Need help with just question 10d

8 A current io is established the current is removed, the current in the circuit deca b A new al = -iR. ormation technology com dt a Show that i = ige " is a solution of this equation. at $1, and by the end of the year the Again assuming the exponential b Given that the resistance is R = 2 and that the current in the circuit decays to 37% of the initial C = 100elf current in a quarter of a second, find L. ( Notice that 37% = !. ) ii Find the value of e. 9 A tank in the shape of a vertical hexagonal prism with base area A is filled to a depth of 25 metres. The During which month will the share liquid inside is leaking through a small hole in the bottom of the tank, and it is found that the change in d What will be the (instantaneous) volume at any instant t hours after the tank starts leaking is proportional to the depth h metres, that is, the nearest cent per month? dy = -kh. 12 Given that y = Aoek, it is found that di kh a Show that an a Show that it is not necessary to ev di b Find y (3 ) in terms of An . b Show that h = hoe "A is a solution of this equation. c What is the value of ho? d Given that the depth in the tank is 15 metres after 2 hours, find e How long will it take to empty to a depth of just 5 metres? Answer correct to the nearest minute. 13 The growing population of rabbits 10 The emergency services are dealing with a toxic gas cloud around B model, with N = Noe2. When the a leaking gas cylinder 50 metres away. The prevailing conditions SERVICES N = Cte ' with the constants mean that the concentration C in parts per million (ppm) of the gas increases proportionally to the concentration as one moves towards 50 that time. a Find the values of B and C in te dx the cylinder. That is, "= KC, where x is the distance in metres b Show that the population reach towards the cylinder from their current position. a Show that C = Coe is a solution of the above equation. b At the truck, where x = 0, the concentration is C = 20000 ppm. Five metres closer, the concentration is C = 22500 ppm. Use this information to find the values of the constants Co and k. Give k exactly, then correct to three decimal places. c Find the gas concentration at the cylinder, correct to the nearest part per million. d The accepted safe level for this gas is 30 parts per million. The emergency services calculate how far back from the cylinder they should keep the public, rounding their answer up to the nearest 10 metres. i How far do they keep the public back? ii Why do they round their answer up and not round it in the normal way