A. Directions: Convert the following statements to mathematical symbols. 1. John is neither healthy nor wealthy, but John is wise. 2. If both John and Kevin do not pass the examination, then John and Kevin will both not receive the allowance for the week. 3. If it rains today, then I will not bring any umbrella if and only if either John or Kevin brings an umbrella.

Q: -1 if -2<x<-1 (a) Find the Fourier series of f(x)={ x if -1<x<1 , and f(x+4)= f(x) 1 if 1<x<2

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A: Applying the definition of greatest common factor in solving the problem.

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Q: Use induction to prove that for every n E N, we have 5" = 1+ 4n (mod 8)

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Q: Q3: Find the first derivative at x 2 for the function given by the data 1.0 1.5 2.0 3.0 Y 0.4057…

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Q: Question 4 The well-known Fibonacci Sequence Fo, F1, F2, ... is generated by the relation Fk = F1 +…

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Q: I Simplify each of the following expression. (8!7!) 5!4! 7. 12! 3!2! 10 8. 4!3! 45! 0. 43!5!

A: 7. Consider the given expression, 8!7!12! Use the formula n!=n×n-1×n-2×⋯×2×1,…

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Q: Graph the vector function 7(t) = (t3 + 1)ĩ + tj:

A: Given vector function is r(t)=(t^3+1)i +tj

Q: (b) By using mathematical induction, show that n(n + 1)(n + 2)(n + 3) 1.2.3+ 2.3.4 + ...+ n(n + 1)(n…

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Q: ective 3 – Medians and altitudes 1. Name 3 altitudes in the picture below. 2. Name 3 medians in the…

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Q: (a) x = 2+ (y – 2)², x = 3; about the x – axis. (b) y = Vx, = 2y; about the line x = 5.

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Q: Express the system of differential equations in matrix notation x"-7x' +1'y- (tan t)x= 0 y" +2y"…

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Q: 20. [The l'Hospital's rule.] (a) Find the limit lim x In (1 + !), and then show that lim (1+ !)* =…

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 7 cos(t)i +3 sin(t)j +…

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Q: NEED ASAP laplace{cos3t cos8t}

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Q: Let u = and v = Show that is in Span (u, v} for all x and y. y -1 5

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Q: 3. Let X be a topological space. Show that for every subset A of X and for ever U we have AQU =…

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Q: Example 12.13. Find all the basic solutions of the following system of equations iden- tifying in…

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A: Here we have to find maximum profit.

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

Q: You decide to Contribute to amutuof fund that loutrifide. 4.6%. returm pen year. q you averinger…

A: Solution:   Part (a) P = Quarterly contribution = $425 n = 10 years*4 = 40 Quarters r = Quarterly…

Q: Example 10.26. Using Picard's method, find approximate values of y and z corre- sponding to x = 0.1,…

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Q: Two tugboats that are a = 145 ft apart pull a barge, as shown. If the length of one cable is b = 218…

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Q: A brine solution of salt flows at a constant rate of 8 L/min into a large tank that initially held…

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Q: 2: Use the Gauss-Seidel method to obtain the solution of the system (Two Iteration ) 3x1 - 0.1x2 -…

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A: All of we know that Sum and Difference of two Rational number is also Rational. Here Supposing pi is…

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A: Vertically opposite angles are equal. Now, in the given figure 80° and angle a are vertically…

Q: Q:Determine a solution for the pDE, and canjecture the form of the general Solution マン fnbtれてhiy h-

A: Given, homogenous Partial differential equation  uxx-4uyy+2ux+4uy=0 Substitute uxx=D2u, uyy=D'2u,…

Q: Calculate sx²z dS, where S is the cylinder (including the top and bottom) x² + y = 16,0 < z < 5.…

A: To calculate  ∬Sx2zdS where S is cylinder (including the top and bottom) x2+y2=16, 0≤z≤5.

Q: 4. Let R be endowed with its standard topology. Let A be a topological subspace of R. a) Is {3} open…

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Q: JO find onthononmal bases:(Using 2 3 %3D 1 O'5 V2 = 2 0:2 1

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Q: 2. Find the converse and the contrapositive of the following statemnents: (a) If m divides 2+j²,…

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

Q: Solve the boundary value problem numerically - du = r, 0 < IS1 subject to u(0) = 0 = u(1)

A: d2udx2=-x2⇒dudx=-x33+c⇒u=-x412+cx+du(0)=00=du(1)=00=-112+cc=112u(x)=112(-x4+x)

Q: Q2: Use the Gauss-Seidel method to obtain the solution of the system (Two Iteration) 3x1 - = 7.85 0.…

A: To find- Use the Gauss-Seidel method to obtain the solution of the system (Two iteration) 3x1 -…

Q: Calculate x²z ds, where S is the cylinder (including the top and bottom) x + y = 16,0 < z < 5. (Use…

A: We can solve this using parametric equation