1. What is the slope of the line in the graph below? Show your work.

Q: If (x + iy)³ = u + iv, then show that И V ---- + w y = (x² - y²).

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Q: Consumers' Surplus The demand function for a certain brand of mattress is given by P = 400e-0.08x…

A: Given the demand function for a certain brand of mattress is given by…

Q: d) real numbers x, y s.t. there exist two disjoint neighborhoods of these numbers.

A: (d) For x,y any two elements.  To Prove or disprove: there exists two disjoint neighborhoods of…

Q: Let F(x, y, z) = (y² cos z, 2xy cos z, – xy² sin z) and C₁ : R(t) = (t², sint, t), t = [0, Evaluate…

A: The given vector function is, F(x,y,z)=y2cosz,2xycosz,-xy2sinz, the curve is: C1: R(t)=t2,sint,t,…

Q: Show that (cos+ i sin 0)" = cos no + i sin ne for 0 € R and n € Z.

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Q: How do you find the radius of convergence of a power series ∞ Σen n=0 cn (x − a)"?

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Q: f (x) = 6x6 + 13x5 + 3x4 − 2x3 − 30x2 − 56x − 24. (a) Use the Rational Zeros/Roots Test to list all…

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Q: Use Stokes' Theorem to evaluate (integral) F (dot) dr. C is oriented counterclockwise as viewd from…

A: here we will use stokes theorem for any vector field F  ∫CF.dr=∫∫S curlF dS where C is a positively…

Q: 120 students are signing up for classes. 80 of them are signing up for a Math class (M) and 50 of…

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Q: Estimate the slope of the tangent line to the curve at the given point (-5.5,4.911) on the graph to…

A: Given Point P(x, y) = (-5.5, 4.911) The slope of a line passing through points  ( x 1 , y 1 )  and…

Q: A restaurant is upgrading its dining room for $20,000. The upgrade will bring in a continuous stream…

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Q: 1 1 1 1 If where, a, b, c, de R a+w b+w c+w d+w @ and wo is a complex cube root of unity then find…

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Q: If linear, find and interpret the rate of change. If exponential, find and interpret the percent…

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Q: Suppose that you have a curve C that is given by r(t) = (t2, 2t, t3) from t = 0 to t = 1. Let…

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Q: Suppose R is the shaded region in the figure. As an iterated integral in polar coordinates, B D If…

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Q: Diagonalize A the matrix A. -27 2 3 4 3+ i√5 0 0 [S+W³² $ "VE] [3+1 0 3-i√√5 i√5] 0 0 [-³+1 0 O…

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Q: K Let A = 90 01 Find 4A + 2B. 4A+2B= and B= -9 2-6

A: Solution :-     The given matrix are                                                           A =…

Q: Consider the vector field Find a direction f(x,y) = 20e 7 Ty a in which the directional derivative…

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Q: Part D is missing. Can you please solve it

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Q: Choose the graph that goes from concave up to concave down as x increases OA A B OB f. Choose the…

A: The graph (C) goes from concave up to concave down as x increases. So the correct option is (C).

Q: You loaned a friend 1000.00 at simple interest of 4%. If total interest your friend paid was 150.00,…

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Q: A franchise of a chain of Mexican restaurants wants to determine the best location to attract…

A: There are three x and y coordinates are given as the location of the places.  Places x-coordinate…

Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answer as…

A: THE GIVEN LINE IS, x=y=z WE CAN REWRITE IT AS, x-01=y-01=z-01 SO, THE DIRECTION RATIOS FOR THE LINE…

Q: Use the method of undetermined coefficients to find a general solution to the system x'(t) = Ax(t) +…

A: Given That : A=0-30-300003 , ft=e6t3sin3t9t To Find : Use an undetermined coefficient to find the…

Q: Circulation and flux For the following vector fields, compute (a) the circulation on, and (b) the…

A: The given vector field F=-y, x and R is an annulus region r, θ; 1≤r≤3, 0≤θ≤π. We have to find the…

Q: 3. Let X be a topological space and let f: X→ Sn a continuous map to the n-sphere. Prove the…

A: Given That : Let X be a topological space and f:X→Sn a continuous map to the n-sphere . Prove That :…

Q: Evaluate - III, ³ 3xz dV where E = {(x, y, z) | 1 ≤ x ≤ 4, x ≤ y ≤ 2x, 0 ≤ z ≤ x + 3y}

A: The given problem is to evaluate the given triple integral over the given region E.

Q: 2 Find the length of the curve y = 3/2 from x = 0 to x = 4.

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Q: Solve the system of congruences r = 1 mod 10 = 2 mod 7

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Q: Show that the equation Z+22³ +37² +4Z+ 5 = 0 has no root which is either purely real or purely…

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Q: a that have the same boundary curve and orientation. ., True, False or Indeterminate: If S is a…

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Q: A population has the following characteristics. (a) A total of 25% of the population survives the…

A: We are give that a total of 25% of the population survives the first year. Of that 25%, 75% survives…

Q: Suppose R is the shaded region in the figure, and f(x, y) is a continuous function on R. Find the…

A: We have to find the limits of the given integrals.

Q: w is an imaginary root of unity. Prove that (i) (a+ba+ca²)³ + (a+ba² +ca)³ = (2a-b-c) (2b-a-c)…

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Q: ← A researcher in physiology has decided that a good mathematical model for the number of impulses…

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Q: Find the steady-state vector for the transition matrix. X = 0 1 0 000 Need Help? 1 8 1 0 1/1/00 Read…

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Q: 16 D 13 18 27 10 a 10 24 B 11 E 20 2 Find the shortest path from vertex A to vertex B. Give your…

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Q: The annual amount of energy produced in a country from dry natural gas (in trillion cubic feet) can…

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Q: Use the trapezoidal rule with n = 20 subintervals to evaluate sin 3x -S₁ √x²+x+1 places. Answer:…

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Q: Use the revenue and cost graphs on the right to find the approximate profit from manufacturing…

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Q: Z X Requirements: ✓Give the vertex set Give the edge list Give the degree of each vertex Give the…

A: (i)   The vertex set is = {A, B, C, X, Y, Z} (ii)   The edge list is = {(A,X), (A,Y), (A,Z), (B,B),…

Q: 2. Numerical Methods. Using h = 0.2, approximate the value of y (3) for the given differential…

A: The given differential equation is, dydx=x4-y3xy2+x3y4. Initial condition y(1)=3, and h=0.2. To…

Q: Find the absolute extrema of the function over the region R. (In each case, R contains the…

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Q: Let x, y, z be (non-zero) vectors and suppose w = 6x - 6y - z. If z = 3x - 3y, then w3x+-3 y. Using…

A: The given nonzero vectors are x, y, z and w=6x-6y-z. The vector z=3x-3y. Therefore, w=3x-3y. The…

Q: 3. Numerical Methods. Using Improved Euler method, solve for yı if x₁ =1.0: y = ² + e-x² y(0) = 0.2…

A: Given Data: Let us consider the given data, y'=y2+e-x2y0=0.2n=0x1=1

Q: Find general solutions of the differential equation (a) 9y(³) +12y" + 4y' = 0.

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Q: Let be a homomorphism f : R3 → R3 defined by the following matrix in a certain base B of R3.…

A: Eigenvector: A non-zero vector x such that it satisfies the matrix equation Ax=λx, for a square…

Q: 4. Write y as the sum of two orthogonal vectors, y, in L and y₁ in L Let y = YL = 1 and u = 2 7 Let…

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Q: a) f(x) = -e (x+1)-1 x y = 2-x Transformation: Domain: b) f(x) = sin ¹(x + 1) + 1/2 P = x=y= sinx…

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Q: The left end of a rod of length I is held at temperature 0, and the right end is insulated. The…

A: Given: A rod of length L such that: Temperature at left end is 0 Right end is insulted. Initial…