Please show your work.

\f10. (1 point) 13. (1 point) A hot air balloon takes off from the edge of a mountain lake. Given f(x) = Inx, g(x) = x2 +3 and h(x) = sinx, Impose a coordinate system as show below and assume that the find fogoh: path the balloon follows is the graph of the quadratic function (fogoh) (x) = f(x)=-2500-12 + 9x Answer(s) submitted: The land rises at a constant incline from the lake at the rate of 1 vertical foot for each 5 horizontal feet. (incorrect) y 14. (1 point) Lake Answer the following questions: (a) Find a formula for the height above the land as a function. h(x) = (b) At what x value does the balloon hit the ground? feet (c) At what x value does the balloon have maximum height above the ground? (a) f-1 (2) = x = .feet ( b ) f-' (f ( 2 ) ) = _ Answer(s) submitted: (c) Sketch the graph of f on the same axis. Answer(s) submitted: (incorrect) (incorrect) 15. (1 point) 11. (1 point) In 1941, British physicist G.I. Taylor noted that the radius R Find the maximum value of the quadratic function y = ->+ of the blast of a nuclear explosion should initially depend only Lx where L is a parameter. on the energy E of the explosion, the time : after the denotation, y = and the density of the air. The only number having dimensions Answer(s) submitted: of length that can be constructed from these quantities is: (incorrect) R= S (E12) 1/5 where S is a dimensionless parameter. [Note: p is rho.] 12. (1 point) Assuming the above function for the radius of the blast as a If the alleles A and B of the cystic fibrosis gen occur in a function of time t, R(t), find the inverse function ?(R) and ex- population with frequencies p and 1 - p (where p is a fraction plain what it means. Be sure to give the domain of the inverse between 0 and 1), then the frequency of heterozygous carriers function. (carriers with both alleles) is 2p(1 - p). Which value of p gives 1(R) = the largest frequency of heterozygous carriers? Domain of t(R) is Please use interval notation. P = Answer(s) submitted: Answer(s) submitted: (incorrect) (incorrect)16. (1 point) (a) Express the quantity as a single logarithm: 20. (1 point) 5 In(x1/2) + In(9x) = _ (a) Find all angles between 0 and 2nt for which sin(0) = 2. 0 = (b) Solve the equation for x: In(x4) - In(x2) =9 (b) If tan(0) = c and 0