You have a set of N dice, where each die d has m faces numbered 1, ..., m. How many ways are there to arrange the dice so that the total sum is equal to some value M? You don't need to write an algorithm here just define how to calculate the answer by breaking the problem into smaller subproblems, and the base case.

Q: (b) 3s²+55+1 (d) 금 (c) 5s+2

A:

Q: 1. Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx.

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: SturmLiouville 10 Consider the differential equation (4x² - 1) y" + 4xy' + y = 0 (a) For what values…

A: Solution: Given Equation, 4x2-1y"+4xy'+λy=0 Now,

Q: Test for exactness, and solve the Initial Value Problem for the following first-order ODE below: dy…

A:

Q: (b) Evaluate the characteristic value of k in the following differential equation w "+k²x³w = 0 w…

A:

Q: Let k be a real number and (M) be the following system. (M): (x+y=k-1 2x+y= 0 Using Cramer's Rule,…

A:

Q: H.W: Find Laplace Transform for following functions: b) f(t) = VE e2t

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: 2. Use Method of Undetermined Coefficients: 5 y" - 2y + 5y = 4e*cos2x + x² 2

A:

Q: Find an equation for the plane that is tangent to the given surface at the given point. z=√√y-x…

A: Introduction: The formula of the tangent to the plane F(x,y,z)=0 at the point a,b,c is given by,…

Q: Using Linear Approximation, evaluate √81.4305 using the given function and initial value below.…

A:

Q: Romberg integration for approximating f f(x)dx gives R21 =7 and R22 = 7.21 then f(1) = 4.01 -0.5…

A: Solution :-

Q: Let T be the linear transformation defined by T(x, y) = (y - 4x, 8x - 3y, -5x - 6y, 7x). Find its…

A:

Q: Show that for any 1 ≤k≤n. T (1) = n²(n²-1²)...(n² (k − 1)²) 1.3.5 (2k-1)

A:

Q: 2ydx + x(2 + x²y) dy = 0

A:

Q: I Let X = {m, n} and A = {o, X, {m}, {n}} be a o-algebra on X. Define the function m A→ [0, ∞] by S…

A:

Q: A pizza parlor offers 12 toppings. a. How many 8-topping pizzas could they put on their menu? Assume…

A: Solution :-

Q: 4... Estimate the value of ³√5:2 Power series

A:

Q: Question 1 Determine the inverse Laplace transforms of: 2s²-5s-1 (a) (s+3)(s²+9) (b) 3s²+55+1 (d)…

A:

Q: Find a solution to the system 3 1 [] D-640 = 1 by solving the IVP with initial condition = 3 -1 x(t)…

A: Solution

Q: Q3. (a) Find the binomial expansion of (1-x)-1 up to and including the term in x².

A:

Q: 3 1a). Let V be the volume of the shape formed between the parabloid z = 2x² — y² and the cone z² =…

A: Solution: Given that z=32-x2-y2 and z2=x2+y2Now, using polar coordinator; x=rcosθ, y=rsinθ, r=x2+y2…

Q: D Use Intermediate Value Theorem to explain why the function has a zero in the given interval.…

A:

Q: 1. Given f(x) = 12x²-8x+4 and g(x) = 6x²+3x-9. Evaluate (f-g) x. 2. Given f(x) = 6x³ +7x²-5 and g(x)…

A:

Q: from an island-town with 2000 people. He goes to the mainland with a friend and there they catch a…

A: Given, Lau came from an island town with 2000 people. He goes to the mainland with a friend and…

Q: If A⊂B, prove that if B is bounded, then A is also bounded. Is the converse true?(if not true give…

A: Let A⊂B, where B is bounded. Then there exist two real numbers k and K such that k ≤ b ≤ K for all b…

Q: Find the volume of the solid obtained by rotating the region bounded by y = x3, y=8, and X=0 about x…

A:

Q: The diagram shows a triangle ABC. 5 cm 6 cm B The lengths of AC and BC are 5 cm and 6 cm…

A:

Q: The following data gives an approximation to the integral M= f(x) dx f N₁ (h) = 2.2341, N₁ () =…

A: Solution:-

Q: 3. Let A = {a, b, c, d, e} and B = {x,y,z, 1,2,3}. Find the power sets P(A) and P(B).

A:

Q: A formula of order 4 for approximating the first derivative of a function f gives: f'(0) 4.50557 for…

A: Solution:-

Q: Consider the subgroup H = (i) of the the group (C\{0},.). LIT TT TT?

A:

Q: E. Compute the 1st, 2nd and 3rd order Taylor polynomial of the exponential funchon f(x) = e² around…

A:

Q: Let Po be a point inside a circle of radius a and let h denote the distance from Po to the center of…

A:

Q: Q3. (a) Find the binomial expansion of (1 − x)-¹ up to and including the term in x².

A:

Q: Find a, b and c so that the quadrature formula has the highest degree of precision [ f(x)dx = af (1)…

A:

Q: Determine the inverse Laplace transforms of: 2s²-5s-1 (a) (s+3)(s²+9)

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: mtegrals ▸ Example 4 Evaluate over the triangular region R enclosed √f (2x - y²) dA R between the…

A:

Q: 7. (a) 8. (a) 2 л 10 36° (b) 72° (c) 144° It is known that sin >0 and tan 0 (b) cos 0 or cos <0 are…

A:

Q: A pizza parlor offers 12 toppings. a. How many 8-topping pizzas could they put on their menu? Assume…

A: Solution:-

Q: solve the following ODE problem using the power series method and y" - 2xy' - 2y = 0 Problem…

A:

Q: Q3. (a) Find the binomial expansion of (1-x)-1 up to and including the term in x².

A:

Q: Which of the following series converge? II. ΙΣ i=ing a © I, II., and III. I. only. III. only. I. and…

A:

Q: 3. 5 10 7 28 7.

A: 510=12 10 divided by 5 is equal to 2. So smallest form is 1/2. Or 0.5

Q: It is known that the range of the function f(x)= a sinx+1 for xER is -2<f(x)≤4, then a = ?

A:

Q: Consider / = (2x + 1) dx with b > 0. If R₂ = 2 then the value of b is: O 1.5 1 05 0 2

A:

Q: Given the function f(x) = -x² - 4x³ determine its critical points and classify them, determine the…

A:

Q: Question 4 Assume that you are dealing with three squares and a right triangle, what is the area o…

A:

Q: Solve the linear system using both gaussian and gauss-jordan elimination X1 - 3x3 = 10 3x₁ + x₂ -…

A: To solve the given linear system of equations using Gaussian elimination method.…

Q: Explain the difference between Finite Difference Approximations and Ricardson Extrapolation methods?

A:

Q: How many number between 10 and 20 give a given remainder of 2 when divided by 3

A: Step 1 : Understand the problem We need to find the numbers between 10 and 20 that gives remainder 2…