using c language:

Add two vectors of doubles. Name this function vect_add(). Subtract two vectors of doubles. Name this function vect_sub(). Multiplies element by element two vectors. Name this function vect_prod(). Compute and return the dot product of two vectors. Name this function vect_dot_prod(). The dot product operation is the result of taking two vectors(single dimension arrays) and multiplying corresponding element by element and then adding up the sum of all the products. For example, if I have 2 vectors of length 3 that have the following values {l, 2, 3} and {3, 2, l} the dot product of these two vectors is: 1*3+2*2+3*1 = 10 Compute and return the mean of a single vector. Name this function vect_mean(). Compute and return the median of a single vector. Name this function vect_median(). First sort the array. If the length of the sorted array is odd, then the median is the middle element. If the length is odd, the median is the average of the middle two elements. Compute and return the maximum element of a vector. Name this function vect_max(). Compute and return the minimum element of a vector. Name this function vect_min(). Write a function that reverses the elements in a given array. This function will change the original array, passed by reference. Name this function vect_reverse().

The equation y(x,t)=Acos2πf(xv−t) may be written as y(x,t)=Acos[2πλ(x−vt)].

Use the last expression for y(x,t) to find an expression for the transverse velocity vy of a particle in the string on which the wave travels. Express your answer in terms of the variables A, v, λ, x, t, and appropriate constants.

Find the maximum speed of a particle of the string. Express your answer in terms of the variables A, v, λ, x, t, and appropriate constants.

The two half cell reactions can be expressed as follows:

Li⁺¹ + e- + C₆ à LiC₆                           E_o = -2.84 V

Li⁺¹ + e- + CoO₂ à LiCoO₂           E_o = +0.25 V

A. Which of the two reactions will undergo reduction and which one will undergo oxidation when the battery discharges (spontaneous reaction)?

B.What is the theoretical voltage that can be produced by this cell at standard conditions?

C.Write the complete spontaneous redox reaction that combines the half cell reactions.

The electrical power generated by a wind turbine can depend only on L, the length of the turbine’s blades, ρ the mass density of the air, and v the speed of the air. Use dimensional analysis to show that the power created by the turbine must be proportional to the cube of the air speed, v. If the air speed doubles the power generated will increase by nearly an order of magnitude! Note that power in the MKS system is measured in Watts where 1[W] = 1 [J/ s] = 1 [kg · m^2/ s^3] .

(a) Once an ideal inductor is connected to a 220 V, 50 Hz a.c supply and later the same inductor is connected to 220 V, 100 Hz a.c supply. What happens to the current flowing through it in both the cases? Will the current be the same or different? Give brief reason (2marks)

(b) A current of 12A flows in a when connected to a 240V , 50Hz AC mains and 2A from a 12V DC mains. Find the values of (i) the resistance (ii) impedance (iii) inductance of the coil         (3marks)

1. Let V = { S, A, B, a, b, λ} and T = { a, b }, Find the languages generated by the grammar G = ( V, T, S, P } when the set of productions consists of:
   1. S → AB, A → aba, B → bab.
   2. S → AB, S → bA, A → bb, B → aa.
   3. S → AB, S → AA, A → Ab, A → a, B → b.
   4. S → A, S → B, A → abA, A → a, B → baB, B → b.
   5. S → AB, A → aBb, B → bAa, A → λ, B → λ.

Chem Lab/Biology Question

You need to prepare 350ml of an extraction buffer with the following composition: 125 mM NaCl (MW=58.44), 100mM Tris base (MW=121.1), and 3% (w/v) sodium dodecyl sulfate. You have access to water, powdered Tris base, 6 M NaCl solution, and 40% (w/v) solution of sodium dodecyl sulfate. How much of each component is needed (you may assume that solids contribute negligible volume to a solution)?

Water in a piston-cylinder assembly is at 1 MPa, 500◦C. There are two stops, a lower one at which Vmin = 1 m3 and an upper one at Vmax = 3 m3. The piston is loaded with a mass and outside atmosphere such that it floats when the pressure is 500 kPa. This setup is now cooled to 100◦C by rejecting heat to the surroundings at 20◦C. a. Show the path of the process on T-V and P-V diagrams. b. Determine the heat transferred and work done during this process.

Let ? ∈ {1, 2} and ? ∈ {3, 4} be independent random variables with PMF-s:

?_x(1)= 1/2 ?_x(2)= 1/2 ?_Y(3)= 1/3 ?_Y(4)= 2/3

(a) Write down the joint PMF

(b) Calculate ?(? + ? ≤ 5) and ? (? − ? ≥ 2)

(c) Calculate ?(?? ), ?(?²? ),Calculate E((X²+1)/(Y-2))

(d) Calculate the C??(?, ? ), C??(1 − ?, 3? + 2) and V??(2? − ? )

(e) Calculate C??(??, ?), C??(??, ? + ? ) and V?? (?/Y)