11.[2] Show that vectors A = 4ax - a₂, B = ax + 3ay + 4az, and C = -5ax 3a, 3az form the sides of a triangle. Is this a right angle triangle? Calculate the area of the triangle. Answer: [yes: 10.5] - -

Q: Question 3. Let m be a constant. For x ≥ 0, the line y = mx divides the region enclosed between y =…

A: Given a line y=mx divides the region between y=2x-x2 and y=0 into two equal area. Plot : The diagram…

Q: rotate the vector v = The rotation matrix R = H IT by an angle of in the CLOCKWISE direction. The…

A:

Q: 1: Let f be the function graph below. Sketch the graph of each transformation described. Label where…

A: Given: Graph of a function f, To find: Graph of each transformation of f given below. (d) f2x+1 (e)…

Q: Solfe Linear differential equa bien 1) XY²+ (1+x) Y=e* 2) 5 = 2X + (x + 1)² 27 X+1

A: Since you have posted multiple questions , we will provide the solution only to the first question…

Q: Take the Laplace transform of the following initial value and solve for Y(s) = L{y(t)}: (sin(nt),…

A:

Q: Question 24 Let k = -2, A = O 1 0 Compute (B+C) (kA). O -12 -12 -18 12 6 -12 -2 -3 -2 2 2 1 4 8 -12…

A:

Q: Define a relation on Z as follows: For m,n ∈ Z, m∼n ⇐⇒ 5|(m−n). (5.1) Prove that ∼ is an equivalence…

A:

Q: Ruel is the brother of Bella. Dina is the sister of Ruel. Matthew is the brother of Tanya. Tanya is…

A: We are given a few relations and we need to find who is the uncle of Matthew. Whereas for 4th…

Q: QUESTION 3 (3.1) Find the analytic function f(z) = u(x, y) +iv(x, y) given that u(x, y) = sin x…

A:

Q: Solve the Goursat problem:    Utt − c 2Uxx = 0 u|x−ct=0 = x 2 u|x+ct=0 = x 4 . Hint: Use the…

A:

Q: The figure to the right shows the number of full-time employees of a company (in millions) as a…

A:

Q: Prove by induction on n that for all n € N, <2 14+24++(n-1)4 < (When n = 1, the sum on the left-hand…

A:

Q: Heller Manufacturing has two production facilities that manufacture baseball gloves. Production…

A: Answer :-

Q: Consider the wave equation Utt- c²Uxx = 0 ᏆᏆ the half-line x = [0, ∞) with boundary condition U (0,…

A:

Q: Find the root of the function using the following methods. Modified Newton-Raphson Method

A: The given function is fx=x3-8. We have to find the root of the given function using the Modified…

Q: 1. You have taken some medication and the doctor tells you that you will lose about 5% in your…

A: Since you have posted a multiple question according to guildlines I will solve first(Q1)   question…

Q: Problem 1. The ciphertext IPQASEKZYSLA comes from a Vernam encryption with the short keys A and B of…

A: Please find the attached image

Q: S(1) = 1; S(n) = S(n − 1) + n, n ≥ 24

A: The idea is to telescope the series and find the value for S(k) for any fixed k. Telescoping means…

Q: Determine the transformation that produced the following images: b) a)

A: The objective is to find the transformations udes. a) To get the image of DHF, do the following…

Q: Q8. Suppose 8₁ = 4 and g₂ = 1. The rest of the terms in a recursive sequence are given by the…

A: Here given that g1=4 and g2=1  The rest of the terms in a recursive sequence are given by the…

Q: Problem 1. If roll three fair dice, what is the probability that we get a total of 15?

A:

Q: Consider a continuous function f with 1 < a < b < 2, and such that it is differentiable f(a) 0 and…

A: This is a problem of application of calculus.

Q: Find the 5 number summary for the data shown 10 17 40 41 46 52 53 59 65 98 5 number summary: IQR: D

A: Introduction: The middle value in a sorted list of numbers is called the median, and it may be used…

Q: Select 2 choices. The cost (in dollars) of a custom-made sweatshirt is represented by 3.5n+29.99,…

A: If a function y=f(x) is given then y is the value of the function and x is input for the function.…

Q: Let f(x) = 6x² + 2x³. Select all intervals where f(x) is INCREASING, (3) (0, ∞) (,0) (-∞, -3¹²¹)

A:

Q: In Exercises 8 and 9, which of the given subsets of the vector space, P2 are subspaces? 8. The set…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Suppose f(x,y) = C is the solution of the given Differential Equation. Determine the value of the…

A:

Q: 2. Let A 0 1 0 0 0 1 2 -5 4. Is A diagonalisable? If so, find a basis for M2,1 (C) consisting of…

A: It is given that the characteristic polynomial of the matrix A is cpAx=x-12x-2. We have to check…

Q: a. Find the open intervals on which the function shown in the graph is increasing and those on which…

A:

Q: 1. Let T be a linear operator on V. Prove that if T is uninvertible then ST and TS are uninvertible.…

A:

Q: Formula for rebate fraction

A: Introduction: The Rebate fraction is calculate by summing of the digits of the number of payments…

Q: using T= πT integration TT/2 dn= *2 O cos x cosnx dx

A: We know that: cosAcosB=cosA+B+cosA-B2∫cosaxdx=1asinax+C

Q: 3. Pick an interesting positive integer a with a > 20. (a) How many nonnegative integer solutions…

A:

Q: √n-3 n²+2 does the series converge or diverge.l

A:

Q: Given that f(x) = 4 1 x² Evaluate the 2022nd derivative of f(x) at x = 0.

A:

Q: Suppose the second derivative of a function ƒ(x) is ƒ"(x) = 2x – 1. Suppose x = 1 is a critical…

A:

Q: Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the…

A:

Q: In Cay({(1, 0), (0, 1)}:Z4 ⊕ Z5), find a sequence of generators thatvisits exactly one vertex twice…

A: Given,         Cay(1, 0), (0, 1) : Z4⊕Z5.

Q: Write out the third order Taylor poly- nomial about 0 to approximate e−0.5. (i) Show that the…

A: Introduction: The most crucial use of Taylor series is probably to estimate functions using their…

Q: 1. 2. Quantity A 0.01410 pitzon ¹410 adiant Quantity B 0.0141 Quantity A The average price of the…

A:

Q: 1. Describe the graph of the inequality y - x² ≥ 1 in R² and in R³. Sketch a graph in each case. 2.…

A:

Q: 2. Sketch the graph of a continuous function f(x) with domain [-1, 8] which is differentiable on…

A: There is continuous function f(x) whose domain is [-1,8] and differentiable on -1,8, which…

Q: the denominator of a fraction is 8 more than the numerator. if both the numerator and the…

A: The given problem is to find the fraction where the denominator of a fraction is 8 more than…

Q: a) Prove that every integer can be written a sum of powers of 2. b) Write 14, 17, 27 as a sum of…

A: We have to prove the every integer can be written a sum of power of 2 and write 14, 17, 27 as a sum…

Q: 3. Suppose you'd like to save enough money to pay cash for your next car. The goal is to save an…

A:

Q: Find the root of the function using the following methods. c- One-Point Iteration Method

A:

Q: Suppose n € N. Let S be the following statement: If n is prime, then 2n + 1 is prime. (a) Write down…

A:

Q: Chapter 6, exercise 4.3: (a) Compute the left cosets of the subgroup H = {1,x5} in the dihedral…

A:

Q: O Two vertical poles be reinforced by op the ground 15 and 20m wire a poles are tied to in the…

A:

Q: 1 5/6 + 1/2

A: