Given set { x | x = 4k + 1, and k is a natural number} = {4×1+1, 4×2+1, 4×3+1, 4×4+1, ... } = {5, 9,…

Q: 6. [ACS] For each of the following regions X CC, determine whether it is (i) open, and/or (ii)…

A: As per guidelines, I can do only three subparts of a question.

Q: e.) Generalize your findings and extend them to sum, difference, product, and scalar product of…

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Q: Prove the argument by contraposition. For any integer n, if n² is odd then n is odd.

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Q: D. I. x LPU G. Which of the following representations below is a function? Select all possible…

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Q: Let G = &lt;z | z6 = 1l and H = &lt;x, y | x2 = y3 =1, xy =yx&gt;. Showthat G and H are isomorphic.

A: Given :  G = z : z6 = 1 and  H = x, y : x2 = y3 = 1, xy = yx To show : G and H are isomorphic.