Use separation of variables to find a product solution to the following: ди ди x=y Ox ду u=c --( * )*² Он=c x 3y"2-1 u=cpx;+ly":-1 °* (²) 2 И=c

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Q: The function f(t) = 8000 e -0.02t represents the rate of flow of money in dollars per year. Assume a…

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Q: please answer the same way above the former one. a) What is the velocity of the particle at t = 2.8…

A: Answer of (a) as follows :

Q: ^. Use linear algebra techniques to find the center and the radius of the circle a(x² + y²) + bx+cy…

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Q: Find the volume of the colid obtained by rotating about th bounded by y=2x² axu the region and yo

A: First we plot the curves and identify the region which is to be revolved about y-axis. at…

Q: Given 25 __3__8 what digits must be placed in the blank to make it divisible by 9 a. 8 and 9 b.6 and…

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: Johan trains for running. He doesn't train in 2 days. He runs 6 km on a day 2 days a week. The rest…

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Q: ntegers, fractions, multiples

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Q: 13. Show that the following functions are contin- uous but not differentiable: (a) z (b) |z²2 (c)…

A: 13) We need to show that given functions are continuous but not differentiable. We know that , a…

Q: Find the Inverse Laplace Transforms of the following. 4 1) | S-3

A: We will use laplace transformation table to find inverse laplace transformation

Q: Determine whether the set {P1, P2, P3} is linearly independent in P2, where p₁ = 2+x+3x² + 4x³, p₂ =…

A: Let V be a vector space . let v1,v2.....vn ∈V are linearly independent iff c1a1+c2a2+...+cnan=0…

Q: x3 - 3x²y = c =

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Q: Determine whether the set [p., pa, p3] is linearly Independent in Pa, where pi= 3+x+3x²+4x3 Pa = 4+…

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Q: Triplets Peter, Reeta and Nikita have two for getting home from school each day: cycle on a tandem…

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Q: Among all rectangular solids defined by the inequalities 0≤x≤a, 0≤y≤ b, 0≤z≤ 1, find the one for…

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Q: T: R² R² rotates points (about the origin) through 31/2 radians (in the counterclockwise direction).

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Q: 1. f sin(u-v)y(v)d(v) + y(u) = 10u 2. x"(t)-5x' (t) + 10x (t) = e-3t, x(0) = 0, x'(0) = 0

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Q: If V is the space of all vectors in R*that are orthogonal to W = Span{(1,0,2,1),(0,0,1,5)}, then…

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Q: 4. Solve the system by using the matrix exponential 1 480 x' = 0 1 -2 -5 -4

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Q: Prove using Mathematical Induction that: The sum of the squares of the first n positive integers is…

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Q: 5. Proving (Learning Packet #1) Given: LVLOE Prove: LOVE R is the midpoint of LV and OE. L R E V

A: It is given that  LV  is perpendicular to OE and R is the midpoint of LV and OV To prove LO≅VE Take…

Q: 1. Solve the following Linear Systems of Equations by Gaussian Elimination: 2.) 3x + 3z = 0 2x +2y =…

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Q: Consider a system with the following state-space representation X(t) = [₁]x(t) + B₂Ju What values of…

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Q: and is directed to the right and up, making a , and the acute angle it makes with the ver place and…

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Q: When (100-x)¹/2 s(x) = 10 ,find them. (1) 17P19 0≤x≤ 100 (2) 15936 (3) 15/13936 (4) μ36

A: Let us start solving the problem step by step  Given s(x) value x varies between 0 and 100

Q: 2. It is possible for two angles of a triangle in the hyperbolic plane to each have a measure of 2.

A: In hyperbolic geometry , a hyperbolic triangle is a triangle  in the hyperbolic plane. It consists…

Q: I. Evaluate each determinant. -5 -3 -4 3

A: The determinant of given matrix -5-33-4 is  -5-33-4 =(-5 x-4)-(-3 x 3)=20+9=29

Q: If A = B = C = are the coordinates of a triangle, compute: A с B length of AC units length of AB…

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Q: II. SET-UP a triple integral that will solve for volume of the solid S bounded by the sphere x² + y²…

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Q: What is the value of the summation? a.) 2 3 Σ Σ(i+j) i=1 j=1 b.) 8 Σ 3· 2 j=0 c.) 4 Σ (-2) j-0

A: a) ∑  i=12∑   j=13 (i+j) b)∑j=083·2j c)∑j=04-2j We have to find the value of the given summation .

Q: TON (B) Discuss the convergence of the given sequence: a(n) = sin 2

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Q: Given the plot of normal distributions A and B below, which of the following statements is true?…

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Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x² + y² + z² = 1 is…

A: The given problem is to find the maximum and minimum of temperature equation on the given sphere of…

Q: Let Z -[₁ 2i -2+i -3i 3-2-1-i] 2+1] and -2 1-4 and W-1+34 2-3. Then, solve fo

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Q: 16. Given: 6x + 15y = 51. What are the possible solutions of x in the given Diophantine equation if…

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Q: c{ts Find the Laplace Transform L e-t sin t t dt}

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Q: Sketch the solid whose volume is given by the following integral and evaluate the integral. S/2/4…

A: Note : φ= constant  , represents a cone  and ρ= constant  , represents a sphere .

Q: Find the inverse of the congruence 6x = 1 (mod 29) using Euclidean algorithm. (Show your work)

A: The given problem is to solve the given modular equation by find the inverse of congruence using the…

Q: 1. Find the cofactor of 6 in matrix D 9 8 4 2 7 -9 3 4 D= -3 3 9 2 6 8 W NW 3

A: Given matrix  D =98427-9346-3238932 The co-factor of 6 in matrix D =-1i+j 842-934932 Here i=3 and…

Q: 11. SET-UP a triple integral that will solve for volume of the solid S bounded by the sphere x² + y²…

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Q: GIVEN THE FOLLOWING MATRICES 5 -2 -4 2 3 2 4 E = -4 -4 0 4 -3 3 FIND THE FOLLOWING 1. (1,2) entry of…

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Q: Find the convergence radius and convergence interval of the next series 14. Σ (-2)" √n (x+3)" n = 1

A: Problem is solved using concept of convergence.

Q: 1.What is the GCF of 16,  -24,  and – 40 2.The product of two numbers is 2700. If their GCF is 15,…

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Q: Compare and contrast the Fundamental Theorem of Calculus and the Fundamental Theorem of Line…

A: compare and contrast the fundamental theorem of calculus and the fundamental theorem of line…

Q: Using Fixed Point Iteration Method in Excel, Given: f(x) = e^x - 3x^2=0 and its new function as sqrt…

A: The fixed point iteration method uses the formula: xn+1=ϕ(xn) to perform the iterations an to…

Q: 1.4.5 Given that λ = 1 is a three-times repeated eigenvalue of the matrix -3 -7 -5] A = 4 2 2 2 1 3…

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Q: 1. Find the Inverse Laplace Transforms of the following. 3s 2) s²-4 2

A: L{cosat}=s/(s^2+a^2) L{coshat}=s/(s^2-a^2)

Q: 11. An ideal elastic string of length L is fixed at its right end, but its left end is attached to a…

A: The given problem is to find the solution for the given wave equation partial differential equation…

Q: Karim wants to invest $100000 in two investments at 8% and 10%. How much should he invest in each if…

A: The formula is I = Prt, Where I = interest earned, P = principal, r = rate of interest, t = time.

Q: matrix but not necessarily in natural order is called *       Unit Matrix       Scalar Matrix

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