a) Let a = 2i – 3j + xk and b = -3i + j + xk. Find the values of x for which vectors a and b are at right angles.

Q: Find the general solution of the differential equation and check the result by differentiation. (Use…

A: Proceed as shown below...

Q: b) Consider the vectors a = 2i + 2j + k and b = xi + j – k. Find the value of x for which the angle…

A: Given: a→=2i+2j+k, b→=xi+j-k We know that angleθ between two vectorsa→=x1i+y1j+z1k, b→=x2i+y2j+z2k…

Q: Sketch the region bounded by the curves x = Vy+ 8 , x = y – 4 and evaluate the area.

A:

Q: Find the Fourier series expansion of e3-2x² around -1. O a. е — 4e(х + 1) + бе (х + 1)2 — 8е(х + 1)3…

A:

Q: 3. Find the solution of the PDE in terms of two arbitrary functions. 2uxx 4uxt + Up = 0

A:

Q: Using Variation of Parameters compute the Wronskian of the following equation. y" – 2y' +1 = (x+…

A: we have to find the wronskian using variation of parameters

Q: Question 1: Determine the length of y = 8(1+ x)ž,8 < y< 64.

A:

Q: 3. Find eigenvalues and eigenvectors of the matrix 8-21 3-8

A:

Q: Find the area of the region bounded by 5x, y = 125x, r = -5, x 5 %3D %3D Give your answer to the…

A: This question is based on application of integration.

Q: Obtain the Fourier series expansion of the periodic function defined by ƒ(t) = t³ + 3t for (0<t <…

A: Given the function f(t)=t2+3t, 0&lt;t&lt;2π. Find the Fourier series expansion of the periodic…

Q: Find an explicit solution of the given initial-value problem. dx 4(x + 1), x(7/4) = 1 dt

A: Given that      dx/dt = 4(x2 + 1) , x( π /4) = 1 Here we find an explicit solution of the given…

Q: 32. Probability% = ABCD is a square and AB = 8 yd. %3D D

A:

Q: Show whether the equation given below is exact or inexact? If exact what is solution? points) abD dC…

A:

Q: could you please help to answer this question? thank you

A: The data represents the number of minutes required to fall asleep with and without the relaxant. The…

Q: The great circle of a hemisphere has a circumference of 18x mm. Find the surface area of the…

A:

Q: 7. Find the volume of the frustum of a pyramid. 12 cm 6 cmAS lo zanal ni 15 cm 9 cm 16 cm

A: Here we find the volume of frustum pyramid.

Q: I need help to solve this question.

A: loga(mn2) = 20

Q: The asset turnover ratio (ATR) is the ratio of a company's revenues to the value of its assets…

A: The formula of CV is,

Q: Unit processing times (in hrs) Product 1 Product 2 Minimum Working Hours Plant 1 2 4 16 Plant 2 4 3…

A: To formulate the given problem as a linear programming problem, identify the decision variables, the…

Q: dy dx 3x + 2y + 2' 3x + 2y y(-1) = -1

A:

Q: Q. Solve the equation to find matrix A. (2a + (? ))" - (4 9) Hint: Use the properties of Matrix…

A: We will find out the required value.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.