find u (x, t) for 0 < x < 1 and t> 0 which solves Ut - Uxx = e¹, u (x,0) = 1, u (1, t) = u (0, t) = 0.

Q: Show that for 0≤k≤n (-1)* (α), (a)n-k=(1-α-n) k Note particularly the special case α = 1.

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Q: Advanced Math Question

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Q: When should they stop their engine so that they reach the space station? What is there position when…

A: We will use the fact that once engine is stopped the space craft will move along tangent to the path…

Q: (a) Give an example of a bounded sequence that diverges.

A: Since all questions are different ,so according to the guidelines I will solve first question. That…

Q: 6 -4 Find an orthogonal basis for the column space of 2 6 1 O 0 -2 0 1 -2 0

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Q: Using any technique from this class that you like, show that if (sn) is a Cauchy sequence of…

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Q: Find the solution to the recurrence relation an 2an-1 +5an-2 = 0, ao = 1, a₁ = 5 -

A: Given a recurrence relation an-2an-1+5an-2=0,  With initial conditions a0=1 and a1=5. We have to…

Q: b) Consider the following recursive sequence s So = 1, Sn = 2 * Sn-1. Prove for all i 20 that s; =…

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Q: - Let an = NCN such that la 3+1. Use the definition of convergence to show that an →3 as n →∞o. That…

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Q: Snack A provides 10 grams of protein and costs 2 dollars, snack B provides 6 grams of protein and…

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Q: Find an orthogonal basis for the column space of 6 -4 2 6 1 0 0 1 0-2 -2 0

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Q: Determine whether the linear transformation T is one-to-one and onto. a -B- b T: R³ (a) one-to-one…

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Q: Show that (u₁, u₂ is an orthogonal basis for R2. Then express x as a linear combination of the u's.…

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Q: Determine whether the set of vectors is orthonormal. If the set is only orthogonal, normalize the…

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Q: Blake receives a gift of $80.00. He spends $60.00 on a new game and $8.00 on snacks. a. Draw a…

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Q: 2. Show that the equation. has no integer solutions. 4x = y² + z² + 1

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Q: a) Similarly to the unit vectors i and j in Cartesian coordinates, we can define unit vectors u, in…

A: To find the unit vector in the radial direction ur and uv in the azimuthal direction for any point…

Q: Solve the system by the method of your choice. X y 3 OB. = -1 3 3 x + 3y = - 11 Select the correct…

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: Find the Area of the Illustrated Figure. Write the result as a decimal as needed. ft2 Assume…

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Q: Evaluate ∞     n = 0 (−1)n 2n + 1 as 1   0f(t) dt where f(x) =  ∞     n = 0(−1)nx2n =  1 1 + x2

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Q: 1. For each of the following binary relations p on Z, decide which of the given ordered pairs belong…

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Q: i=1 ow, assume that the series 1 an with nonnegative terms an> 0 is a convergent series. Use ✓n= e…

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Q: Determine a vector equation for the line of intersection of the planes: 9z - 6x = 63 and 4x - 6y +…

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Q: Suppose g is a function which has continuous derivatives, and that g(6) = 1, g′(6) = −3, g″(6) = −2,…

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Q: Find a formula for sin(3thetha) in terms of sin(thetha) and cos(thetha) using the sum and double…

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Q: Consider sets in R^2 with the usual topology. Is the closure of a set connected by paths connected…

A: To Find : Is the closure of a set connected by paths connected by path ? Is the converse true or not…

Q: Use summation properties and formulas to rewrite and evaluate the sum. 21 Σ ( − 9i² − 6i + 9) i=1

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Q: 1. In the diagram below, there are 9 points and 8 lines: (a) Let be the relation between the points…

A: Given, In the diagram below, there are 9 points and 8 lines. a) Let ⋄ be the relation between the…

Q: Approximate the area under the curve graphed below from x = approximation with 4 subdivisions. →→ -1…

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Q: f(t) = cos 3t sin t

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Q: Suppose an urn contains red, green, blue, and black marbles. Suppose you draw marbles from the urn 5…

A: If an event with n different possibilities are repeated r number of times, then the number of…

Q: Not everyone pays the same price for the same model of a car. The figure illustrates a normal…

A: Given mean = 22,000 and standard deviation = 1000 we have used the 68-95-99 rule to compute the…

Q: Find an equation for the plane through the points (5, −5, −7) and (14, −5, −9) and perpendicular to…

A: The given problem is to find the equation of plane that passes through the given points and…

Q: Evaluate the surface integral. [[ (x+y+z) dS, S is the parallelogram with parametric equations x = u…

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Q: Show the faction 13/17 is less and the fraction 4/5, which is less than the fraction 14/17 without…

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Q: What are 3 irrational numbers between 4 and 5? And 3 irrational numbers between 7 and 8?

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Q: Use Orthogonal Similarity Transformation to transform the following matrix into Hessenberg Matrix 21…

A: To transform the following matrix into Hessenberg Matrix using orthogonal similarity transformations…

Q: Solve the inequality -2x+3 ≤ -5. a. X24 b. x54 О А О в о с O D с. X2-4 dx>4

A: -2x+3≤-5⇒-2x≤-8, by subtracting 3⇒x≥4, by multiplication of -12 HERE ANSWER: x≥4 i.e., A…

Q: Show directly from the definition that if an is a positive real sequence with limn→∞ an = 0 and…

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Q: Consider the given graph. b C Does the given graph have an Euler circuit? (You must provide an…

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Q: Solve the system of linear equations using matrices. -X = 2 + 5y + 5z -5y + 4z = 19 - 4x x + 5y -z =…

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Q: A = [ 2 B =[ 3 C[ 1+i 5+2i 1 + i 15+i 3-i; i; 1-4i; 3i 52i 1- i 7 1 5 3+ i 4 + 3i; 3; -i i 2+5i; 4i…

A: The given matrices, A=25+2i3-i5-2i74+3i3+i4-3i1B=31+ii1-i13-i31C=1+i15+i1-4i3i5-i2+5i4i-3+i2-7i We…

Q: 9. O. y 7/2 a 37/2

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Q: Graph the polar equation by dragging the number of petals point, they symmetry point, and the other…

A: Given: r=-18cos4θ We have to graph the given polar equation.

Q: Topology Let X and Y be two compact spaces, show that X×Y is compact.

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Q: On May 15th ​, Alberto rented a car with a full tank of gas and 10,496 mi on the odometer. On May…

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Q: P2 Consider the two power series f(x) = x + Σ n=0 8 g(x) = Σ n=2 (3x)2n+1 (2n + 1)! (x + 1)n 3nn…

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Q: 2. Examples. Justify your answers briefly. (a) Give an example of a nonconstant complex sequence…

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Q: Let A = (²2²) 22 Find et and the general solution to X' = AX + (1)

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