Find the present value of a continuous income stream F(t) = 20 + 5t, where t is in years and F is in thousands of dollars per year, for 15 years, if money can earn 2.4% annual interest, compounded continuously.

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Q: II. In Fi

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Q: Let F : R" → R™ and g : R" → R. Prove that d(gF)[a; h] = g(a)dF[a; h] + F(a)dg[a; h].

A: let the functions be  F:ℝn→ℝm , g:ℝn→ℝ prove that  dgFa;h=gadF[a;h]+F(a)dg[a;h]

Q: 5. Write the formal proof that 2"+2 + 32n+1 is divisible by 7 for all positive integers.

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A: Let f(x) = x3 + 3x2 - 10x - 24

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Q: 124x1 + 245x2 + 35x3 + 24x4 = 24 %3| 356x + 24x2 + 35x3 + 75x4 = 2 %3D 24x1 + 56x2 + 35x3 + 67x4 = 4...

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Q: Consider the series (In(2n + 1) –- In(2n - 1)). n=1 (a) Let a, = In(2n + 1) – In(2n – 1). Does {a,} ...

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Q: Problem 2. Let a = (1,6, –4), b = (1,2, 3) be vectors in R3. (-2, —9,8), с %3 (3, 19, –7), d = (3, 1...

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Q: a. Consider the system of differential equations given by: Yı(0) Y2(0) -3 34 y = where some initial ...

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Q: Please answer with explanation. I will really upvote

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Q: 4n – 1

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Q: ördering or arrangement of the elements of a given set of objects. a. Permutation b. Combination c. ...

A: As we know  P(n, k) = (n!) /(n-k)!  

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Q: 9. Let F : R" → R". Prove that for each a the mapping h→ dF[a; h] is linear on R".

A: Given: F:ℝn→ℝm   To prove: For each a, the mapping h↦dFa;h is linear on ℝn  

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Q: l2: = 1-s, y = 3+ s, z= 3+2s l: =1+t, y = 2- 2t, z= -3+t Determine whether the given lines are paral...

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Q: Let C: |z-i|=9. Then ſ. 1-z -dz = z(z+1) а) 0 b) 2ni c) -2ni d) 4ni e) — 4лі f) 2п а. b. С. d. е. O ...

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Q: H.W: Given the following matrices, please solve the questions below and if you can't solve the probl...

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Q: The degree sequence of a graph is the sequence of the degrees of the vertices of the graph in non-in...

A: We have given that , degree sequence ,  4 , 3 , 3 , 2 , 2. We need to find number of edges. We know ...

Q: Use the cofactor expansion to compute the following determinant: 10 -9 3 det -5 6 -7 = 0 -7 1 -9

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Q: A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 ...

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Q: The temperature T (in degree centigrade, °C) in a solid metal sphere is given by the function e-(2+y...

A: Given T(x,y,z)= e-(x2+y2+z2)1)The rate of change of temperature in the direction of X-axis is ∂T∂X∂T...

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A: We can solve this by using given information

Q: 1. Suppose b,, b2, b3 .. Is a sequence defined by b, = 3, b2 = 9, bu2 + br-1 for all integers k >= 3...

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Q: 5. S sen 8 cos/3@ de

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Q: In this problem you will use variation of parameters to solve the nonhomogeneous equation y" – y = 6...

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Q: Consider the series >(In(2n + 1) – In(2n – 1)). n=1 (a) Let a, = In(2n + 1) – In(2n – 1). Does {a,} ...

A: Introduction: For an infinite series ∑n=1∞an, the sequence of partial sum SNN=1∞ is expressed as SN=...

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Q: 3. The fractal C is constructed as follows. (i) Begin with the line segment Io = [0, 1]. (ii) Remove...

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Q: QUESTION 7 An optimal solution requires that all artificial variables are there are no special requi...

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Q: Find y as a function of a if y" – 8y" + 15y/ = 8e", y(0) = 28, y(0) = 14, y"(0) = 12. y(x) = 52.04-(...

A: We have to find the solution of differential equation.

Q: Question 3. Use the method of finite-differences to find a closed-form expression for the sequence 0...

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