2. Show that the following functions are convex by verifying the condition that V²f(x) 20 is satisfied for all a in the domain of f: (a) f(u₁, u₂) In(e": +e"), (b) f(u₁, U2, U3, U4) -In(1-₁-₂-3-4) over the domain {u E R¹|u₁ + ₂ + 3 + U₁ ≤ 1}.

Q: Let A and B be non-empty and bounded subsets of R such that inf A < inf B. Prove the following: ∃a…

A:

Q: If AABC having vertices A(a cos 0₁, a sin 0₁), B(a cos 02- a sin 0₂), and C(a cos 03, a sin 03) is…

A: Given that triangle ABC is equilateral, having vertices  and  , then we have to prove…

Q: Fill in the missing entries to complete the matrix representation of the given graph. 2 3 4 5 0 (a)…

A:

Q: •• An air traffic controller observes two airplanes approaching the airport. The displacement from…

A:

Q: Orthocentre and circumcentre of triangle ABC are (a, b) and (c, d), respectively. If the coordinates…

A: Given that the orthocentre H(a,b) and the circumcentre O(c,d).Since relation between H, O and G…

Q: Use determinants to decide if the set of vectors is linearly independent. 3 5 - 12 4 2 - 6 0 8 - 2 -…

A:

Q: -5 14 -3 -2 -1 5 4 3 2 -1 -2 -3 -4 -5 h(x) The function h graphed above is: Increasing on the…

A:

Q: Logic Problem 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. There are exactly five dorms.…

A: Now, let's use this information to deduce who drinks coffee and who has a dog:••We know that there…

Q: 3.118 Let B be the standard basis for P3. In each part of this exercise, (i) give B coordinate…

A: Since you have posted a multiple question according to guidelines I will solve first question for…

Q: Use determinants to find out if the matrix is invertible. - 10 - 1 - 2 - 2 3 - 4 0 -5 6 The…

A:

Q: Use Euler's method with step size 0.1 to estimate y(2.5), where y(x) is the solution of the…

A: Step size

Q: (2) Let V₁ = V2 An Echelon form of (c) The linear system " [360 37 30 1 10 36 20 and V3 = Choose all…

A:

Q: The simplex method can be used to solve the following linear programming problem. Minimize this…

A:

Q: he coordinates of point P are (-3,8) and the coordinates of point Q are (5,3), M is the midpoint of…

A: Result: If  . Let M be the mid point of the line PQ then .

Q: MovieFlix - Advertising and Subscriptions Year  Advertising Expenditure       $ 000   Membership…

A: Year Advertising Expenditure(X)  Membership Subscriptions(Y)      $ 0002013…

Q: For a certain company, the cost for producing items is 55x + 300 and the revenue for selling x items…

A: Let us solve above problem

Q: 15. 10 Σ 2+1 – 2 i=0 What is the value the sums of terms of a geometric progression

A:

Q: Exercise 4: Recall that in Exercise 3 we looked at Euler's method applied to the equation x = x with…

A:

Q: Let a and b be positive integers with ged(a, b) = 1. Show that if d > ab, then as + tb = d has a…

A: 4. Given that a and b be positive integers with gcd(a, b)=1.     To prove that if then has a…

Q: 1 for convergence, you 2k5 +9k8 will use the Limit Comparison Test, comparing it to the p 1 series…

A:

Q: 11. a) U₁₁ A₁ Let A₁ = {i,i+1,i+2,...} for i=1,2,3,.... Find b) Ai

A:

Q: -10 e(x) m(x) 5 15. 10- S i -10- -15- L in 10

A:

Q: In Exercises 15-20, W is a subspace of R4 consisting of vectors of the form X = X1 15. x₁ - 2x2 + x3…

A:

Q: Construct a truth table for the following compound propositions. b) (p ^~q) →q 2. a) (~pv q) → (p@q)

A:

Q: Which of the following is true? Select all that apply. ei (0+π/4) = e¹(0+π/4) = ei(0+3π) √2 2 i√2 2…

A:

Q: 8. d²y dy Solve the Cauchy-Euler equation x²- +8x +6y=0. dx² dx

A:

Q: , z) ¤ K³| 3x – 2y — z=0}, _W = {(x, y, z) = K³| x

A:

Q: 1. Due to the quarantine, the demand for Nine Tendo On/Off console suddenly peaked and is expected…

A: Decision variables:xq : number of units purchased in quarter q.yq : number of units held over from…

Q: f(x, y) = 4 + x² - y² R = {(x, y): x² + y² ≤ 9}

A: Surface area of the given surface

Q: Draw an appropriate Venn diagram and use the given information to fill in the number of elements in…

A:

Q: 5. Write the differential operator that annihilates the following functions. (a) f(x)=xº sin(√√5x) +…

A: To find the differential operator that annihilates the given functions, we need to determine the…

Q: For the system of differential equations (D+1)x + (D-1)y = 2 3x + (D+2)y = -1 solution for y(t). 9.…

A:

Q: A car of mass m moving at a speed v₁ collides and couples with the back of a truck of mass 2m moving…

A:

Q: (sin (2x)) dx = sin(2x)e-7x 7 sin(2x)e-72 7 Step 9 Hide steps Simplify. Hide steps + Simplify the…

A:

Q: The fission reactor of a nuclear plant explodes at t = 0. The following function d represents the…

A: (a)This method is useful for obtaining an approximate response, but it cannot provide an absolute…

Q: 3 13 5 -7-17-5, observe that the first column plus twice the third column equals the second column.…

A: We have to find the non trivial solution such that

Q: 1. Consider the matrices -3 0 2-2 A₁ ¹ = ( ₁ ) ₁4₂ = ( −8 −2 ) ₁4₁ = ( −² − ²). 4 1 13 , , A3 0 -2…

A: We have to match the given matrix with the function represented in the graph

Q: DON'T USE AI | DON'T USE AI | DON'T USE AI | DON'T USE AI | Exercise 2. Find the coordinates of a…

A: If ?1(?1,?1) and P2(x2,y2) be the endpoints of the given line segment AB and P(x,y)  be the point…

Q: 1. Prove the following polynomial is 0(n¹). Use algebraic manipulations. P(n) = 5n -10 n³ + 20 n² +…

A:

Q: Solve for the exact first order differential equation. Find the appropriate integrating factor and…

A:

Q: Suppose the 9-vector x = (1, 1, 2, 3, 2, 1, 0, -1, 0) represents a time series. (a) We wish to…

A:

Q: (a) Using the table below, find the average rate of change in the world's population, P, between…

A: The rate of change refers to how one quantity changes concerning another. It's a fundamental concept…

Q: 4. Let x, y € R. Which of the following inequalities is TRUE? (Circle your answer(s).) • zy ≥ (²+v)…

A:

Q: Let S := a + √2 b + √2 : a, b EN Prove that S is countably infinite.

A: To prove that the set S defined as S={a+2b+2|a,b∈N} is countably infinite, need to establish a…

Q: Consider the problem: Cube equal squares and number. Use al Khayyami's method and identify two conic…

A:

Q: Let λ be an eigenvalue of invertible matrix A. Prove that exists and is an eigenvalue of A-¹. What…

A:

Q: Activity 25.22. One advantage of decomposing a permutation as a product of disjoint cycles is that…

A: The idea of permutation will be used in solving this problem

Q: Please write 2(b) again

A:

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

A: