Find an explicit formula for a sequence of the form a, a, a, 4, 8, 16, 32, 64, 128, 256 I an = with the initial terms given below.

Q: Find all integers n such that o(n) = 40.

A: Use the multiplicative property of ϕ:  if n and m are relatively prime then  ϕ(nm) = ϕ(n)ϕ(m). 40  =…

Q: 4. L {t ['sin Tdr}

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Q: Let x, y, and z be integers. If zly and ylz, then ra

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Q: A landscaper has 8 different flowering plants. She needs to plant 4 of them in a row in a garden.…

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Q: 1. Use the principle of mathematical induction to prove that 1 +r+r² + ³ + ... + pn = 11 pn+1 - r-1

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Q: 4. Find parameters a such that zero solution of the following system is asymptotically stable. * =…

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Q: x² + x³y + y² x² + 2y² Explore lim (x,y) →(0,0) f(x, y) either proving it does not exist or…

A: fx,y=x2+x3y+y2x2+2y2limx,y→0,0fx,y=limx,y→0,0x2+x3y+y2x2+2y2 Let y=mx fx,mx=x2+x3mx+mx2x2+2mx2…

Q: f(r,0) = e-to Find the regions where f is the analytic function Consider the function

A: Given that     f(r,θ) = e-iθr Since  fr,θ = ur,θ + i vr,θ  and  e-iθ = cos(θ) - i sin(θ)…

Q: e. lim_f(x) lim f(x) i. f(1) 2 2 b. lim f(x) f. N j. lim_f(x) lim f(x) 2 2 m. Write the equations…

A: Since you have asked a question with multiple sub parts , we will solve the first three sub parts…

Q: Compute the product. 9 II = 3 i(i + 2) (i − 1) (i+1) ||

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Q: You have 6 math books and 6 history books to put on a shelf with five slots. In how many ways can…

A: If a particular event can be done in n different ways and an other event can be done in m different…

Q: 4. f(t)=e¹+7. 5. f(t)= test. 6. f(t) = tcost. 7. f(t) = t sint. 8. f(t) = et sint.

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Q: For any integer z, if 3 divides z2, then 3 also divides z.

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Q: Given the differential equation: y (4)_2y"+y=xe* Choose All Correct Answers Below A There is…

A: Given differential eqyuation  y4-2y''+y=xex We can also write it as D4-2D2+1y=xex

Q: Sketch a polynomial graph by matching the behavior to the given characteristics. Leading Coefficient…

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Q: Determine whether the following statement is true or false: Given matrices A of the size 3 × 5 and B…

A: Matrix multiplication

Q: Determine whether the following statement is true or false: If both matrices A of the size 6 x 4 and…

A: Echelon form of the matrices properties

Q: A certain amount of an indissoluble substance containing 2 kg of salt in its pores is subjected to…

A: As given , initial amount of salt S=2 kg. After 5 minutes, remaining amount of salt is 1 kg. Also,…

Q: Suppose there are two standard 52-card decks of playing cards (meaning there are four suits -…

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Q: Find bases of the image and kernel of the matrix 1 1 1 A = 201 2 2 0 2 3 2034 204 5

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Q: A pizza parlor offers a choice of 16 different toppings. How many 6-topping pizzas are possible?…

A: The number of ways r items can be selected from n different items is equal to C(n,r). The formula…

Q: n can be written in the form orm, 7₁ and 12 d²y dt² dt 0 y = C₁e¹¹t+C₂¹₂ T₁ < T₂

A: Given Differential equation:d2ydt2-9dydt=0To find: General solution of the form y=C1er1t+C2er2t…

Q: 1. The function(x)=x-1 has a discontinuity, say where and justify the response. Classify the…

A: Given f(x)=x4-1x-1. to check the discontinuity of f(x).

Q: Solve the matrix equation AX = B for X. 1-2-3 HH - 1 4 6 B= 6 1 -1 -2 A = 3 7

A: First convert given system of equation in augmented matrix then solve by Gaussian Elimination…

Q: Consider the periodic function f(t) defined as follows: - 2t f(t) = 2 e for 0≤ t < 2, and f(t+2) =…

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Q: 2) Find what conditions must be placed on b, b, and b¸ in order for the 1' 2' following linear…

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Q: State A: - 6x + y = 11,600 State B: 141x+y=7,000 where x = 0 corresponds to the year 2000 and y is…

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Q: b) Let c) find the solution set of 670 s.t. b I show that Lib(x) = log bx is one to one. ( 1½/2 ) *…

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Q: Solve the following initial value problem: dx dt dy dt = = 3x - 4y 2x - y x(0) = 2, y (0) = -1

A: We will find eigenvalues and eigenvectors and then we wiil get the general solution.

Q: Find the zeros and the corresponding multiplicity of the following polynomials and then draw the…

A: To determine zeros of polynomial f(x) then put f(x) equal to zero.  Multiplicity of a zeros is how…

Q: (a) Find the reduced row echelon form of the given matrix. Record the row operations you perform,…

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Q: bases. Find the volumes of several such boxes. Does it appear that there is a maximum volume? If so,…

A: Here, in the question, a box with an open top is to be constructed from a square piece of cardboard…

Q: The owner of Oak Hill Squirrel deposits $2,000 at the end of each quarter into an account paying…

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Q: What is the inverse matrix of. SE S FOR SE Pemb CEPURE AGRE PAPERS SPORT TELE P PRECES CHEAPES…

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Q: For each of the following two LP models, respond to the following questions using graphic tools and…

A: (1) The constrain which are binding the solution is  3x+4y≤242x+y≤10x≥1y≤5y≥0 (2) The redundant…

Q: Solve the following inequalities: (i) 5(11 − ?) < ? + 49…

A: We will use x in place of ? to solve these inequalities.

Q: 3. If the eigenvalues of A are 5 and -1, with multiplicities 2 and 3, respectively, find the…

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Q: Find s12  for the series 2 + (-4) + 8 + (-16) + …

A: The given series is                                2+(-4)+8+(-16)+···

Q: Given: f(x)= = x³ x²-3' with f'(x) = x4-9x² (x² - 3)² and f"(x) = 62³ +54x (x² − 3)³ Make a table…

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Q: 3. Let R-Z18. Determine the units and zero divisors of R giving the explicit unit or zero divisor…

A: We know that  no of units in ring Zn = phi(n), and  no of zero divisor of Zn = n - phi(n) -1

Q: Prove n (1+x)n-1= Σ c(n, k) k xk-1. k=1

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Q: Solve the system by back substitution. 2x+4y+z +3w= -1 y+6z+2w = 8 -2z-2w = -4 -2w=-6 *** The…

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Q: a) Determine the domain of the function and write it in interval notation b) Determine the…

A: We know that, if we draw the graph of an odd function then it has rotational symmetry with respect…

Q: K Use the indicated row operation to transform Interchange R₁ and R3. The transformed matrix is 9-3…

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Q: A pair of parametric equations is given. x = e²t, y = et (a) Sketch the curve represented by the…

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Q: So the maximum is (-0.5, -16e^(-1))? And the minimum is (0.5, 16e^(-1))? I need the answer in…

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Q: Let a) Use the fact that the Find the domain and range of b) show that tp (x) = 6² is decreasing…

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Q: Given that f(x) = 3x + 1 and g(x) = x2 - 2x - 4, find (g * f)(6). (g * f)(6) =

A: Composite function value

Q: Consider the system described by ÿ ₂ 3 7 + 2 j + 47 au + = Derive a state-space representation of…

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Q: Find the Laplace transform of the periodic function f(t) whose graph is given below. --1 1.0 -1 1,0…

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