### Linear Equation Application Word Problem : Distance Between a Point and a Line

Determine the length of pipe that a gas company will need to connect a house which is situated at the point (-6,8) to a gas line whose equation is y=-3x+2.

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Determine the length of pipe that a gas company will need to connect a house which is situated at the point (-6,8) to a gas line whose equation is y=-3x+2.

1) Which of the following equations describe the same line as the equation 3x+ 4y =5? a. y = (3/4)x + 5 b. 6x + 8y = 5 c. y = (3/4)x + 5/4 d. 5 - 3x - 4y = 0 e. none of the above 2) The equation of the vertical line passing through (-3,5) is a. x = -3 b. x = 5 c. y = -3 d. y = 5 e. none of the above 3)

Suppose that E is a normed linear space. Prove that if E* is separable, then E is separable. **See attachment for complete problem. Thanks!

Suppose that is a Banach space over K. A subspace M of is said to be complemented in if there exists a subspace N of such that =M N, that is if , then there exists in M and in N such that , and M N . Prove that each finite dimensional subspace of is complemented in . Hint: Suppose that M is a finite dimens

An electron is accelerated in a linear particle accelerator. At time t = 0, its speed is v0 along the axis of the accelerator, and it is subjected to a force producing a constant acceleration of magnitude a. Select the option which represents the formula most appropriate for finding the distance s that the electron has travel

I must solve the following linear equations using matrix methods. x+y-z=-8 3x-y+z=-4 -x+2y+2z=21 I am trying to understand the method of solving for variables of linear equation by forming them into a matrix and solving for the variables. Please help.

Let A = {see attachment} a. Solve x' = Ax b. Solve x' = Ax subject to x(0) = 0

Subject to the conditions x(0) = 0 and y(0) - 1, completely solve the following system of differential equations: x' = x y' = xy + e^t

(x^2 - x + 1)y" - (x^2 + x)y' + (x + 1)y = 0

Please solve the attached problems on bounded linear operators and bounded invertible equations.

Solve for x(1), x(2), x(3); 1. 27,954.606 x(1) + 11,969.843 x(2) - 7515.1688 x(3) = 6124.3394 2. 11,969.843 x(1) + 5900.332 x(2) - 3586.4121 x(3) = 3054.3092 3. -7515.1688 x(1) - 3586.4121 x(2) + 2513.4532 x(3) = -1756.4525

A-Solve: 4x=3y-6 4y=3x+1 b-Solve: 3x+4y=8 y=-3x+2

Let p be a prime in Z. Define Z(p) = {m/n in rational Q | p does not divide n} i) Show that Z(p) is a subdomain of Q ii) Find the units in Z(p) ,

1) Let { 1, 2, 2........... n} be a basis of an n dimensional vector space over R and A be n Matrix . Let ( 1, 2, 3............... s) = ( 1, 2, 2........... n) A Prove that dim (span { 1, 2, 3............... s}) = Rank (A). 2) Let V1 be the solution space of x1 +x2 + x3............+xn = 0 let V2 be the solution spac

.....is a commutative diagram of groups and that the rows are exact,... being homomorphisms. Prove that (a) if and are surjections and is an injection, then is an injection. (b) if , and are injections, then is an injection. 2. For a group extension {e} B H G {e} Prove that G ~ H/ (B).

See attachment for question. 1 Suppose that  is a finite dimensional normed linear space. a) Let be a basis for . Define Prove that 1, the closed unit ball in , is compact in (, ) b) Prove that any two norms on  are equivalent.

Suppose that N is a normed linear space. Prove that each finite dimensional linear submanifold of N is complete and therefore closed.

1. Let G be a group and H be a subgroup of G of index equal to 2. Prove that H G 2. Let (G,?) be a group and H G. Prove that if G/H is a p-group and is a p-group then is a p-group H. Please see the attached file for the fully formatted problems.

Given a 3x3 matrix M whose individual rows add up to 1 find a 3x1 vector v (not all zero) such that v=Mv. (Hint: Do a few examples.)

An event F is said to carry negative information about an event E, and we write.... Prove or give counterexamples to the following assertions... (See attachment for full question)

A, B and C are matrices. What are their ranks? A) 1 2 3 4 5 6 B) 1 1 1 1 C) 3 3 7 7 11 11

10. A psychology laboratory conducting dream research contains 3 rooms, with 2 beds in each room. If 3 sets of identical twins are to be assigned to these 6 beds so that each set of twins sleeps in different beds in the same room, how many assignments are possible?

1. Many free software mathematics packages on the Internet will solve a system of equations given the coefficients in the system. Problem: find out which of the four techniques (the Method of Addition, the Method of Substitution, Gauss-Jordan Elimination, and Cramer's Rule) is used in the majority of these types of software p

Please see the attached files for the fully formatted problems. This question is concerned with finding the solution of the first order simultaneous equations where a = -2, b = 8, c = -24, d = 30 (i) Find the particular solutions to the differential equations which satisfy the initial conditions x = 16 and y = 3 at t

1) An augmented matrix of a linear system has been reduced by row operations to the following form. Continue the appropriate row operations and describe the solution set of the original system. Please show every step no matter how minor, use the brackets for each reduction and write out every equation change. Please leave

8. Let R be a relation on a set S such that R is symmetric and transitive and for each x ε S there is an element y ε S such that x R y. Prove that R is an equivalence relation (i.e. prove that R is reflexive)

51. Solve the system: x^2 + xy^3 = 9 3x^2y - y^3 = 4 using Newton's method for nonlinear system. Use each of the initial guesses: (x_0, y_0) = (1.2, 2.5), (-2, 2.5), (-1.2, -2.5), (2, -2.5) Observe which root to which the method converges, the number or iterates required, and the speed of convergence.

The reduced row-echelon forms of the augmented matrices of three systems are given in the attachment. How many solutions does each system have? 1. The reduced row-echelon forms of the augmented matrices of three systems are given below. How many solutions does each system have? a. │1 0 2 0│ 	

27. Emile and Gertrude are brother and sister. Emile has twice as many sisters as brothers, and Gertrude has just as many brothers as sisters. How many children are there in this family? Please see attachment for the rest of the questions.