If gcd(a, m) = 1, then the unique solution xo to ax = b (mod m) is equal to (1) xo = ab (mod m)

Prove or Disprove: For all real valued functions f, if f(n) is O(2¹), then f(2m) is 0(2m).

Let Express in terms of 1 A = [₂ 2 and 2-² = [2] Α B-¹ 3 and find all its entries. ((BA)T)-¹ A and B-¹

An insulated, electrically-heated (100 kW) tank contains400 kg of water at 65°C when its power is lost. Water iswithdrawn at a steady rate of 0.4 kg/s and cold water (at12°C) enters the tank at the same rate. Assume the tankis well-mixed, and neglect heat gains or losses throughthe tank walls.  For the water, c=cp=cv=4200 J/kg C(a) Create a script (m-file) in MATLAB to calculate howlong will it take for the tank’s temperature to fall to 25°C.(b) Display the entire program code used for your scriptcreated in MATLAB. Make sure that running the scriptprovides a numeric result and include your name as acomment.