Let n be a positive integer. Let S(n) = n sigma j=1 ((1/3j − 2) − (1/3j + 1)). a) Compute the value of S(1), S(2), S(3), and S(4). b) Make a conjecture that gives a closed form (i.e., not a summation) formula for the value of S(n). c) Use induction to prove your conjecture is correct.

3. Write a Matlab script that describes the dynamics of Pressure and Flow in the systemic arteries and Left Ventricle. Assume that :

1) Pressure in the Left atrium (P_LA) and in the Systemic Veins (Psv) remain constant.

2) A time dependent LV compliance

3) Opening/Closing of the heart valves instantaneously with the direction of flow (i.e. valves are at an open or closed states. Use parameter values from the handout.

A 105‑turn circular coil of radius 2.41 cm and negligible resistance is immersed in a uniform magnetic field that is perpendicular to the plane of the coil. The coil is connected to a 14.7 Ω resistor to create a closed circuit. During a time interval of 0.167 s, the magnetic field strength decreases uniformly from 0.481 T to zero. Find the energy, in millijoules, that is dissipated in the resistor during this time interval.

Consider the following family of sets: For any n∈N, we define Q_n={ q \in Q | q= \frac{m} {n^k} for some k, m \in Z}

(That is, Q_n is the set of rational numbers expressed with the denominator that is a power of n.)

a) Is this set closed under addition, subtraction, multiplication, and division?

b) Decide the truth value of the following statement: Q 12 ⊆ Q 18 . Justify.

After "Black death", output and capital per worker increased, what was the impact of the increase in technology? And why does tech change cause investment if the return on capital is constant?

Write an IT professional statement of purpose from using the following skill and expertise:

FROM LEADERSHIP, PROJECT MANAGEMENT, COMPUTER REPAIR, NETWORKING, INFORMATION TECHNOLOGY INSURANCE AND MANAGEMENT, CYBRSECURITY)

Compare and contrast the impact poverty has on rural children and urban children in the United States by focusing on enrollment levels, finances, access to technology, equity in education, and child welfare.

Discuss custom techniques for managing shipping process for Toyota around Globalism. Your answer should include software and hardware specifications, technology upgrades,And backup and recovery strategies.

Discuss custom techniques for managing shipping process for Toyota around Globalism. Your answer should include software and hardware specifications, technology upgrades,And backup and recovery strategies.

explain in 1-2 paragraphs the ways in which the underwriting capabilities of marketplace lending platforms have been enhanced by new technology and data which are superior to that of the credit bureaus.