15. What is the sum of the 11th row of Pascal's triangle? a. 2048 b. 1024 C. 976 d. 2056

Q: Q19) The general solution of 2x²y" + 3xy' - 15y = 0, is: a) y(x) = = ₁x² + ₂x³ b) y(x) = c₁x + ₂x-3…

A: As per our company guidelines we are supposed to answer only the first question. Kindly re post the…

Q: Q1) One of the following is correct for functions the f(x)=1.g(x)=x³ and h(x) = a) f(x), g(x) and…

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Q: Solve the following Differential Equations with Laplace Transforms y" - 6y + 15y = 2 sin(3t), y (0)…

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Q: randomly pulling a black marble from the bag are 3:8.   A new drawing of the bag of marbles is…

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Q: Use trapezoidal five interval rule to find the area of the region shown below: 1.4m 1.3m 1.7m 1.2m…

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Q: Given the region R on the right, a. Using vertical strip, SET UP the double integral that will solve…

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Q: (a) Given the set T = {0, 1, 2}, together with an operation *. Suppose that the identity is 0.…

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Q: alance), y, based on th

A: Consider as, x=time in weeks y=balance in dollars

Q: Ge + c₂0 c) y(x) = c₂e²x + c₂e² Q11) L(y") = a) s² L(y(x)) + sy(0) - y'(0) c) s² L(y(x))-sy(0)-y'(0)…

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Q: Prove that Qis dense in R

A: We prove that Q is dense in R.

Q: Solve the following Differential Equations with Laplace Transforms y" - 6y' + 15y = 2 sin(3t), y (0)…

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Q: Consider the function f(x) = x³ + 2x + 5. 1. Estimate the root to two significant digits using…

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Q: Using five significant figures in the computations, determine d(sinx)/dx at x = 0.8 from a) the…

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Q: Answer the following points i. Find the first three nonzero terms of Maclaurin series for the…

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Q: Let M(R) denote the set of all mappings from R to R. For mappings f,g: R → R, define pointwise…

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Q: Show that the differential equation x²y³ + x(1 + y²)y' = 0 is not exact, but becomes exact when…

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Q: 5. Find ds² in spherical coordinates by the method used to obtain (8.5) for cylindrical coordinates.…

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Q: As shown in the required readings or videos The Fibonacci Numbers are a sequence {F} = Fn-1 + Fn-2.…

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Q: Which of the following differential equations with initial condition yields a solution curve that…

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Q: Q1: Choose the correct Answer: 1- The linear system A) uniqe solusion E) Three solution 02:…

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Q: Let R be the region enclosed by the curves y = x³ and y = 2x². If we revolve R about the line y =…

A: This is a question of multi-variable calculus.

Q: W1 3. Let w = V = 2 W2 gram formed by w, v is equal to 2.5 1.5 0.5 is W Referring to the image…

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Q: Consider

A: We prove given converse of given statement.

Q: Use a graphing utility to graph the equation. Use a standard setting. y = |x + 5|   Approximate any…

A: Solution :  Given that the equation   y=|x+5|

Q: 8 c) f(t) = e+e-2t d)f(t) = -est+=e²t 8 Q23) The kernel of the Laplace transform of f(t),t> 0, is:…

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Q: x 2y V. Consider the lines : *+1-2/4/ = 2z - 6 and m: x= -1 + 10t, y = 7t, z = 2+t. 5 7 1. Determine…

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Q: Evaluate the integral ₁2-11-1 Sindz.

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Q: An elliptical plate, major axis 6 units, minor axis 4 units, is submerged vertically until its…

A: We will find force on a horizontal slice of the plate and then integrate it to find total force .

Q: 2. Calculate the centroid of the thin plate R which bounded by r= 1, y = 0 and, z² + y² = 4.

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Q: 5.1 Express p(t) = at²+bt + c as linear Combination of P₁ = (+-1)= P₁₂₁ = +-1 and P/3 = 1.

A: I just used the definition of linear combination

Q: Determine whether the differential equation (7x² - 2xy + 8) dx + (2y² = x² + 7) dy = 0 is exact. If…

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Q: Evaluate (6+3 cos x) dx using Simpson's 1/3 Rule (n=4). O 12.114624 O 12.42518 O 12.386215 O…

A: Simpson's 1/3 Rule n=4: ∫abf(x) dx≈h3f(x0)+4fx1+2fx2+4fx3+fx4 Where                  h=∆x=b-an

Q: Using two nodes of Gaussian integration, find the area of the region bounded by y = xe-x²₁x = 1,x&y…

A: The given problem is to find the area of region bounded by given curves y=xe-x^2 , x=1, x&y axes…

Q: State the following theorems and definitions: 1. The Fundamental Theorem of Calculus (First Form) 2.…

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Q: function Q1: For, 0 < |z| < 1, evaluate the following integral where g is analytics g(5) Sc a) fc…

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Q: Given the group (G, *). 1 (a) Show that for nonempty HCG, then (H, +) (G,) a,b Ha*b¹ € H. (b) For…

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Q: Use Euler's method to find approximate values of the solution of the given initial value problem at…

A: Let us start solving the problem step by step using euler method

Q: A forest has a population of cougars and a population of squirrels. Let a represent the number of…

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Q: Suppose that G = (a), a e, and a³ = e. Construct a Cayley table for the group (G,.).

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Q: Let C be the parametric curve with parametric equations [x=t(t² + 1)-¹1/2 te [-3,3] y = 2t - 2…

A: As per the question we are given a parametric curve C for parameter t ∈ [-3, 3] And we have to find…

Q: My - Nx N If = Q, where is a function of x only, then the differential equation M + Ny = 0 has an…

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Q: Using five significant figures in the computations, determine d(sinx)/dx at x = 0.8 from a) the…

A: Given that fx=dydx=sinx To use forward difference approximation to find f'0.8 using step size that…

Q: Let f(x, y, z) = In(4xy) z² + sin(xy² + ye²). Find fxyz?

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Q: 1. DETAILS 00 Which of the following function has the Macularin series (-1)"4"x²n n=0 1 1 A. B. 4-x²…

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Q: II. Let C₁ be the unit circle, C₂ be the polar curve with polar equation r = 2 cos 30, and points A…

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Q: 2. Use Laplace transform to solve with y(0) = 1 and y'(0) = 0. y" + 2y' + 2y = 8(t = π)

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Q: (a) Describe the symmetries of the Figure below. Assume that o is the centre of rectangle abcd. a b…

A: We are given a figure including a rectangle abcd and its centre O connected by ao &amp; ob And we…

Q: What is the degree of the sequence 3, 6, 13, 25, 45, 78, ...? A degree of 1 B degree of 2 C degree…

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Q: 30 *.The equation (y"+x3y'+y=0)is............ differential equation Non Linear,2nd order, Non…

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Q: Find the value of y (0.3), given the differential equations y = y²-y-x, y (0) = 1, h = 0.1 O…

A: We can solve this using euler method