Write a function that will accept one integer matrix E and one column vector F by reference parameters, and one integer I as a value parameter. The function will return an integer v, which is the i-th coefficient of row vector denoted by E*F (multiplication of E and F). For example, if V = E*F, the function will return v, which is equal to V[i].

Explain the time complexity of this function inside of the function code as a comment.

in c++ program

A battery of ? = 2.10 V and internal resistance R = 0.600 ? is driving a motor. The motor is lifting a 2.0 N mass at constant speed v = 0.50 m/s. Assuming no energy losses, find the current i in the circuit.

(a) Enter the lower current.

(b) Enter the higher current.

(c) Find the potential difference V across the terminals of the motor for the lower current.

(d) Find the potential difference V across the terminals of the motor for the higher current.

Let T,S : V → W be two linear transformations, and suppose B1 = {v1,...,vn} andB2 = {w1,...,wm} are bases of V and W, respectively.

(c) Show that the vector spaces L(V,W) and Matm×n(F) are isomorphic. (Hint: the function MB1,B2 : L(V,W) → Matm×n(F) is linear by (a) and (b). Show that it is a bijection. A linear transformation is uniquely specified by its action on a basis.)

need clearly proof

1. Calculate the mass fraction stochiometric ratio for the combustion of

n-Butane (C₄H₁₀) in air ( 20% v/v O₂   80% v/v N₂)* ratio 4:1.

Given the following Atomic Weights for the elements and their valencies.*

Element            Symbol         Atomic Weight           Valency

Hydrogen              H                          1                             1

Carbon                  C                         12                            4

Nitrogen                N                         14                            3

Oxygen                  O                         16                            2

*Note these numbers have been rounded for ease of calculation.

Use the following tax rates and taxable wage bases: Employees' and Employer's OASDI—6.2% both on $127,200; HI—1.45% for employees and employers on the total wages paid. Employees' Supplemental HI of 0.9% on wages in excess of $200,000 was not applicable. Karlie Hastings is a writer (employee) for the Santa Fe Gazette and has an annual salary of $49,000. This year, she also realized net self-employment earnings of $85,000 from a book she wrote. What portion of her self-employment earnings is subject to the two parts of the social security tax? a. OASDI taxable self-employment earnings $ b. HI taxable self-employment earnings $ c. OASDI self-employment tax $ d. HI self-employment tax $

Required information

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In 2018, the Westgate Construction Company entered into a contract to construct a road for Santa Clara County for $10,000,000. The road was completed in 2020. Information related to the contract is as follows:

Westgate recognizes revenue over time according to percentage of completion.

3. Complete the information required below to prepare a partial balance sheet for 2018 and 2019 showing any items related to the contract. (Do not round intermediate calculations.)

0 times a week - 32 students

1 time a week- 18 students

2 times a week - 29 students

3 times a week - 26 students

4 times a week - 33 students

5 times a week - 31 students

6 times a week - 27 students

7 times a week - 54 students

The data given shows how many times a week students drink caffeine. With this data, state the null and alternative hypothesis, calculate the test statistic and p-value, and calculate the confidence interval.

3. Let P be an nxn projection matrix (which means that it satisfies P²=P and P^T=P). The goal of this problem is to show that P as a linear transformation is the orthogonal projection onto the range of P.

(a) Show that if v is in the range of P, then Pv=v.

(b) Show that if v is orthogonal to the range of P then Pv=0. (Hint: PPv lies in the range of P, hence is orthogonal to v. Study the dot product of v with PPv.)

(c) The previous parts show that P and the projection map act the same way on vectors that lie either in the range of P or the orthogonal complement of it. Why does this imply that P and the projection map agree on all vectors?

An absorption column operates at 1 atm to separate compound A from air using pure water as solvent. If the concentration of A in the inlet air stream is 900 ppm and the Henry's law constant for A in water is 1000 atm/ppm:

a) What is the equilibrium line equation? (** draw on chart and label)

If the desired outlet air is to contain 200 ppm compound A:

b) What is (L/V)min? (** draw on chart and label)

c) If the actual operating (L/V) is 1.285(L/V), what is the operating equation? (** draw on chart and label)

d) If the actual operating (L/V) is 1.285(L/V), what is the required number of ideal stages? (** draw on chart)

Consider a thin flat rectangular region that of size 4 x 2 m2 and it is electrically insulated at its four corners. (A)Solve Laplace’s equation  2 V(x,y) = 0 in the rectangular region 0 < x < 4 m and 0 < y < 2 m using the separation of variable technique subject to the following boundary conditions:
V(0,y) = 0
V(4,y) = q(y) = 50 sin (3π y / 2)
V(x,0) = 0
V(x,2) = f(x) =100 sin (π x / 4)
(B) Use the result of part (A) to find the corresponding electric field inside the region.