Given the differential equation (ax+b)²d²y/dx²+(ax+b)dy/dx+y=Q(x) show that the equations ax+b=e^t and t=ln(ax+b) reduces this equation to a linear equation with constant coefficients hence solve

(1+x)²d²y/dx²+(1+x)dy /dx+ y=(2x+3)(2x+4)

what are the thermal properties of composite materials??? with references, please.

Let C be the closed path that travels from (0, 0) to (1, 1) along y = x^2 , then from (1, 1) to (0, 2) along y = 2 − x^ 2 , and finally in a straight line from (0, 2) to (0, 0). Evaluate Z C e ^3−x √ 3 − x ) dx + (5x − y √ y^2 + 2) dy

give one of the major application of graph theory in real life

find the solution of the given initial value problem

1. y''−2y'−3y=3te^2t, y(0) =1, y'(0) =0

2.    y''+4y=3sin2t, y(0) =2, y'(0) =-1

Question 4:
Oranges are grown, picked, and then processed and packaged at production centers in Sargodha,
Risalpur, and Sahiwal. These centers supply oranges to the company’s distributors each month in
Peshawar, Lahore, Multan, Faisalabbad, Karachi and Quetta.
Supplier Monthly Supply (Tons)
A. Sargodha 4,000
B. Risalpur 5,000
C. Sahiwal 3,500
12,500
The distributors, spread throughout six cities, have the following total monthly demand:
Distributor Monthly Demand (Tons)
1. Peshawar 1800
2. Lahore 2100
3. Multan 1700
4. Faisalabbad 1050
5. Karachi 2350
6. Quetta 1400
10,400
The company must pay the following shipping costs per ton:
to
from 1 2 3 4 5 6
A. $0.50 $0.35 $0.60 $0.45 $0.80 $0.75
B. 0.25 0.65 0.40 0.55 0.20 0.65
C. 0.40 0.70 0.55 0.50 0.35 0.50
(a) Determine the minimum cost shipping routes for the company using stepping stone
method.
(b) The Adams Fruit Company management has negotiated a new shipping contract with a
trucking firm between its Sargodha farm and its distributor in Karachi that reduces the
shipping cost per ton from $0.80 per ton to $0.55 per ton. How will this cost change
affect the optimal solution?
(c) Sometimes one or more of the routes in the transportation model are prohibited. That is,
units cannot be transported from a particular source to a particular destination. Because of
an agreement between distributors, shipments are prohibited from Sargodha to Quetta.
Shipments are also prohibited from Sahiwal to Lahore because of railroad construction,
what will be the effect on the optimal shipping routes? Solve this problem

Question 1. How many statements are true? (A) 0 (B) 1 (C) 2 (D) 3 (E) 4

Statement 1. Scheduled receipts are future receipts of past order releases

Statement 2. The MPS contains the GR of the end -item.

Statement 3. The POR is the inventory policy of the MRP

Statement 4. MRP minimizes cost.

Part 2. Questions 2,3,4.

Consider the end-item weekly MRPs for May 1 with Qd missing in each MRP. Match the correct MRP with the proper lot size discipline.

3,1. Suppose that the price of an asset at close of trading yesterday was $350 and its volatility was estimated as 1.4Voper day. The price at the close of trading today is $347. Update the volatility estimate using
(a) The EWMA model with A = 0.95,
(b) The GARCFI(1,1) model with tir = 0.000003, o= 0.05, and B = Q.<15. (5)
3.2 The number of visitors to websites follows the power law in equation (10.1) with q = 2.
Suppose that 1 .5% of sites get 550 or more visitors per day. What percentage of sites get
(a) 1,500 more visitors per day
(b) 2,500 or more visitors per day

For example, a definite integral of a velocity function gives the accumulated distance over the period. You should also be growing more comfortable with how the units work – for example, integrating meters per second with respect to seconds gives meters.Your job is to find an article that refers to a definite integral. It is possible that you will be able to find an explicit mention of a definite integral. Much more likely, though, the definite integral will be implied – the article will actually be about accumulated change. You may look on the Internet, or in any newspaper, magazine, or trade journal. Your example must come from a setting outside of calculus. In particular, you may not use any example from our textbook, any other math textbook, or any other discussion of calculus you find online.

1. A copy of the article with complete source information. Highlight or write the part of the article that mentions the definite integral. 2. Write a few sentences telling what the integrand (the function inside the integral) represents, what the limits of integration are, and what the definite integral represents.3. Assign some letters to the variables here. Using the letters/variables you have chosen, write the definite integral that you have found. Show that the units work properly in your example. (I do not expect you to compute anything here.)

"Brief Discuss Homogeneous Differential Equations."
This is the presentation topic of my Subject Differential Equation

What are some valuable life skills that learning math sharpens or improves?

a. Prove that for any vector space, if an inverse exists, then it must be unique.

b. Prove that the additive inverse of the additive inverse will be the original vector.

c. Prove that the only way for the magnitude of a vector to be zero is if in fact the vector is the zero vector.

In each case below either show that the statement is True or give an example showing that it is False.

(V) If {x1, x2, . . . xk, xk+1, . . . xn} is a basis of R n and U = span{x1, . . . xk} and V = span{xk+1 . . . xn}, then U ∩ V = {0}.