Prove by mathematical induction that Vn E Nwith n 2 4 2 n3

Q: Part A If a = 5 in. and h = 3 in. , locate the centroid (a, y) of the composite area.(Figure 1)…

A:

Q: Please use Laplace Transform Method Consider the following IVP: y" -10y' +9y = 5t, y(0) = -1, y'(0)…

A:

Q: After 10.32 years, Mary's money became 2 % of its initial value. The money was compounded…

A: here we will use compound interest formula  If P is the amount invested  r is rate of interest per…

Q: If a > 0, show that sin(nx) lim d.x 0. n→∞ nx

A: Solution

Q: Identify and sketch the graph of the following equations in R z = 1 – e"

A: We will have to sketch the graph of z=1-ex in ℝ3.

Q: Determine the general equation of the plane 2 passing through the point P(1, –4, –5) and parallel to…

A:

Q: Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the…

A:

Q: The following graph is called Petersen graph, it is named after Danish mathematician Julius…

A: Multipart :    We have given a Petersen graph , (d) To show that , Petersen graph is not planar ,…

Q: The Mega Millions lottery is available in multiple states including New Jersey. A Mega Millions…

A:

Q: The payment on a 15 year loan at 9.36% compounded weekly is $180.00. Calculate the amount of the…

A:

Q: p. 18. a) Find (i) GU H and (ii) GnH V2 V3 Vs V3

A: Given the diagrams To find G∪H

Q: e-iw 3. 2 + iw

A: The given problem is to find the inverse Fourier transform of the given function. Given function…

Q: Use substitution method

A:

Q: Find the inverse of laplace, f(t) if: 8s + 12 10. F(s) = (s – 2)(s² – 6s + 13) -

A:

Q: Define the function zlm(z) z +0 f(2) = Z = 0 1. Prove that f is continuous at the origin. 2. Prove…

A:

Q: • b. Σ n =1 3n – 1 -

A:

Q: Suppose that {A;};eI and {B;};ej are families of nonempty dasses with the same index dass I. Prove…

A: Given that Aii∈I and Bjj∈J are families of non empty classes with the same index class I.

Q: The initial value problem (4 – t2) y' + 2ty = 3t2, y(1) = -3 has a unique solution in the interval…

A:

Q: 3. Use the third degree Maclaurin polynomial of f to approximate th value of 0.2 ln(1.1), give your…

A: Macluarin polynomial of the function

Q: Give an equation of a plane described below. Determined by intersecting lines L1 and L2 L1: x = 2t y…

A:

Q: TRUE OR FALSE. Determine each of the following statements if it is true or false. If a^3 divides…

A: In 1st question given that a3 divides c2 so c2a3=k where is real number. Now c2a3=k…

Q: Prove that an angle of θ radians is constructible if and only if the real number cosθ(sinθ)…

A: Since θ is constructible, by definition, (cosθ, sinθ) is a constructible point.

Q: For this reason it is called the Lorentz matrix for the velocity v. (hint: Substitute 2 – 32 = 1 and…

A:

Q: How many solutions are there to the equation x1 + x2 +3 + x4 + x5 = 39, where each x; is an integer…

A: Solution

Q: Find the Maclaurin series for the function below by altering a known power series appropriately. 4+…

A: We have to find the maclaurin series for f(x).

Q: For a general graph of a function x = g(y) that may go to the left and the right of the y-axis,…

A: Given graph is x=g(y) and the definite integral is from y=c to y=d.

Q: Steady State - Solving Manually 3. Manually solve for the steady state distribution. 0.5 0.51 P =…

A:

Q: Suppose p and q are distinct primes such that ordp a = h and ordq a = k Prove that ordpq a= lcm(h,…

A: Here we use basic group theory.

Q: Please help me find the sum or divergence with telescope methods

A:

Q: 3. Find the remiander when 7^(103) is divided by 25 4. A card is drawn at random from a…

A:

Q: Circles P and Q are externally tangent. Find the length of the common external tangent if their…

A: We have to find the length of common tangent

Q: Determine the inverse Laplace transform of the function below. 3s+40 s +10s + 50 Click here to view…

A:

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: Simplify the given function by squaring the expression inside the parentheses.…

Q: Given #= (1+--). dy 2 dx What is the value of k such that y is parallel to the curve y = 3x +1 at x…

A:

Q: e Lagrange multipliers to find the maximum and minimum f subject to the given constraint. Also, find…

A:

Q: R(x.y) = 25x + 65y +0.07xy – 0.02x2-0.01y², C(x.y)=3x +2y + 200 e the first order partial derivative…

A: P=R-C   P(x,y)=R(x,y)-C(x,y) P(x,y)=25x+65y+0.07xy-0.02x2-0.01y2-(3x+2y+200)…

Q: 1. Consider the shaded area below the graph of the function y = x² + 1, above the x-axis and between…

A: We will use Riemann sum to find area under curve y=f(x) in the interval x∈a,b Area ≈Δxfx0…

Q: 2. Use the Mean Value Theorem to show that f(x) = 2x sinh(x - 1) + 2* -x has a critical number…

A:

Q: True or false: 7. The points of inflection are found by solving the first derivative equal to Zero…

A: 7. no, points of inflections are not found by solving first'order derivative, it's by finding second…

Q: Maria invested a total $26000 into three accounts: a saving account paying  3% interest, a CD…

A:

Q: Find the mass of the solid with density p(x, y, z) and the given shape. P(x, y, 2) - 48, solid…

A: Mass of the solid bounded by the region

Q: If E is the solid described below with density function P(x, Y, 2) = x + y2, find the following…

A:

Q: Find the radius of convergence, R, of the series. n= 1 R= Find the interval, I, of convergence of…

A: Interval of convergence

Q: Answer the following. 1. Verify if the following numbers form an amicable fair, Support your answer…

A:

Q: 99. Determine the concavity of the curve x= 2t + In t, y = 21 – In t. %3D

A:

Q: Provide NEAT and COMPLETE solutions for the following problems. 4. Let n ∈ Z. Prove that if n is…

A: Given: Prove that if n is odd, then n = 4k + 1 or n = 4k + 3 for someinteger k.

Q: Your investment account pays 3% interest. If you deposit $10 a day how much will you have after 5…

A:

Q: 1. What is the rank of A?

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: appropriately. (1 – 5æ) a) Express the Maclaurin series of f(x) in the form ak. Enter the summand…

A:

Q: Answer the following. 1. Find x if 2x309 is divisible by 9 2 Find the canonical prime factorization…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…