a. Write the rational number 0.3234234234... as a ratio of integers. b. Prove that if x # 0 is rational, then 1/x is rational.

Q: A. Solve the following matrices using the following methods (a) matrix method, (b) determinant…

A:

Q: t 12² 12=2 / 1x1₁2) dy dxde you (18) Consider the triple integral Bron 1₁ 122 √2-2 Which will not…

A: Introduction: A more than one crucial is a specific crucial of a characteristic of many actual…

Q: part b

A: As per the question we are given an optimization problem for which we have to find a better solution…

Q: Let a(t) represent the number of tumor cells at time t (with exponential grow factor a > 0), and…

A: As per the question we are given a nonlinear optimization problem. And we have to find the optimal…

Q: Given the function below f(x, y, z) = 2 cos (r) + xy - xz - y² - e²% +2% (a) Show that the origin…

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

Q: For each of the following systems, find all the equilibrium points x₁ = x₂ a) (x₂ =−x₁ - x₂ + ² -X1…

A:

Q: 1. Consider the sequence defined by the explicit formula AN = N² +1. a) Find A₁ = b) Find A100 = c)…

A:

Q: Question 2: (a) Insert 4 arithmetic means between 1 and 15. (b) Insert 5 geometric means between 3…

A:

Q: Prove that the following functions are Riemannian integral over the period [0,3 ] with finding the…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: (a) Is the function f(x, y) = xy(x²-x²) when (x, y) = (0,0) and f(0, 0) = 4 continuous at origin.…

A:

Q: C) Sketch the region of integration and write an equivalent double integral with the order of…

A:

Q: Need help with the last 2 I'm pretty sure the first one is correct

A:

Q: Using any of the methods discussed for both numerical differentiation and numerical integration…

A: Given,Integral,I=∫021xdxTo find: Value of given integral using any one of the numerical methods

Q: 1) Mr. Ang's money became Php165,000 @ the end of 10 months. If the bank pays 12% annually, how much…

A: Given that,  Mr. Ang's money became in 10 months Php 165000 at the rate 12% annually. Let the…

Q: The real part of cot(1 + j2) is.

A:

Q: The natural numbers are l PEN N={1,2,3,...). The prime numbers are P= {2,3,5,7...}. True or false?…

A:

Q: Compute the volume of the solid that results when the region enclosed by the curves is revolves…

A: Given : Equations of the curve, y=x, y=0, x=1, x=4 and axis x=-2. To find: Volume of the solid that…

Q: Hw Leto: R S be a ring homomorphism. Show that If A is a subring of R, then (4) is a subring of S

A: We have given that ,  φ : R → S be a ring homomorphism. If A is subring of R. We need to show that ,…

Q: Write the Mayan numeral as a Hindu-Arabic numeral. notation 4x10+6×10 The equivalent Hindu-Arabic…

A:

Q: 3: A student is riding on her bike. The wheel of the bike is 1 m across. A pebble is stuck in the…

A: To find the given conditions :-

Q: se the Sales information above to answer this question. he value x = 42.538 should be used in the…

A: In this question, the number of widgets is to be determined.

Q: Solve the given partial differential equation a²z 8 a²z Ət ² 2 dx² =

A:

Q: Discuss find following surfaces and Traces. the intercepts and их 4x₁²² + 4y₁² + 2² -16=0

A: Intercept: In a three dimensional space, an intercept is a point on the graph of the quadric surface…

Q: A. Solve the following matrices using the following methods (a) matrix method, (b) determinant…

A:

Q: (sin³3B) (cos3 B) dß Apply the transformation method

A: Solution :-

Q: ering different paths of approach, show that the function has no limit as (x,y)-(0,0). f(x,y)=- Find…

A:

Q: Sketch the region bounded by the given lines. Then express the region's area as an iterated double…

A:

Q: 3) Use a Use a Imear approximation of the function _fix, y) = estimate f(x,y) to appropiate point…

A:

Q: Problem 1. Suppose f: R → R is a continuous function which can be uniformly approximated by…

A: Given: A function f: R → R is a continuous function that can be uniformly approximated by…

Q: Solve the Laplace equation subject to the given boundary condition ди = u(0, y), u(π, y) = 1 axx-o…

A: As per the question we have to solve the Laplace's equation : ∆u = uxx + uyy = 0 With respect to the…

Q: Let A = {(x,y) = RXR; 0<max{|x-3], ly- 2|}<1}, then: *

A:

Q: Evaluate [²²* 0 3 y² sin z6 dx dy dz

A: Consider: ∫01∫0z2∫03 y2 sinz6 dx dy dz So, evaluating this we get: ∫01∫0z2∫03 y2 sinz6 dx dy…

Q: A100 =

A: Given sequence as, AN=2N+33N-1

Q: time a c) 1/5 d) y e) Some other Calculate the curvature KIt) at rit) = < 2 cost, 2 sint, e²) 170 67…

A:

Q: 29,369 as the forec

A: Given data: weight on actual value of 0.34.

Q: 4. (a) Rayleigh's equation is y" + ((u)² − 1) y + y = 0, where is a constant. Show that differenti-…

A: Here given the system of equation u'=vv'=μ1-u2v-u

Q: L-1 -3s²-12s-87 의 (s+2)3

A:

Q: Solve for Newton's Backward formula to find the interpolating polynomial of degree which…

A: Solution : Newton's backward difference method, y=f(x) Table for x and y x -1 1 3 5 y 1 -1 2 -2…

Q: Evaluate LU'(3-2x) [f'(3-2x) - 4] dx.

A:

Q: Exercise 7.2.9. Suppose G is a group and H, K ≤ G finite subgroups such that gcd (|H|, |K|) 1. Prove…

A:

Q: circles, C1 and C2, are drawn such that the area of the first, A1, exceeds the area of the second,…

A:

Q: (d) Show that for all integers n > 1 S(n, 1) = 1 = S(n,n), then, using the above relation (or…

A: Solution : Stirling number S, defined by, S(n,k)=1k!∑i=0k-1ikik-in d) S(n,1)=1 Only one way to put n…

Q: c) Define the linear transformation T: R³ →R² by T([])= [² = ³6 ] a - 3c +b- Find a basis for the…

A:

Q: A pencil cup with a capacity of 33 in.3 is to be constructed in the shape of a right circular…

A: Volume of the cup (V) = 33 in3  Material for sides costs = 29 c/in2  Material for base costs = 46…

Q: Finite Mathematics In linear programming, explain why the corners of the feasible region are…

A:

Q: Estimate 3x + x² using Mid-point method (n=6), then find the error estimate.

A: Given integral is ∫143x+x2dx. We have to estimate the given integral by using Mid-point method.…

Q: 1. Find the sum of the first 20 terms of the sequence: -2, 2, 6,10,14, ... (Note: Type the VALUE…

A: To find the given terms and the sum of the given sequence :-

Q: Exercise 10. Let Z be the set of integers and R be the relation on Z defined by: aRb if and only if…

A:

Q: 3. Consider a predator-prey model, z (r-ray), r r, K, a>0, (1) y(-b+cz), b, c> 0. (2) The variable z…

A: Given: The predator-prey model, dxdt=xr-rxK-ay, r,K,a&gt;0 dydt=y-b+cx, b,c&gt;0 Here, the variable…