please show all woking out as i want to compare it to my work thank you

1. [13 marks] A stream. which is polluted with insecticide at concentration 9 gfm31 ows at a rate of 25 mgfday into a pond of volume 2000 m\". At the same time. water from the pond is owing into the sea at rate 25 m3fday. rl'he initial insecticide concentration in the pond is 2.5 gfm3_ {a} Let Flt} he the amount of insecticide [in grams] in the pond at time E {days}. \"'irite down and solve an appropriate differential equation for t} along with the appropriate initial condition. {h} After a long time. what happens to the concentration of insecticide in the pond? [c] It is known that if the insecticide concentration in the pond reaches 7 gfni' the water beetles in the pond will die. Hourr many days does it take for the insecticide concentration to reach this threshold? 2. [13 marks] Find the derivatives of each of the following. showing the working and simpli- fring- { J as = (2:052... + 31\"\" {h} g{t] = tang? 2.2-\") (c) 5* {dl W = ylizrj. where zcosy + sin{3:l: 4y] = 3 ME} = cos 1mm] 3. [3 marks] Find the following integrals exactly. Show all working. gm . {a} f cos{2:r.') esmlhl dr I'.I {h} an + :'r1 a; =1. [ll marks] In a suburban area. hourly internet usage is measured and recorded from zl'IIDAIN-l on October 1. 2023. It is observed that the hourly usage Ht}. measured t hours from this time, is a sinusoidal function {a sine or cosine curve). The maximum usage is 5TB (MGR). This maximum! peak usage occurs at 2AM. 10AM and PIl-I each day. The minimum usage is 1TB. {a} \""hat is the period of t}? {h} Find the formula for t} and sketch the graph of t} for El 5 t E 24. [c] Find the time{s]| at which the minimum usage occurs each day. showing the reason- ing. {d} Find fig} and evaluate f(3} exactly. ls the internet usage increasing or decreasing at t = 3 and why