If a(1) = 2, and a(k) = 5a(k-1) for all integers k >= 2, then what is the 4th term of the sequence?

Q: (a) Find the orthogonal trajectories of the family of curves x* + y - 6x y = constant. (6) Show that...

A: According to our guidelines we can answer only one question and rest can be reposted. 

Q: Solve the recurrence an= 4an-1- 4an-2, ao=1, a1=1

A: a2= 4a1 - 4a0 So, a2= 4×1 - 4×1=0 Again, a3= 4a2 - 4a1 So, a3=4×0 - 4×1 = -4 Again, a4= 4a3 - 4a2 So...

Q: In the question that follows, the "Units Digit" or the "Unity Digit"of a number is the last digit in...

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Q: Find the extreme values of f on the region described by the inequality. (If an answer does not exist...

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Q: and W Consider the subspaces V = {(x. v. Z. w) : 6x = w, y = 3z} ((x, y, z, w): y-4z + 2w = 0} of ve...

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Q: Let y be a solution of the differential equation * + (1+ )y= =, where x > 0 such that y(1) =1+÷. If ...

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Q: For the following complex numbers; perform the indicated operations. Express results in rectangular ...

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Q: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector orthogo...

A: Given vectors are y=466−1, u1=1101, u2=−120−1 and u3=−1011. We have to write the vector y as a sum o...

Q: Q. Sketch the given region and then evaluate appropriately xy şdydx 1+ x2 + y (i)

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular ...

Q: ind and classify all critical points of the function f(x,y) = 3x²y + y³ – 3x² – 3y² + 2.

A: We have to find and classify the critical point of f(x,y).

Q: Find k such that the function is a probability density function over the given interval. Then write ...

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Q: For each of the following, draw possible diagrams that match the given measurements. Then calculate ...

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Q: Use mathematical induction I to prove that for all integers n2 3, 2·3 + 3 · 4 + ·· ·+ (n – 1) · n = ...

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Q: Prove using the formal definition of a limit that the following sequence converges: +00 S-n3 + 2n – ...

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Q: Let L: M2x2 → M2x2 be the linear transformation defined by L(A) = : 14, %3D 13 for matrix A in M2x2....

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Q: Sx². cos x-5 du 1-sin2x

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Q: Q1 Assuming that the equations in Exercises 25-26 define y as a differen- tiable function of x, use ...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: Consider the vectors [1,0,0,-1]; [0, 1, 1, 0]: [1, 1, 1, 1]; [1, 1, 1, 0) (a) Show that they do not ...

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Q: Please solve using Cramer's Rule.

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Q: 2z x(z) = 2 1 2

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Q: Show that E is a measurable set if and only if for every E > 0 there is a closed set F and an open s...

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Q: Let V be the vector space of polynomials of degree < 2 with real coefficients, endowed with the stru...

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Q: 1. Find the surface area of the region S in the plane z = 3x + 2y such that 0 <x < 10 and 0 < y < 20...

A: We have to find the surface area of the region S in the plane z = 3x + 2y such that 0&lt;=x&lt;=10 a...

Q: Matrix A: 1 3 4 6.

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Q: Consider the three points A(-1,2,0), B(-4, 5,0) and C(-2,6, –4). You are given that, -3 AB = and AC ...

A: Consider the points A(-1,2,0), B(-4,5,0) and C(-2,6,-4) And Given AB→=-330,  AC→=-14-4 Projection of...

Q: (a) Create a graph with six vertices of degrees 2, 2, 2, 3, 4 and 5. Construct the matrix of the gra...

A: Multipart:    We know that , degree of vertex of graph G is the number of edges passing through it. ...

Q: 3 -2 -45 -5-

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Q: Determine whether S is a basis for the indicated vector space. S = {(0, 0, 0), (2, 4, 6), (6, 3, 2)}...

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Q: Graph an appropriate periodic extension of f(t) = 3t, 0<t< T, and hence find its half-range cosine s...

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Q: Consider a closed storage tank S with walls given by the curved surfaces x = y', z > 0 and r = 2 – y...

A: 1st we will draw the diagram of tank and then find limit for all variable to use integration as surf...

Q: Factor 977101 by Pollard's p-methond; use the function f(x) =x+1 with seed xo = 2.

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Q: Determine the area bounded by the conic sections y = x² – 6² and y = 6² – 2². O 576 O 183 O 281 O Th...

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Q: A. Directions: Refer to the figure below in answering the following. 1/2 3. 4 6. 1. If mz3 = 60, wha...

A: According to our guidelines we can answer only three sub-parts and rest can be reposted. 

Q: II. Determine whether or not the following sets of vectors {u , v , w} are both orthogonal and ortho...

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Q: Over the past 40 years, Interest rates have varied widely. The rate for a 30-year mortgage reached a...

A: Given: A home sells for $125,000. A down payment of $25,000 can be made. So, $100,000 needs to be bo...

Q: (-1)" x2n + (2n+8) (-1)" x2n+1 (2n +4) Let y= 2 be the power series solution to the I.V.P n=0 y" +p(...

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Q: Finch eign Valucs and eiguvecmo for the salloes or the ollawi

A: Given A = 344-3

Q: Let T: P3 Pa be the linear transformation defined by T(at3 + bt2 + ct + d) = (a - b)t3+ (c- d)t. The...

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Q: Q2/ Solve the differential equation by using the appropriate method y' = (x + y – 5)²

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Q: Being fa differentiable function. Consider the relation where z is implicitly defined in terms of x ...

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Q: Find the equation of the tangent line to the graph of the function at the given value of x. f(x) = x...

A: Given f(x) = x2 + 5x

Q: Consider the function sin sin(xy) = y a)use implicit differentiation to find the derivatie y(x) at ...

A: Given that  function sin sin(xy) = y To find the derivative of tye function and equation of the tang...

Q: 1. Fill in the blanks Let y be a solution of the differential equation cos y sin y de = (1), where s...

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Q: A possible graphical representation for the surface of equation (y -k)? +B(x-h) = 0, with B > 0, is:...

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Q: Locate the centroid of the solid generated by the area bounded by 2x+y=D2, ×3D0, y%3D0 about x-0. O ...

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Q: An investor has at most $40,000 to invest in government bonds, mutual funds, and money market funds....

A: To determine the amount of money that should be invested in each fund.

Q: Find the angle 0 between the vectors. (Round your answer to two decimal places.) u = (-3, –5), v = (...

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Q: Give an example of a linear operator TE L(R*") which is not diagonalizable. Justify your answer.

A: give an example of a linear operator T∈Lℝ3,1 which is not diagonalizable. justify ur answer. it is k...

Q: Let T E L(F<") such that T( for any z, w E F. (a) Find all the eigenvalues of T and their correspond...

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Q: Let z = axy1 + bx³y*, with a and b constants. P is a point given by (1, 1) and it is known that: dz ...

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