Find the last two digits of 3125 and 39999. Find the last three digits of 7403. only HANDWRITTEN answer needed ( NOT TYPED)

Q: Find the coordinate matrix of x in Rn relative to the basis B'. B' = {(8, 11, 0), (7, 0, 10), (1, 4,…

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Q: A certain investment is subject to continuous compounding. The value of the investment after t years…

A: The given investment function V=4000e0.04t. We have to graph the function and find whether the graph…

Q: Given the following bases for R2, find P, the change of coordinates matrix from B to C. C-B -13…

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Q: Use a least squares approximation to find the best linear fit (i.e., the best line) L(t) = C + Dt,…

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Q: Simplify your answers if possible (write the answer in the simplest form, cancel all common factors…

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Q: Prove by contradiction the following theorem For integers, the sum of two odd numbers is even.

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Q: Find the general solution to the nonhomogeneous equation using the method below: y^2 + 8y + 25 =…

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Q: CAN YOU SOLVE |x² - 9 = 3x - 9|

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Q: Using the Venn Diagram find: A' 8 U 1 A 2 9 5 3 11 7 6 B 4 12 10

A: Here from given venn diagram we have to find the value of A'.

Q: THEOREM 9.5. Let X be a Hilbert space and let A: X₁, X₂, ... be an orthonormal set in X. Then, if EF…

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Q: Transform the differential equation 9y" +14-81 - 126y= 5et y(0) = 0 3/(0) = 0 3'(0) = 1 into an…

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Q: 2. Find projection of the plane 2x - 3y + 4z = 5 under the matrix multiplication with the matrix A.…

A: Ans-In this we have to find  projection of the plane 2x - 3y + 4z = 5 under the matrix…

Q: Use a least squares approximation to find the best linear fit (i.e., the best line), L(t) = C + Dt,…

A: The given problem is to find the best fit line L(t)=C+Dt by finding the values y-intercept C and…

Q: The volume of the tetrahedron enclosed by the coordinates planes and the plane 2x+4y-z = 6 is given…

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Q: Prove that if a and b are integers of the form 4n+ 1, then ab is of the form 4n +1

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Q: IV. Write the general form of the following equations of the lines that pass through the point and…

A: We have to write the general form of the equation of line passing through the point (-3,2) and is…

Q: The base of a certain solid is the triangle with vertices (0,0), (2,0), and (0,4). Cross-sections…

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Q: wer: Find the determinant of the following 2 x 2 matrix. ¯–1 -7] -6 -3

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Q: A scientist observed that the speed S at which certain ants ran was a function of T, the ambient…

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Q: The depth (in feet) of water at a dock changes with the rise and fall of tides. The depth is modeled…

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Q: Which of the answers below is the ordering of these running times from fastest to slowest? a)…

A: We have to arrange the following sequences in order from fastest running times to slowest. (a)…

Q: Find the local maximum and minimum values and saddle point(s) of the function. You are encouraged to…

A: Given: A function fx ,y=x3+y3-3x2-9y2-9x. To Find: Maxima, Minima, and saddle points and also plot…

Q: Sketch the graph of the plane curve r(t) and the vectors T(t) and N() at the given value of t. r(t)…

A: The objective is to graph the plane curve r(t) and the vectors T(t) and N(t) at the given value of…

Q: Prove that the closed interval [a, b] is homeomorphic to [0, 1]. Use topological definition of…

A: Please to the answer in the next step

Q: 2. Prove (choose the most convenient method of proof) For 2 ≤ n ≤4,n² ≥ 2".

A: To Prove: For 2≤n≤4,  n2≥2n.

Q: 2. Solve the initial value problems 2.1 x²y + xy + y = 0, y(1) = 1, y'(1)=2 2.2 x²y"-3xy' + 4y= 0,…

A: (2.1)  Given IVP is x2y'' + xy' + y = 0   ,    y1 = 1 ,  y'1 = 2                    Tis is…

Q: #6 Find the stability of the equilibrium value(s) from Problem #5. Graph the equilibrium (as a…

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Q: Maximize the function P= 10x - 4y subject to What are the corner points of the feasible set? The…

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Q: Problem 4. Below are two views of the surface z = x²(x + 1)(2-x)e-y² Find the equation of a plane…

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Q: Let T: R² → R² be the linear transformation that first rotates points clockwise through 120° (2/3…

A: Let T:ℝ2→ℝ2 be the linear transformation that first rotates the point clockwise through 120° and…

Q: Recall that lines through the origin are subspaces of R². 2x and W₂ is the line y = If W₁ is the…

A: Given, W1 is the line y=2x and W2 is the line y=-3x ,we have to find which statements are true about…

Q: C a e Give the adjacency matrix of the graph with lexiographically ordered rows and columns.

A: To give the adjecency matrix for given graph.

Q: Do the series converge absolutely or condition n (2) Σ(-1)^+1 n +3 (b) Σ(-1)"+1 n! 3√√n (c) Σ…

A: Check whether given series converge absolute or conditional.

Q: Orthogonally diagonalize the following symmetric matrices. (a) 13 2 2 (b) 23 2 (c) 1 2 2 4 -4 -2-4 4

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Q: 2. (a) r = 2 (b) 0 = 2 Match each equation with its description: O Vertical line O Horizontal line O…

A: (a) In the graph for r = 2, θ varies from 0 to 2π.       i.e., if we try to convert in rectangular…

Q: B: Represent the area of the regions A, as a double integral in polar from, then evaluate it. A₁…

A: The give figure is: We have to express area of the region A1 as double integrals in polar form and…

Q: Integrate f(x,y,z)=18xz over the region in the first octant (x,y,z > 0) above the parabolic cylinder…

A: Ans- In this given question we have to Integrate f(x,y,z)=18xz over the region in the first octant…

Q: Problem 4. When attempting to compute the expectation of the Cauchy random variable in the previous…

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Q: Find the local maximum and minimum values and saddle point(s) of the function. You are encouraged to…

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Q: Consider a spring-mass system that is acted upon by an external force in its direction of motion.…

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Q: The surface defined by z = f(x, y) = 2x + y hovers above the region defined by the graphic below.…

A: The given function is z=fx,y=2x+y and the given region is To find the volume of the space above the…

Q: . Show that SML arg min P(r|s) = arg min P(sr) = SMAP SEE(S) SEE(S) for Ps(s) = E(S)-¹.

A: note : Since you have posted multiple questions, we will provide the solution only to the first…

Q: Let A = {1,2,3,4,5,6}, and consider the following equivalence relation on A: ! = {(1,1), (2, 2), (3,…

A: Given that  A=1, 2, 3, 4, 5, 6 and consider the following equivalence relation on A: R=1,1, 2,2,…

Q: Problem 3. Find the general solution of the differential equation r²y" + 4xy' + 4y = 0.

A: The given equation is           x2y" + 4xy' + 4y = 0   . . . . . . . . . . . . . . (1)  Let,       z…

Q: 3. Do a direct proof using domain knowledge: The sum of three consecutive integers is divisible by…

A: I have explained everything with in the solution. Please go through that.

Q: Find the volume of the solid obtained by rotating the region bounded by the curves: y=1/x5, y = 0,…

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Q: Exercise 3. Let T be a set such that |T| ≥ 3 and let G = Sym(T) be the group of permutations of T.…

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Q: A mirror in the shape of a rectangle capped by a semicircle is to have perimeter 100 inches. Choose…

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Q: Set up the system for the linear least squares approximation for the data (-2,0), (2,3) and (3,1)

A: Given: Data points are -2 ,0 ,2 ,3 ,3,1. To Find: Set up a system for linear least square…

Q: 1 X₁ + 2x₂ + 4x₁0 2X₂ + 5 = X₁ 3X₁ = X 3 Ⓡ X₂ + x3 = 1 X₁ + x3 = 2 2X₂ + x₁ = L 3 Gaussian method…

A: x1+2x2+4x3=0x1-2x2=53x1-x3=0∴1241-2030-1x1x2x3=050124:01-20:530-1:0→R'2=R2-R1124:00-4-4:530-1:0→R'3=…