Question # 7.3A vector y = [R CE) F(t)]' describesrats R(t) andthe papu lationsfalcons FCt). 'The populationsof someobey the system of defferential equations given byy'= Aywhere-171A =880-36185The rat population starts atthe rat' population toof the form RCt) = Roet with no other terms, how manyfalcons are needed at time t=0?(nate that eigenvalves of A are X=5 and 9.)19000. If you wantas a Simple exponentialgrow

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Answered: Question # 7.3 F(E)]' describes A…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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(7) A particle of mass 2kg is moving with velocity V= (5 i+4j - 2 k) what is its angular momentum about origin at the instant its position vector is (t+ j+ k )m ? (8) IF: A = 1+j+ k, B= 1+2) - 3k Find A-B|, Ā.B , 2Ā.3B , Ā B, (A+ B) (A-B) (9) Find the angle between two vectors: A = 31+4-5k, B = 31+4j+ 5k using: (1) Scalar product. (2) vector product.
1. A line passes through the points A(2, 3) and B(-2, 1). Find a vector equation of the line. [x, y] = [-4, -2] + 12, 3] [x, yl = [2, 3] + 41-4,-2] [x, y) = [2, 3] + 1-2, 1] A В D 2. A line has slope 3 and y-intereept 5. Find a vector equation of the line. [x, y] = [1, -3] + [0, 5) [x, yl =[-3, 5] + -3, -31 [x, y] = [0, 5] + [1, –3] [x, yl - [5, 0j + j0, –31 A B _ 3. The Cartesian cquation of the plane with normal vector - [1, 2, 1] and passing through the point (3, 2, 1) is: x+ 2y +z+ 8 = 0 x+ 2y + z- 8 - 0 3x + 2y +z-8 =0 3x + 2y +z+8 = 0 A B D _ 4. The equation of a plane is [x, y, z] = [3, 1, 3] + s[=1, 1, 2] + [2, 1, 1]. Find a normal vector to the plane. [3, 1, 3] [-1, 5, -3] [-1, 1, 2] [2, 1, 1] A В D 5. The equation of a plane is x+ 2y+ 3z- 6 = 0. Find the y-intereept of the plane. -1 C 3 В 2 D -3 _ 6. Two planes are parallel if their normals are perpendicular are collincar dot product is zero are different в D 7. Which of the following determines a plane? A a line and a point…
(19) Consider the vector function 7(t) = (cos (3t), sin (3t) , 3t). Write 7" () in the form ar () T () + aN () N () by finding all four of these quantities.
(a) Suppose that a 120-vector a represents the age distribution of the customs in a bank, where a, is the mumber of customs with i year olds, for i = 1, .,120. Consider that 1 is one vector, whose elements are equal to 1, and that b is a 120-vector with b, = i. Use words (NOT equations) to explain the meaning of (i) 1"a bTa 1Ta (b) Consider that x, y and z are m-vectors, and that ß is a scalar. Discuss the efficient proceđure to compute B(x)"y+ß(x)"z. Show the mumber of additions and the number of multiplications of your suggested procedure.
8. A theme that will later unfold concerns the use of coordinate systems. We can identify the point (x, y) with the tip of the vector drawn emanating from the origin. We can then think of the usual Cartesian coordinate system in terms of linear combinations of the vectors ej = e2 = V2 V1 (2, –3) 42,–3} Figure 2.1.8. The usual Cartesian coordinate system, defined by the vectors ej and e2, is shown on the left along with the representation of the point (2, -3). The right shows a nonstandard coordinate system defined by vectors v1 and v2. The point (2, -3) is identified with the vector — 2е1 — Зе2. If we have vectors v1 = ,v2 = we may define a new coordinate system, such that a point {x, y} will correspond to the vector xv1 + yv2. For instance, the point {2, –3} is shown on the right side of Figure 2.1.8 Write the point {2, –3} in standard coordinates; that is, find r and y such that а. (», у) 3 {2, —3}. b. Write the point (2, –3) in the new coordinate system; that is, find a and b such…
At time t = 0, a particle is located at the point (5,9,4). It travels in a straight line to the point (2,1,3), has speed 5 at (5,9,4) and constant acceleration - 3i-8j - k. Find an equation for the position vector r(t) of the particle at time t. The equation for the position vector r(t) of the particle at time t is r(t) = (Type exact answers, using radicals as needed.) i+ j+ k.
Determine if the vector x̄=(-12i-j-5k) can be expressed as a linear combination of ū=(1,-1,0), v̄=(5i+k) and w̄=(1,1,-2). Are they linearly dependent?
Find a vector parametric equation r(t) for the line through the points P = (4, -3, 4) and Q = (3, -6, 2) for each of the given conditions on the parameter t. (a) If 7 (0) = (4, −3, 4) and 7(2) = (3, −6, 2), then r(t) = (c) If the points P and Q correspond to the parameter values t = 0 and t = -4, respectively, then = 3t 3,4-> -3 9 7(8) = Q, then 3t 121,6-321 ,10-t>
Use the function to find the image of v and the preimage of w. v = (1, 1), w = (-7z, 2, -20) + Var 2v. -v. 2. V1 + V2" 2 2 (a) the image of v (b) the preimage of w (If the vector has an infinite number of solutions, give your answer in terms of the parameter t.)
Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4V2 - V1, 4V, + 5v,), v = (1, –4, -3), w = (5, 22) (a) the image of v (b) the preimage of w (If the vector has an infinite number of solutions, give your answer in terms of the parameter t.)
Chapter 11, Section 11.3, Question 033 If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from point P to the line L is equal to the length of the component of the vector AP that is orthogonal to the vector AB. Use the method above to find the distance from the point P(-3, 1,7) to the line through A(1, 1.0) and B(-2,3, -4). Distance = Edit Click if you would like to Show Work for this question: Open Show Work

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