HbR is reported to have P50=14torr and a Hillcoefficient=1.2. Calculate ΔYO2 for a climber with HbR assuming that, at 14,000 ft (∼4300m), PO2=50mmHg in lungs and PO2=10mmHg in muscle capillaries.

1.) Suppose that the statement form ((p ∧ ∼ q)∨(p ∧ ∼ r))∧(∼ p ∨ ∼ s) is true. What can you conclude about the truth values of the variables p, q, r and s? Explain your reasoning

2.Use the Laws of Logical Equivalence (provided in class and in the textbook page 35 of edition 4 and page 49 of edition 5) to show that: ((∼ (p ∨ ∼ q) ∨ (∼ p ∧ ∼ r)) ∧ s) ≡ ((r → q) ∧ ∼ (s → p)) where p, q, r and s are statements

Solve the cauchy problem (x^2)*y''-9*x*y'+21*y=0, y'(1)=5 on the interval (1,3). Plot the graphs of y(x) and y'(x)

Please Provide only MATLAB Code.

The Cauchy-Schwarz Inequality Let u and v be vectors in R 2 .

We wish to prove that ->    (u · v)^ 2 ≤ |u|^ 2 |v|^2 .

This inequality is called the Cauchy-Schwarz inequality and is one of the most important inequalities in linear algebra.

One way to do this to use the angle relation of the dot product (do it!). Another way is a bit longer, but can be considered an application of optimization. First, assume that the two vectors are unit in size and consider the constrained optimization problem:

Maximize u · v

Subject to |u| = 1 |v| = 1.

Note that |u| = 1 is equivalent to |u| 2 = u · u = 1.

(a) Let u = a b and v = c d . Rewrite the above maximization problem in terms of a, b, c, d.

(b) Use Lagrange multipliers to show that u · v is maximized provided u = v.

(c) Explain why the maximum value of u · v must, therefore, be 1.

(d) Find the minimum value of u · v and explain why for any unit vectors u and v we must have |u · v| ≤ 1.

(e) Let u and v be any vectors in R 2 (not necessarily unit). Apply your conclusion above to the vectors: u |u| and v |v| to show that (u · v) ^2 ≤ |u|^ 2 |v|^ 2 .

Calculate the final dates on which cash discounts for the following invoices may be taken, and the amount to remit. Invoice total is $5,500 and invoice date is 6/13. Merchandise is received on 6/19. (5 pts.)

a. 6/10 EOM

b. 4/15 n/30

c. 3/10 ROG

Proposition 6.18 (Division Algorithm for Polynomials). Let n(x) be a polynomial that is not zero. For every polynomial m(x), there exist polynomials q(x) and r(x) such that

m(x) = q(x)n(x) +r(x)

and either r(x) is zero or the degree of r(x) is smaller than the degree of n(x).

Prove

Question 2 Materials Requirements Planning An MRP exercise is being implemented over an 8-week period and the following relevant information is provided: One (1) unit of A is made of two (2) units of B, two (2) unit of C, and two (2) units of D. B is composed of two (2) units of E and one (1) unit of D. C is made of two (2) units of B and three (3) units of E. E is made of two (2) units of F. Items B, C, and E have one (1) week lead times; A and F have lead times of two (2) weeks; D has lead time of three( 3) weeks. Assume that lot-for-lot (L4L) lot sizing is used for Items A, B and F; lots of size fifty (50), fifty (50) and one hundred (100) are used for Items C, D and E respectively. Items C, E and F have on-hand (beginning) inventories of twenty (20),fifty (50) and fifty(50), respectively; all other items have zero beginning inventory. We are scheduled to receive ten (10) units of A in Week two (2), fifty (50) units of E in Week one (1), and also one hundred (100) units of F in Week one ( 1). There are no other scheduled receipts.

a) Draw the product structure tree with low level coding [5 marks]

b) Draw the corresponding time-phased diagram showing lead times to scale. [5 marks

] c) If forty (40) units of A are required in Week eight (8), determine the necessary planned order releases for all components {6 schedules}

Use the Laplace transform to find the solution of the IVP:

a.) 2y' + y = 1, y(0) = 2 (answer should be y(t) = 1 + e^{-t / 2} )

f.) 4y" + y = 0, y(0) = -1, y'(0) = -1 (answer should be y(t) = -sin(t) - cos(t))

Please show work!

What is the difference between multiplying a matrix times a vector and multiplying two matrices?

For Exercises 1-4 below, (a) verify that y1 and y2 satisfy the given second-order equation, and (b) find the solution satisfying the given initial conditions (I.C.).

2. y′′−3y′+2y=0; y1(x)=e^x,y2(x)=e^2x. I.C.y(0)=0,y′(0)=−1.
3. y′′−2y′+y=0; y1(x)=e^x,y2(x)=xe^x. I.C.y(0)=1,y′(0)=3.

Let a sequence {xn} from n=1 to infinity satisfy

x_(n+2)=sqrt(x_(n+1) *xn) for n=1,2 ......

1. Prove that a<=xn<=b for all n>=1

2. Show |x_(n+1) - xn| <= sqrt(b)/(sqrt(a)+sqrt(b)) * |xn - x_(n-1)| for n=2,3,.....

3. Prove {xn} is a cauchy sequence and hence is convergent

Please show full working for 1,2 and 3.

The post office uses a multiple channel queue (M/M/C), where customers wait in a single line in front of two service providers for the first available window. If the average service time is 1 minute and the arrival rate is 7 customers every five minutes, find, the average number of people waiting in line?

The standard error of the estimate for the above bivariate data is:

Question 3 options:

Show that if 100 people of different heights stand in a line, it is possible that we find neither 11 people of increasing heights nor 11 people of decreasing heights (describe a counterexample) (Hint: Apply the Erdos-szekeres theorum)

3. Suppose that in any given period an unemployed person will find a job with probability .6 and will therefore remain unemployed with a probability of .4. Additionally, persons who find themselves employed in any given period may lose their job with a probability of .3 and will have a .7 probability of remaining employed.

   1. Set up the Markov transition matrix for this problem

   2. There are 1000 people in the economy. At period 0, half of the

      population is unemployed, what will be the number of unemployed

      people after 1 period?

   3. What will be the number of unemployed people after 4 period?

   4. What is the steady-state level of unemployment?