35) y+ y, =-5cos(2t), y+y, = 5cos(2t), y;(0) = y{(0) =1, y,(0) =-1, y,(0) = 1.

Q: a) Given the vectors in R3 v, =(11 -3), vz= (1 -3 1), v3=(-3 11) Using the system of linear…

A:

Q: f the sum of the co-efficients in the expansion of (a + b)" is 1024, then the greatest co-efficient…

A:

Q: Show that the centre of a ring R is a sub ring of R. And also show that the centre of a division…

A:

Q: Find the solution of the equation = e cos y dy? which tends to zero as x → 0o and has the value cos…

A:

Q: Advanced Math A company estimates that the production cost function of x product is giving the…

A:

Q: use two and three Points of Gaussian Guadrature xp = 1 %3D

A:

Q: Consider the problem of maximizing the algebraic expression q given by q = V6 – (x + 2)² – y²…

A:

Q: 4. Find the centroid of the region bounded by graphs of y = 4x – x², y = 2, and r = 0.

A: As per guidelines we experts are allowed to solve one problem at a time. Please reupload the fifth…

Q: Consider the function g defined by 1 g(x, y) = sin (7/æy) + log3(æ – 3y)' Do as indicated. 1.…

A: gx,y=sinπxy+1log3x−3y

Q: The measure of the linear density at a point of a rod varies directly as the third power of the…

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

Q: 3. Consider the vector space V p<? = {ax? + bx + c : a,b, c E R} of quadratic polynomials. Let B be…

A:

Q: For any positive integer n show that 1 n + 1 holds for any f e C'[0, 1] satisfying f(0) = 0. Verify…

A:

Q: Find the volume of the solid under the plane z = 3x + y and above the region determ

A: Given the plane                       z=3x+y and                y=x7,  and   y=x

Q: find general and particular solution of differential equation 4y" - 4y' - 3y = 0 with the given that…

A:

Q: 1 3 5. -2 ? Why? 5. -2 2 B = 3 -1

A:

Q: Q3/ Use Gramers rule to solve the system of equations: 3x + y + 2z = 3 2x - 3y -z = -3 X +2y +z = 4

A:

Q: 1. Provide any set S1 and S2 such that: (a) Si and S2 are subspaces of R", and that (b) Si U S2 is…

A:

Q: (c) Let M be the surface with the equation r³ +y³ +z = 9 that is above the right triangular region…

A:

Q: 31) y +y, = 2cos(1), y, + y, = 0, y, (0) = 0, y,(0) = 1.

A:

Q: Scheduled payments of $900 due two years ago and $1,200 due in five years are to be replaced with a…

A:

Q: 8) (D + D,)'u = 0 %3D

A:

Q: o f > 0 and f" 0, for a > 3.

A:

Q: Solve using Lagrange Multipliers, final answers should have 4 decimal places. Find the maximum and…

A:

Q: Evaluate F. dS, S where F(x, y, z) = (3xz – Vy? + 2?, sin(x – 2), e" - z²) and S is the surface…

A: Since S is the boundary of closed region in space. So we apply the Gauss Divergence Theorem.

Q: Consider the following optimization problem: Determine three positive real numbers such that their…

A: Solution

Q: Now suppose this is the graph of f'(x). Answer the following: + + b + a d A) Where is f(x) the…

A: (A) The graph of the derivative f'x lies below the x-axis which represents that the function is…

Q: What is the principle part for f (z)

A:

Q: if 0<a < 2 (2 ) if !<«<1 if 0 <x<1 if x 0 na fn (x) n-2 < x<1 2 x and f(x) 0. ISn (x) – f (x)|

A: Follow the steps.

Q: Let V be the space spanned by f 1 = sin x and f2 = cos x. (a) Show that gi = 2sin x + cos x and g2 =…

A: Here we use the definition of basis of vector space is the smallest linearly independent set…

Q: 2 4 -2 -1 W = span({ 0 }) -1 -2 (a) Find a basis B for W. (c) Write down the dimension of W.

A:

Q: 3) A hot cup of tea has temperature T(1) = 198 °F, one minute after it has been sitting on the…

A: To calculate the local linearization of the temperature at t = 1.

Q: The function x2 f(x) = 1 - x is decreasing on (0, 1). Select one: O True O False

A:

Q: Prove that l17 is the only prime number of the form n²- 64.

A:

Q: You deposit $980 in a savings account paying 3.8% simple interest. How much interest will you earn…

A:

Q: 2) Find the o - Congugates ot; c) 5

A: 2. To Find: θ-conjugates of  (c) 54 (d) 1+2

Q: There are 8 balls in a box: 3 red balls, numbered 1 through 3, and 5 green balls, numbered 1 through…

A:

Q: Mr. Smith decides to organize a potluck party with neighbors on a weekend. John Smith and his wife…

A: Every salad and every dessert should be considered as a different dish here.

Q: 5. Solve by finding series solutions about x=D0: (x - 3)y" + 2y' +y = 0

A:

Q: Prove that the only homomorphisms from Z to Z (Z being the ring of integers) are the identity and…

A:

Q: FOURIER SERIES Find the Fourier series of f() as given over one period Sketch f(x). (Show the…

A: To calculate the Fourier series of the below function. fx=−k    If −1&lt;x&lt;0k    If…

Q: Find the number of G-orbits in X := {1,2,3, 4, 5, 6, 7, 8, 9, 10}, where G < S10 is the subgroup…

A: Solution:Let g1 = (1,2), g2 = (3,4,5) - and g3 = (6,7,8,9). All three cycles at sight are…

Q: Calculate the middle rectangle approximation of , Vxdx using five subintervals. O M5 = 0.624 M5 =…

A:

Q: Write the objective function for each situation. 1. Your color television uses 0.2 kwh of energy per…

A: To write the objective function for the following situations Your color television uses 0.2 kWh of…

Q: . The population of rabbits in an island at the beginhling of 2020 was 1000. a. The population has…

A: Solution

Q: 1 2. Given the matrix A = -2 (a) Use the power series definition of the matrix exponential to…

A: Given a 2×2 matrix A = 100-2 . We have to solve two sub-parts :                    (a) Use the power…

Q: Work Problem 2 ( Given the set of the vectors in M22 1 10 0 3 4 6 S = 21 0 2 2 1 86 a) Create the…

A:

Q: Hw1: Calculate the volume under the surface f(x.y) = 6y? - 2x. For R: 0 sxS1, 0 sys2

A:

Q: Suppose z is a function of x and y, and csc Vx2 + yz = 2"esin . Solve for dz and ду

A:

Q: Suppose that a certain population has a growth rate that varies with time and that this population…

A: (a) The differential equation that satisfies the population is as follows: dydt=0.4+sinty4 We will…

Q: 5. Consider the double integral rydA r=4+4 cos(0) = 25 Where R is the region of the XY plane, i1 -io…

A: