The equations of two straight lines are r =i+ 4j – 2k + 2(i+ 3k) and r = ai + 2j – 2k + µ(i + 2j + 3ak), where a is a constant.

Q: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

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Q: For what values of the constants k and c does the line x- 3 ** =- lie in the plane x - y + 2z = c? O…

A: Given equation of   line  ;   x-32=y-2k=z+14plane;  x-y+2z=c key points 1)  given line lies in the…

Q: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

A: The solution is given as

Q: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

A: Given equation, y3+9x2=b Used formulas:…

Q: Consider all the nonzero solutions of the second order linear equation y"-5y'+4y=0. As t+ 0, they…

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Q: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

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Q: The simultaneous linear equations mx + 7y= 12 and 7x+my = m have a unique solution only for A. m = 7…

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Q: Describe all solutions of the following system of linear equations. x +y - w = 1 (x + y+ 2z +w = 1…

A: First we will put the given system to augmented matrix form and use row operations to row reduce it.…

Q: 21 Calculate the coordinates of the point of intersection I of the two lines : 1° (D) : x + 3 = 0 2°…

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Q: Determine the general solutions of the following non homogenous linear equations. 6. (D³, D) y = x

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Q: 18. Find the value of “a" for which the lines ax + 8y + b = 0 and 2x + ay – 1 = 0 are (a). Parallel…

A: Two lines y=m1x+c1 abd y=m2x+c2 having slopes m1 and m2respectively are said to bei parallel if…

Q: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

A: As 2 Question are given , I will solve only one: We are given: 8y=b sinx----(1)⇒8y''=b cos…

Q: , Find two linearly independent solutions of 2a²y" – xy' + (2x +1)y = 0, x > 0 of the form Y1 = r"…

A: (Note: Please scroll to the last step for the final answer.) Given equation is 2x2y''−xy'+2x+1y=0…

Q: 35. The equations 2x – 3y + 4z = 1, 3x – y = 2, x + 2y – 4z = 1 A are linearly independent B are…

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Q: Find the general solution of the following homogeneous linear equations: A. (D5 +8D3+16D)y=0

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Q: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

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Q: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

A: I have stated the used formulas in the solution

Q: (10) Use the result of Exercise 9 to find the general solution of the given equation: (a)…

A: We will use various transformations to solve the problem

Q: Solve the systems of linear equations over the indicated Zp 3x + 2y = 1 over Z7  x + 4y = 1

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Q: (D² + D – 1)²y = 0 ,when x= y = 0 , y' = y'"'' = 1 , y" = -1 %3| %3|

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Q: Find the solution of y'(x) -ay(x) = 0

A: In this question, the concept of the differential equation is applied. Differential Equation A…

Q: Solve these linear equations by Gaussian Elimination. 2w + x – y + 2z = 5 4w + 5x Зу + 62 - -2w + 5x…

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Q: b) Find the solutions of the following homogenous linear equations with the use of equation 4.1.2 D…

A: 1) D3-6D2+5Dy=0We will simplify the auxiliary equation and find the roots.

Q: Solve the systems of linear equations over the indicated Zp . x + y = 1 y+z=O x + z = 1 over Z2

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Q: Given the system of equations 3x + 4y2 = 48 x + ky = 8 find a positive value of k such that x + ky =…

A: Given: equation 3x2+4y2=48x+ky=8 To find a positive value k Line equation formation y=mx+c to be…

Q: Consider the third-order linear equation a" + a = 0 i) Solve the contour problem 2(0) = x'(0) = 0 e…

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

Q: True or False? If the functions Yı and y2 are linearly independent solutions of y/" + p(x)y' + q(x)y…

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Q: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

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Q: (a) If b² – 4ac = 0 and y1 = em# solves ay" + by/ + cy = 0, use reduction of order to get a linearly…

A: Q2 a) Let y=uy1y=uemxy'=u'emx+umemxy''=u''emx+2u'memx+um2emxPutting the value in equation, we get…

Q: If y₁ and y2 are linearly independent solutions of ty" + 3y' + tetty = 0 and if W(y₁, y2)(1) = 4,…

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Q: Consider two paths, Y1(t) = t(1 + i) – 2 and y2(t) = 1 + i(2 + t).

A: In this question, we check the given paths are intersecting or not. we use the equality of complex…

Q: If y,, Yz are two independent solutions of y"+ p(t)y+ q(t)y=0 then Select one: a. V2 w(V1.V2) b. V2…

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Q: 10y" + y" - 7y' + 2y = 0

A: differential equation

Q: If y, and y, are linearly independent solutions of ty" + 3y' + te²"y = 0 and if W(y , y2)(1) = 3,…

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Q: Find the solution of the following linear equations using the methods of Colosse and Coors-Corden…

A: Given equation,a+b+c=0,a-b=4,a+b+2c=6written in matrix…

Q: The formulas for the least squares line were found by solving the system of equations nb + ( Σx)m Σy…

A: Here, the given equations are nb+∑xm=∑y ...(1) and ∑xb+∑x2m=∑xy ...(2)

Q: The solution of the following linear equation xy' + 2y = x² – x +1 is: a. y = --- 3 b.y = c.y =-+ +…

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Q: Consider the system of linear equations below. 2x + 3y = 1 3x + 2y = 3 Compute the coordinates of…

A: The given equations are: 2x+3y=1...(1)3x+2y=3...(2)

Q: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

A: We have to solve for C.

Q: apply gauss jordan method to solve the equations x+y+z = 9 , 2x-3y+4z = 13, 3x+4y+5z = 40 plz fast

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Q: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

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Q: 23. Which of the following equations is nou-linear in the variables z, and za- A. 14r +5z2 +2 I3 B.…

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Q: . 4y"+12 y'+10у %3D16х-50 сos 2x

A: Given: 4y"+12y'+10y=16x-50cos2x

Q: Ify, and y, are linearly independent solutions of y" + 2y + (3 + 1)y = 0 and if W(y1, y2)(1) = 2.…

A: I am solving this in step 2

Q: b) Solve the first order linear system given that r and y are functions of t such that a' =1+y, r(0)…

A: The Laplace transform of the function is represented as or , it is defined as , since the…

Q: B. Determine the general solution of the following nonhomogeneous linear equations using the method…

A: B1 Given differential equation D2−4y=4x−3ex. We have to find the solution of the given differential…

Q: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

A: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

Q: If ax2 1 du and C = 1, determine the solution u = f(x, t) subject to the boundary %3D C2 at…

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Q: 2. Find the solution set of the following linear equations. (а) х — 2у — z%3D —2 - - (b) 3x – 7y =…

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Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.