THe instantaneous rate of change of the value of a certain investment (P）is proportional to its value. That is to say dP/dt = rP if r = 7 and P(0) = 2500:  P(t) = ??

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Q: Find The F.T of the following signals using differentiation prop -2 2. 2 t

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Q: Let S be the set S={a,b,c}. 1. Write all the elements of the power set of S: the set of all subsets…

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Q: Express the range of each function using roster notation. (k) Let A = {1, 2, 3). f: P(A) → P(A). For…

A: A=1,2,3So P(A)=∅,{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}.Thus…

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Q: Problem 6. Prove that the vectors V₁ = (1, 0, -1), V3 = = (0, -3,2) form a basis for R³. Express…

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Q: This question refers to the following information. 12 10 8 6 2 0 Adult Student Marital Status…

A: Number of widowed student =5 Among widowed number of female 3 Therefore the percentage of  widowed…

Q: Apply a second derivative to identify a critical points as a local maximum, local minimum or saddle…

A: The total volume is 450 cm3 We know for a rectangular box, volume = length×breadth×height

Q: 3a4b2c a + 3b4c = 2a + 3c = 11 = 28 - 31

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Q: (a) Is the sequence arithmetic, geometric, or neither? (b) Give a recursive definition for the…

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Q: Any proper subgroup S of a nilpotent group G is proper subgroup of its normalizer in G.

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Q: Show that if p is a prime number, a and b are positive integers and p | ab, then p | a or p | b.

A: The objective is to prove that if p is a prime number, a and b are positive integers and p | ab,…

Q: Theorem 1 (Limit Comparison Test). Let an and bn be sequences such that an ≥ 0 and bn > 0 for all n…

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Q: 4. Find the measurements of a box shipped via USPS that will maximize the volume in order to give…

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Q: Problem 5. Show that for any 3 distinct integers, the sum of two of them must be even. Using this or…

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Q: 7. Express the shaded region in terms of A, B, and C and their com- plements. B

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Q: 1. Give an example of one codeword c E F. Explain how you know it is a codeword. (Note, provide a…

A: Note:- Due to a time limit, we can answer the part (A) only with its sub-parts. For the remaining…

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

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Q: Determine all distinct values of Vi and plot these values in the complex plane.

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Q: H.W: Solve the following equations... 5 3. Begynn **********

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Q: 7. Let A be a square matrix of order 4 and det A = 8. Let A be a square matrix of order 7 and 8.…

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Q: Let G be a noncyclic group of order 21. How many Sylow 3-subgroupsdoes G have?

A: Let G be a noncyclic group of order 21. ⇒G=21=3×7 We know that Sylow's theorem, if G be finite group…

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Q: 1 !] B = 1 1 1 -2 1 denote the subspace which is spanned by the two vectors V1, V2. Set V1 = " = And…

A: The given vectors are v1 = 1111 , v2 = 101-2 and b =1001 Also <v1, v2>=0 i.e. v1, v2 is an…

Q: Use a truth table to determine whether the two statements are equivalent. (r^ q) v p and r ^ (q V p)

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Q: The formula for 1 liter of an elixir contains 0.25 mL of a flavoring oil. What is the per- centage…

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Q: Find all relative extrema of the function. Use the second derivative test where applicable. (If an…

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Q: x Find the natural domain of the function f defined by f(x, y) = and /25 - x² - y² draw a sketch of…

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Q: 2+4+6+ + 2n = n(n+1) for all n ≥ 1. In your own words, what is the difference between the principle…

A: (a) Let P(n): 2+4+6+...+2n=n(n+1) . Let n=1. 2.1=1(1+1). So P(1) is true. Let P(k) is true for some…

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A: Fundamental counting principle: The fundamental counting principle states that if there are p ways…

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Q: Find a general solution to the given Cauchy-Euler equation for t> 0. 2d²z dt +17t- dt +64z=0 The…

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Q: (i) Let A = {1, 2, 3). f: Ax A → ZxZ, where f(x,y) = (x,y+1).

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Q: For each of the following, if it is true prove it and if it is not true give a specific example for…

A: According to the guidelines, we have to solve only the first question, rest of the question should…

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Q: Consider the collection W = {n EN | P(n)} where P(n) is a predicate. Select all that apply. If WØ…

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Q: 2. Construct (with arrows) a bijective function f from {1, 2, 3, 4, 5} to 1, 2, 3, 4, 5} satisfying…

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Q: Prove that (n!)² <n" n! < (2n)! for all positive integers n.

A: We have given that n is any positive integer. We need to show that, n!2&lt;nnn!&lt;2n!. Since n is…

Q: 2. Determine all distinct values of -i and plot these values in the complex plane.

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Q: Given the periodic function over the period [-π/2, π/2] f(x) = x|x| a. Plot f(x) on the interval…

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Q: Use the following definitions to express each union or intersection given. You can use roster or set…

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Q: 3) Show that the functions max: R" R. (₁,...,n) max(₁,....n) and min: R" → R. (₁.) → min(x₁,....)…

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Q: Show that &lt;a, b | a5 = b2 = e, ba = a2b&gt; is isomorphic to Z2.

A: We have to show that &lt;a, b | a5 = b2 = e, ba = a2b&gt; is isomorphic to Z2.

Q: 1) Find the maximum and minimum of f(x, y) = 16x² + y² subject to the constraint 4x² + y² = 16. Set…

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Q: 2) The graph of the function y = f(x) is shown below. Use the facts that F' = f and F(0) = 1 answer…

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