Find all equilibrium points for the following system of equations: dr 10z (1 - 6) – 20zy dt dy = -5y + dt 20

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Q: 1. Points A(2,1,0), B (4,1,6), C(5,3,s) and E (-8,5,t) are the vertices of a triangular prism where…

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Q: Consider where E is the region above the cone z = 2/+ y? and below the top of the sphere a+y 22 4.…

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Q: 3. Consider a set of numbers B = {n E Z|1<n< 900} Answer the following questions. (a) How many…

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Q: 13. Solve the rccursive formula an = an-1 +1+2"-1 with ao = 0. Verify by %3D induction.

A: T

Q: (-1/3 2/3 2/3 2/3 -1/3 2/3 2/3 Exercise 1.1. Let M = 2/3 -1/3) This matrix describes a rotation of…

A: Given rotation matrix is M=-13232323-13232323-13.

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Q: 2. Consider the nonhomogeneous system Ax = b given by a1 + x2 = 3 2.x1 – x2 = 3 *1 – 2x2 = 1 Show…

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Q: 2. Let R = {(x, y) : x, y E R}. Prove or disprove that R is reflexive, symmetric and/or transitive…

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Q: Find the solution of the equation =e* cos y hich tends to zero as x - 0o and has the value cos y…

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Q: Find the indicated term in each arithmetic sequence. a. 15, 21, 27, ... 11 th term 2. 15th term b.…

A: Given, The arithmetic sequence are: a)  15, 21, 27,.....         11th term b)  a1=5, d=-3…

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A: (b) write down an equation for the revenue R. (c) find the coordinates of all the vertices of the…

Q: 2. (a) Find the exact length of the curve (i) r = 1+sin 0, 0<0< 27, (ii) r = 2(1+ sin 0), 0 <0< 27.…

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Q: 2. Solve the following homogenous differential equation dy 2ry = (a + 3y). |3D

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Q: 2. Let R = {(x, y) : x, y E R}. Prove or disprove that R is reflexive, symmetric and/or transitive…

A: Reflexive relation : A relation R is said to be reflexive if (x,x)∈R Symmetric relation : A relation…

Q: Find the general solution to the following differential equations. Solve them for y. dy а. ex+y + ey…

A: In (a) we can use method of seperation of variables. In (b) we can use method of solving linear…

Q: Using only the Laplace transform table to obtain the Laplace transform of the following functions:…

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Q: 1)2xsin-13x x+1 2)y = In- Vx-2

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Q: Exercise Use, mid point prdinote S dess x dx 0.799

A: The height of the each rectangle standing on each subintervals is the functional value at the middle…

Q: -. Consider the equation dy k -y = 0 dt2 for the motion of a simple harmonic oscillator. (a)…

A: Solution :-

Q: 12. Graph each polynomial function. leovlo a. P(x)= x(x² – 1) b. P(x)= x -6 c. P(x) =x* – 10x² + 6…

A: (a) Given, P(x)=x(x2-1).             ⋯⋯1 Calculate the x-intercepts of the function P by…

Q: 50. A coin and a 6-sided die are tossed. Make an array of ordered pairs of all possible results.…

A: If a coin and a 6-sided die are tossed then the total possible results will calculated as, if coin…

Q: Find the convolution of the two functions: f (t) = 2t and g(t) = (Cos 3 t. %3D %3D

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Q: (a) 8) Show that F = (y? - 4r, 2ry - sin(y)) is conservative. (b) Find a potential for F from part…

A: Here we use the partial derivatives to find the potential function and use the fundamental theorem…

Q: O Using Resolution method, show that KB E a, where KB = {(((P^ Q) → R) ^ (Q = R)) ^ (RAT)} and a=T

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Q: b. Find a rectangular-coordinate equation by eliminating the parameter t.

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Q: 6. For the directed graph depicted below do the following (a) find the adjacency matrix (b) find the…

A: Given the directed graph. (a) To find the adjacency matrix: If a directed graph G consists of n…

Q: Q.1/ Find the area of the region bounded by the line y = 1– x and the curve x = 3 – y?.

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Q: 1 Q3\ Evaluate f (x-2)(x-3)

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Q: 1. A large hotel is selling off its beds, before replacing them with new ones. There are two sizes…

A: Write four inequality in x and y representing the constraints :-

Q: Use X = X + X, = eAtC + eAt * e-As F(s) ds to find the general solution of the given system. x- (:…

A: We can solve this using given information

Q: Find T(t) and N(t) at the given point. r(t) = 8 cos(t)i + 8 sin(t)j; t = T() - /3

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Q: 1. Find the Laplace transforms of cosat – cos bt (a) t°sinat (b)te“ sin3t (c) +tsinat t sint sin5t…

A: 2)  We need to use Laplace Transformation of the second derivative to derive the following…

Q: -х - 5у — 5z%3D2 4х — 5y + 4z % 19 x+ 5y – z =-20 a) formulate the appropriate matrix for the system…

A: We have : -x-5y-5z=24x-5y+4z=19x+5y-z=-20 Part(a) The given system can be written as:…

Q: Solve the equation: u = a u 0 Uxx u(x, 0) = f(x), a(0, t) = u(L, t) = 0 %3D

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Q: 1. Use the substitution z = following differential equation xy, where z is a function of x, to solve…

A: Properties of integration  ∫1a2+x2dx=1atan-1xa+C∫xndx=xn+1n+1+CddxUV=UdVdx+VdUdx

Q: 3. Consider a set of numbers B = {n E Z|1<n < 900} Answer the following questions. (a) How many…

A: Given a set of numbers B=n∈ℤ|1≤n≤900. a. To find the number of elements in B divisible by 4 or by 9.…

Q: а (e) Let B = be any 2 x 2 matrix. COS a [sin a (i) Show that there are real numbers U11 and a such…

A: This is a multipart question having two or more interrelated subparts. As per company policy, we can…

Q: 11. Find the sum of each series. 5 10 8 a. (3+4i) b. i=3 c. (2i + 3) с. i=1

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Q: 2a + 2b- c+d = 4 4a +3b - c+ 2d 6 8a + 5b – 3c +4d = 12 3a +3b – 2c +2d = 6

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Q: A property owner wants to fence a garden plot adjacent to a road, as shown in the figure. The…

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Q: Solve the equation: u a uxx 0 0 u(x, 0) = f(x), u(0, t) = u(L, t) = 0_ %3D

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Q: а + 26 +3с- 2d %3 6 За +25-с + 2d - 4 2а -b - 2с-3а%3D2 2а- 3Ь +2с+ а 3D8

A: To solve given system of equations we use the gauss - Jordan elimination method.First of all we…

Q: Use color theorems to show that the chromatic number of a USA graph is four. Please explain why the…

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Q: ct the Fourier series for the function f(x) = (T-x)² for 0 <x < 2n ? %3D

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Q: Use the quotient rule to find the derivative of the following x - 9x + 5 y= X +7

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