Find the inverse of the function g : R ! R, g(x) = { 3x + 5 if x is less than equal to 6

5x - 7 if x > 6

Show the differential equation is not exact and by finding an appropriate integrating factor solve the given initial problem.

(yx+y^2+ y) dx + (x+2y) dy =0

u equals (5,-11,-6)

v equals (-4,8,16+k)

w equals (-4,9,5)

linearly dependent if and only if k equals

Using the techniques described in this chapter carefully read through the case study and determine the most accurate ICD-10-CM code(s) and external cause code(s) if appropriate. Remember, check the chapter specific, sub-chapter specific and category specific notations within the Tabular list. Patient: Lorraine Parnete Physician: Jason Nuouri, MD July 16, 2018 History A well-established, 67-year-old female patient (since 1991) has controlled hypertension with no complications. She is a smoker [cigarettes, about one pack a day] and takes clonidine and HCTZ for her hypertension, and estrogen to address menopausal symptoms. Overall, she is well and fully active. Examination Patient presents with fatigue, about 1 month duration, associated with the withdrawal from estrogen because of published data suggesting an increased risk of breast cancer and other complications. Exam includes complete review of systems. CXR [chest x-ray] and PPD (tuberculin skin test) are negative except for the following: cough with minimal sputum a low grade fever to about 100°F 5 pound weight loss Plan Order for CBC, glucose tolerance test, TSH. Patient to return to discuss lab results. Be sure to list the codes, one code per box, in the correct order, from top to bottom. Capitalization, punctuation, and spacing can impact whether or not your answer is correct. Follow coding best practices. What is/are the correct diagnosis code(s)?

Question 1

a) Prove that if u and v are distinct vertices of a graph G, there exists a walk from u to v if and only if there exists a path (a walk with distinct vertices) from u to v.

b) Prove that a graph is bipartite if and only if it contains no cycles of odd length.

Please write legibly with step by step details. Many thanks!

Consider the following. W(r, h) = 2.8r2(1.08h) + 59r(0.3h2 − 3.3h + 72) when r = 13, h = 63, and Δr = −1.5 (a) Calculate the output associated with the given input values. (Round your answer to three decimal places.) W(13, 63) = (b) Approximate the change needed in one input variable to compensate for the given change in the other input variable. (Round your answer to three decimal places.) Δh =

Write and submit at a Matlab function that sums up a specified number of odd-power terms from the Maclaurin series of sin(x)  using following function format

function s = etaylor(x, n)

% Sum of first n non-vanishing terms of Maclaurin series of sin(x)
% For example, etaylor(0.5, 1) should be 0.5, and etaylor(0.5, 2) should be 23/48
  

Suppose we are given the unit square S in the plane with corners (0, 0), (1, 0), (1, 1) and (0, 1). Let T : R ² → R ² be a linear transformation represented by the matrix A. If T is not onto, will the image of S under the map T be a parallelogram, a line segment, or a point? Be sure to justify your answer.

Consider any two finite sets A and B. Prove that |A×B|=|A||B|

Prove that if A and B are enumerable, so is A x B.

3. Write down the multiplication tables for the direct products

   (i) Z4×Z2;
   (ii) G5×G3;
   (iii) Z2 ×Z2 ×Z2;
   (iv) G12×G4. Which of the above groups are isomorphic to each other?

1. You deposit $4000 in an account earning 5% interest compounded monthly. How much will you have in the account in 5 years?

2. Find the time required for an investment of 5000 dollars to grow to 6500 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
Round your answer to two decimal places
Your answer is t=____ years.

3. You deposit $2000 in an account earning 5% interest compounded monthly. How much will you have in the account in 15 years?

Determine the roots of the following simultaneous nonlinear equations using multiple-equation Newton Raphson method. Carry out two iterations with initial guesses of

x₁⁽⁰⁾ =0.6 and x₂⁽⁰⁾ =1.2. Calculate the approximate relative error ε_a in each iteration by using maximum magnitude norm (║x║∞).

x₁ + 1 - x₂² = 0

x₁² + x₂² – 5 = 0