In Python

1. Calculate the following: (a) 29(2026+2.43)(ln(1.29+11.1))5 (b) tan(105)sec()+sin(1211) (Give exact and approximate answers.) 2. Given a triangle with vertices at the coordinates A(1,3),B(1,1),C(3,7) : (a) Find the lengths of the sides. (b) Use the Law of Cosines formula to find cos(BAC). NOTE the formula can be rewritten as cos(BAC)=2bcb2+c2a2 where a,b,c are BC,AC,AB respectively. (c) Confirm your answer by finding cos(BAC) by using the dot product formula to find the angle between a=AB=2,2 and b=AC=(2,4. NOTE that you found the magnitudes in part (a), and you can compute the dot product by just using arithmetic operations. 3. The monthly payment R required to pay off a loan of P dollars at 100r% interest (so for example, 5% interest means r=.05 ) over t years compounded monthly is given by R=P(1+125)12t112c(1+12t)12t (a) You botrow $200,000 to buy a house at 4% interest. Compute the monthly payment (don't worry about rounding) if your loan is for: (i) 30 years (ii) 15 years (b) Calculate how much total you end up paying for your \$200,000 loan in each case. (HINT: you make 360 payments on the 30 -your loan, but only 180 payments on the 15 -year loan)