Can you use maxima software and show working out handwritten for the rest

Question 3 5 marks You should be able to answer this question after studying Unit 9. You should use Maximo to answer this question. Include a printout or sereenshot of your Mawima worksheet with your solution. Your solution should include a clear statement of the problem and the method used. Remember that for good mathematical communication you should present your answer clearly. Below are the recipes for my three favourite cakes: Flour (in cups) Milk (in cups) Sugar (in cups) Angel cake 2 2 4 Victoria cake 4 l 1 Rainbow cake 8 9 5 Suppose that in my cupboard l have 80 cups of our, 64 cups of milk and 96 cups of sugar. How many Angel, Victoria and Rainbow cakes can I make with these ingredients, assuming that I use all of the ingredients? You should model the problem as a system of three linear simultaneous equations, and then use matrices to nd the number of Angel, Victoria and Rainbow cakes. Question 4 10 marks You should be able to answer this question after studying Unit 10. (a) For the innite geometric sequence (run) whose rst four terms are 8.0, 6.0, 4.5, 3.375, nd the values of the rst term :31 = a and the common ratio r, and write down a recurrence system for this sequence. (b) Write down a closed form for this sequence. (c) Calculate the twelfth term of the sequence to four decimal places. (d) Describe the longterm behaviour of the sequence. Justify your answer. Question 5 5 marks You should be able to answer this question after studying Unit 10. A bank account, which pays no interest, is set lip with an initial deposit of 1000. After a year has passed, 120 is added to the account. After each subsequent year, an amount of money is added to the account that is 20 more than the amount added in the previous year. Work out how much money is in the account after 30 years