11. Given vector u = (2, a, 3), vector v = (1, -3, b) and u x v = (13, -5, -7). Find a and b.

Q: ? Exercise 15.2.3 The region bounded by the curves y = In z and y = e² in the interval [1, 2] is…

A: Area of region bounded by two curves y=fx (upper curve) and y=gx (lower curve) in the interval a≤x≤b…

Q: (b)show that: 1(cosh at cos at) s++4a

A: The solution is given as

Q: Use the given information to decide which lines are parallel. Justify your answers with a theorem or…

A: Fact (1) converse of parallel line theorem  The converse of the theorem is true as well. If two…

Q: A Fourier transform is another integral transform often used in higher mathematics. The Fourier…

A:

Q: 1. Given the set A = {1,2,3,4,5,6}. Given S6 = {f: A→ Alf bijective mapping} is a group with respect…

A:

Q: (D² + 1)y = sec² x csc x

A: Solve the differential equation by the method of variation of parameters : D2+1y=sec2xcscx

Q: Solve the following by Repeated root Method Question 4 X³+ 5x² + 7x-3 = 0

A:

Q: Let f: R→ R' be a ring homomorphism of commutative rings R and R'. Show that if the ideal P is a…

A: Let f : R → R' be a ring homomorphism of commutative rings R and R'. Here , P is a prime ideal of R'…

Q: c. 7 in Z10 under multiplication

A: Solution

Q: NUMERICAL DIFFERENTIATION: Find the first derivative (i.e., general solution) then solve for the…

A: Introduction: Numerical differentiation techniques in numerical analysis estimate the derivative of…

Q: (a) dy Given 4 sin 3x + 2exy = (2x + y)³, find dx'

A:

Q: 1. Newton's Law of Cooling: At 9:00PM., a thermometer reading 70°F is taken outdoors where the…

A:

Q: A solution of a differential equation free from arbitrary constants obtained from the general…

A:

Q: 3x y"+y= e¯x2 - 4x + 2x² + e³x 8-12x - 10x²

A: Let us consider the given differential equation y''+ay'+by=Q(x) To solve the differential equation…

Q: i s'ex eo e V². (-^x) dy dz -jz 00

A: Solution : a∧x.a∧x=1 ∫01∫01a∧x∈0e-jz.(-a∧x)dydz =-∈0∫01∫01e-jzdydz =-∈0∫01e-jzdz =-j∈0e-j-1

Q: Consider the IVP: y" +9y = 40e*; y(0) = 5, y'(0) = -2. Find the general solution. (A) y(x) =…

A: The given differential equation is second order linear, homogeneous differential equations with…

Q: 7. la + d d a d d+n n a n n + al = 4nad

A:

Q: (20pts) For the function f(x, y) = -xy2, find the solution from x = 0 to x = 1 with an increment of…

A: Solution: Given , y′=-xy2y(0)=1h=0.2 Forth order R-K method 1st iteration :…

Q: Suppose m> n. Show that L x"

A:

Q: Summarize what happens in their relationship. (Hint: Think about the eigenvectors. Be sure to…

A: As per the question we have to explain what happens in the relationship (dynamic system) as time…

Q: 2 2. y² dx + ( x² + 3xy + 4 y²) dy = 0 when x = 2, y = 1

A: Solution :-

Q: Find the general solution of dx dy xy+3x-y-3 xy-2x+4y-8

A: Given differential equation is  dxdy=xy+3x-y-3xy-2x+4y-8

Q: Using any of the methods discussed for both numerical differentiation and numerical integration…

A:

Q: Evaluate. 2x lim (e²x + 2) 8118

A: The solution is given as

Q: 4. Let Z5 = {0,1,2,3,4}. 4a) Find the value of x that makes (2+5) X5 4 =_1 in Z5 true. Complete the…

A: Given :  ℤ5 = 0, 1, 2, 3, 4. To find : (i) The value of x in  ℤ5  that satisfies  (2 +5 x) ×5 4 = 1.…

Q: A Fourier transform is another integral transform often used in higher mathematics. The Fourier…

A: Given Fourier transform of the function ft with respect to t Fft=∫-∞∞ft e-iωt dt Fω=∫-∞∞ft e-iωt dt…

Q: Let f(x)=√3x-2 on the interval volume of the resulting solid. 43x 135 83m 125 83x 135 43x -unit3…

A:

Q: Using Fixed-Point Iteration with an initial value of zero, find a root of the function: f(x) = x³ -…

A:

Q: The general solution of (D³-5D2-6D)y=0 is Ay=c₁еx+c₂e²x + c3e³x By=c₁+c₂e²x + C 2x 3x cy=c₁+c₂ex+ C…

A:

Q: Stokes' theorem states that [[ (V x F) - ds = f F. dr. Verify Stokes' theorem by calculating both…

A: We will find both sides of integral and compare there values

Q: Show that the Bessel functions J, (v ≥ 0) satisfy where A, are the positive zeros of J,,. [* IJs…

A:

Q: Create a quadratic model for the data shown in the table 1 -1 X Y -1 -1 Oy=0.85x² +0.11 - 1.78…

A:

Q: What is the missing number in the sequence: 21, 34, 55, 89, ___, 233?

A: To find the missing number in the sequence: 21,34,55,89,__,233.

Q: Given: region R below bounded by the graphs of y=√x-3, y = 9 - x, and y = 0. (7,2) R (3,0) (9,0) (a)…

A: We will use integral to find area and volume  Arc length of y=f(x) from x=a to x=b  L=∫ab1+dydx2dx…

Q: S. (22² 2. 2 (2x² – 3x) dx

A: ∫25 2x2-3x Apply the Sum Rule:    ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx =∫252x2dx-∫253xdx

Q: Numerical Integration: 5 (2x² – 3x)dx 2. 2

A: Given that∫252x2-3xdx⇒  2x33-3x2225⇒  2×(5)33-3×(5)22-2(2)33-3(2)22⇒   2×1253-3×252-2×83-3×42⇒…

Q: d the solution. - 2y'-2y = 0 31 A y = c₁₂e √³1 + B) y = cell-√3)+c_xe (1+/3), -cell-cel+5 Dyce -…

A:

Q: ax-a O cos (0) cos (4) O cos (0) sin (4) O None of the choices O sin (0) cos (4) O sin (0) sin (4)

A: Option 1 is correct

Q: k 21. The following differential equation describes an electrical circuit with I the current at time…

A: The solution is given as

Q: 9. (a) Use the method of Lagrange multipliers to determine the minimum and maximu values of f(x, y)…

A:

Q: The general solution of y" + y = sec³ x

A: First we will find the complementary solution for which we will find the roots of it's auxiliary…

Q: Find the centroid of the solid bounded by x² = 4y and y = 5x - x² about the x-axis.

A: We will draw the region and rotate it about x-axis to create a solid of revolution . We will need…

Q: II. Find the general solution of the following differential equations. dy x+1 1) = dx 2(y+3) dy 2) =…

A:

Q: Problem 1 Find the Fourier transform of the given function. f(t) = 2A -t + A, 7sts ≤t≤ 0; T 2 2A T…

A: Fourier transform of a function ft with respect to t Fft=∫-∞∞ ft eist dt Where i is a complex unit…

Q: y" + 2y' + y = −e* [(− x² + 4x+3)cos x + (− x² + 4x + 3)sin x]

A: As per the question we are given a second order linear non-homogeneous differential equation. And we…

Q: Create a table wherein it shows your score or your • class interval • class width • frequency •…

A: To create a table where a data is shown with the frequency, class interval and cumulative frequency.

Q: x=r-s, y= Q2/ Find ow/or if w= (x+y+z)³, cos(r+s), z = sin(r + s) at the point (r, s) = (0,1)

A: Solution:

Q: ? Exercise 15.2.9 The joint density function for two random variables X and Y is given by f(x, y) =…

A:

Q: y=-3x+5 -10 -8 -6 -4 -2 10 8 6 4 2 -2 -4 -6 -8 -10 2 4 6 8 10

A: Given :  y =-3x+5

Q: The particular solution of (D³-5D + 4)y = 0, when x = 0, y = -2, y' = 8, y" = 0

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…