1. A round column is to be designed with DL = 600 KN, LL = 800 KN, fc’ = 20.7 MPa, fy = 345 MPa. Use ?? = 0.02, 25 ?? ∅ ???? ????, ??? 10 ?? ∅ ???. USE 1.2 DL + 1.6 LL USD AND WSD. provide detailing

Students will be asked to formulate, define, and interpret mathematical modeling (particularly ordinary differential equation) which involves real engineering applications and related to their majoring (E.g. Newton’s law cooling/warming, mixture problem, radioactive decay, spring-mass system, series circuit, deflection of the beam, etc.).. The selected model should be solved analytically using any methods that have been learnt in the mathematic lecture. just give me an example with related topic and how to solve it using math

5)   Solve 2yy’’ = 1 + (y’)^2

Consider ỹ + cỷ +y = 0, and assume y(0) = 1, ÿ(0) = 0. (a) Why is this a homogeneous system?
(b) What would change if this was to be an inhomogeneous system? When is this inhomogeneous aspect applied - this is a technical point, but helps us to understand that the initial condition is an external input too, but is *only* applied at t = 0?
(c) Choose e to make this problem overdamped/critically damped/underdamped.
(d) Follow the 3-step procedure to solve this homogeneous system for the ho- Imogeneous solution y which we call y: Step 1: Get yh. Step 2: Satisfy condition, and Step 3: Sketch. • Solve the overdamped case where c is the critically damped version where c is increased by 1 past the critically damped value. Solve the critically damped case, • Solve the underdamped case where e is the critically damped version where c is reduced by 1 below the critically damped value.

1)Prove that the intersection of an arbitrary collection of closed sets is closed.

2)Prove that the union of a finite collection of closed sets is closed

use power series expansion for y''+xy'+3x^2y=0 to find the recursive formula and find the first 6 terms of the general solution

Use a graph or level curves or both to find the local maximum and minimum values and saddle points of the function. Then use calculus to find these values precisely. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x, y) = 5xye^{−x2 − y2}

1. Determine the form of a particular solution for the following differential equations. (Do not evaluate the coefficients.)

(a) y'' − y' − 6y = x^2 e^x sin x + (2x^3 − 1)e ^ cos x.

(b) y'' − y' − 6y = (2 − 3x^3 )e^3x .

(c) y'' + 4y' + 4y = x(e^x + e^−x )^2 .

(d) y'' − 2y' + 2y = (x − 1)e^x sin x + x^2 e^−x cos x.

2. Find a general solution to the differential equation y'' − 3y' + 2y = x^2 + 1 − x sin x + xe^2x

Prove that if n is an integer and n^2 is even the n is even.

a) The rectangles in the graph below illustrate a    ?    left endpoint    right endpoint    midpoint     Riemann sum for ?(?)=?29f(x)=x29 on the interval [3,7][3,7].  
The value of this Riemann sum is

equation editor

Equation Editor , and this Riemann sum is an    ?    overestimate of    equal to    underestimate of    there is ambiguity     the area of the region enclosed by ?=?(?)y=f(x), the x-axis, and the vertical lines x = 3 and x = 7.

b) The rectangles in the graph below illustrate a    ?    left endpoint    right endpoint    midpoint    Riemann sum for ?(?)=?29f(x)=x29 on the interval [3,7][3,7].
The value of this Riemann sum is

equation editor

Equation Editor , and this Riemann sum is an    ?    overestimate of    equal to    underestimate of    there is ambiguity     the area of the region enclosed by ?=?(?)y=f(x), the x-axis, and the vertical lines x = 3 and x = 7.

1. Provide a regular expression that describes all bit-strings that length is at least one and at most three.

2. Provide a regular expression that describes all bit strings with odd length.

Consider your SID as map it to the vector . K is the index that denotes the number of digits in your SID. Consider now the vector , where Y denotes your year of birth.

„ Write each of the vectors and tell the dimension n=? of the vector space () each of them belongs to. Is it a matrix? If so, what are its dimensions? Would form a “span” of a vector space? Explain why?

„ Is the vector space   belongs to a subspace of the vector space   belongs to? Prove your decision?

SID is studen id number which is 50802030

Y denotes year of birth which is 1992

^**Please give formulas and step by step instructions**^

A cosmopolitan area was deciding what form of security to use in its subway systems. The city ultimately decided to use metal detectors at the entrance of the subway, but it still must hire security personnel to patrol the area. The town currently uses both city police officers (P) and privately contracted security guards (G). The annual cost of one police officer is $65,000 in wages and benefits, while security guards only cost the city $35,000 per year on average. Each security guard reduces the number of muggings and violent crimes by 2 annually and deters 25 free riders. However, because of their focus on more serious crimes, a police officer only deters 15 free riders annually, but their presence prevents an estimated 6 muggings and violent crimes annually. The city must decrease muggings and violent crime by 250 incidents and reduce the number of free riders by 1,000. The town must have at least 12 police officers dedicated to patrolling subways, and because of a previously existing contract, they must employ at least 20 security guards. The city’s objective is to meet these constraints with the least cost combination. How many city police officers and privately contracted security guards should the city hire?

Let G be a group of order 40. Can G have an element of order 3?

The differential equation of motion of ship is given by M d2x/dt2 + C dx/dt + Kx = F + F2*exp(-2t). t >0.

when M = 4.8, C = 3, K = 5, F = 3.8, F2 = 3, x(t=0)=1 and dx/dt (t=0)= 1.

Find:

a)the order of X(s) and the number of poles & Find all poles of X(s)

b)Determine the stability of system.