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

Q: Q-1)Find the optimal solution for the Lpp below by using the graphical method ? Max z=X1+X2 S.TO…

A:

Q: e 6 Consider the integral dx with n = 4. X 1 a. Find the trapezoid rule approximations to the…

A:

Q: 4) Test the divergence theorem for the displacement vector F over the volume of a cylinder of radius…

A:

Q: Find the volume of the solid bounded above by the cone z² = x² + y²2, below by the xy-plane, and on…

A:

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: An inventory consists of a list of 80 items, each marked "available" or "unavailable." There are 50…

A: please find the attached solution

Q: Prove that 3" +4" ≤5" for all integers n ≥ 2.

A: The given problem is to prove the following inequality 3n+4n< 5n for all the integers n>2.

Q: Let A = 61 22 3X=4A + 3B and B = 7 -8-5 1 . Find a matrix X satisfying the given equation. X=…

A:

Q: . During the class, we derived in detail the first order Richardson extrapolated derivative, by…

A: Note: As you asked only subparts (a) and (b) so, i answered here only (a) and (b).

Q: On the Richter scale, the magnitude M of an earthquake depends on the amount of energy E released by…

A: If log a=b, then a=10b. The equation is provided as: M=23logE1011.8.

Q: Find the family of graphs G of order p such that y(G) = p.

A: Please find the attached solution

Q: Prove that every minimal dominating set in a graph G 26. is a maximal irredundant set of G.

A: Given that, Every minimal dominating set in a graph G is a maximal irredundant set of G. We have to…

Q: Apply the inverse power method to approximate, for the matrix A , the ei­genvalue that is smallest…

A: Given : A=310131013 , x0=111 , k=6 To find : smallest eigen value.

Q: let's assume that: v = avi + a22+a33+a44 +⋯+a88 100 50 200 150 175 25 40 200 +as 100 50 200 150 175…

A:

Q: A) Let f: R² R² be defined by k 0 f( = = 0 transformation u, where k is a scalar. The k f is called…

A:

Q: D(G) If G is a finite group, than o(G) = Σ- o(N(a)) where this sum is taken over one element of each…

A:

Q: 1. Let a, b, c E Z and n E N. Assume a = b (mod n) and b = c (mod n). Prove that a = c (mod n).

A:

Q: Question 2 system: a) form; Consider the following linear (−2x₁ + 4 x₂ + 3x₂ = − 3 - 4 x₁ + 3 x ₂ −…

A: Solve the system of questions using reduced row echelon form

Q: Q9. Find some bipartite graph of order p such that i(G) = p - 1.

A:

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: Solve the modified Laplace equation with a source term (Poisson's equation!): Uxx = —Q(x), for Q= =…

A: Please find the attached image

Q: Let S be a set containing the two column matrices shown S = first column be us and the second column…

A:

Q: 4. Use the following Venn diagram for this question. P 67 8 r 4 q (a) List the regions of the Venn…

A: Since you have posted a multi subparts question according to guildlines I will solve first three…

Q: A variable plane lx +my+nz = p (where l, m, n are direction cosines of normal) intersects the axes…

A:

Q: Suppose that U₁,...,Uk are subspaces of V. Prove that V = U₁ ☺ · · · ÐUk if and only if the…

A: Please find the attached solution

Q: Let T: V-->W be a linear transforma­tion between finite-dimensional vector spaces V and W Let B…

A: It is given that,  V and W be the finite-dimensional vector spaces. And,  T : V→W be a linear…

Q: For the graph of a function shown to the right, find (a) the domain and range, (b) the intercepts,…

A:

Q: 1/2+2/2+ 10²

A:

Q: 4. A tank contains 80 gal of pure water. Brine solution with 2 lb/gal of salt enters at 2 gal/min,…

A:

Q: The following statements are made about (right) cosets of a subgroup H of a group G. Say whether…

A:

Q: Count and describe the subgroups of index 3 of the group Z+ × Z+.

A:

Q: 1) Three vectors a, b, and c are said to be coplanar if and only if a = mb + nc where m and n are…

A:

Q: find x, y € Z such that 2261x + 1275y = gcd(2261,1275).

A: we want to find the greatest common factor  we will use Euclid's algorithm 2261=1275×1+986 -----1)…

Q: (a) On a sheet of paper, or using a calculator or other technology, graph the three indifference…

A: Please find the attached answer.

Q: |x|· x x+0+ x² (a) lim x² xxx + √√3x + 1 x² - 10x (d) lim Calculate the following limits, or explain…

A: To Find: Limits ( And explain if it is divergent). (a) limx→0+|x|·xx2 (b) limx→∞x2x+3x4+1. (c)…

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

A:

Q: Use two-timing (or averaging) to obtain the general solution of ï+ ε(x² + x² − 1)i + x = 0 with…

A: Please find the attached solution

Q: If G is a group and H is a subgroup of index 2 in how that H is a normal subgroup of G.

A:

Q: 7. The pair of equations dx dt dy dt -5x + 2xy -4y + 3xy models two coexisting species with…

A:

Q: dx X-Y x+2y

A:

Q: Assume that now = R. Show that x.x=0 [Hint: Differentiate constion't ev]. Deduce that I is a…

A: Please find the attached solution

Q: An aunt wants to make a gift of $90,000.00 to their niece's for her college education on her 21st…

A:

Q: f G is a finite group and Z is its centre, then class equation of G is expressi o(G) o(G) = o(Z) + E…

A:

Q: A variable plane lx+my+nz = p (where l, m, n are direction cosines of normal) axes at points A, B…

A:

Q: Write the system of equations associated with the augmented matrix. 4-36 4 2 2-6 4 4 4 3 6

A:

Q: Question #1: A function is given by f(x) = 6e-3. Now Answer the following: 1. 2. 3. 4. Calculate f'…

A: The central difference formula is given by f'x≈fx+h-fx-h2h (1) For x=0.5. h=0.32…

Q: Let A, B E Rnxn and let R[x] be the set of all polynomials in variable x with coefficients in R.…

A:

Q: Use the inverse of the coefficient matrix to solve the following system of equations. 8x-y + 3z = 12…

A:

Q: (b) Consider the eight vectors V1 = V5 = 1 1 V2 = , V6 = 0 0 V3 = , 07 V4 = V8 = i. Demonstrate that…

A: As per the question we are given a set of vectors in R8 and we have to : Demonstrate that these…

Q: n e induction on 17 to prove the Binomial Theorem (a + b)" = Σ C(n, k) an-kbk for all positive…

A: