a window is being built and the bottom is a rectangle and the top is a semicircle (picture below). there is 12 meters of framing materials. we want to design the window for maximum area. we can have a window with "a tall rectangle and a small semi-circle" or the opposite "a short wide rectangle with a big semicircle" or anything in between. a student is thinking of different scenarios. he picked three scenarios for r=1 m, r=1.5 m and r=2 m. we know that the height of rectangle will depend on radius of the semicircle given that we have only 12 meters of framing. find the height h under any of theses scenarios.
hint: 2h+2r+πr=12
window framing area optimization
select one:
a. h1=6, h2=3, h3=1.5
b. h1=7.25, h2=2.49, h3=1.2
c. h1=3 h2=4.5, h3=6
d. h1=6.86 h2=4.29, h3=1.72

Consider the function y = f(x)=3^x the values of f(1/2) and f(1/4). rounded to the nearest hundredth, are__and__ respectively

An airplane consumes fuel at a constant rate while flying through clear skies, and it consumes fuel at a rate of 64 gallons per minute while flying through rain clouds. let c represent the number of minutes the plane can fly through clear skies and r represent the number of minutes the plane can fly through rain clouds without consuming all of its fuel. 56c+64r < 900056c+64r< 9000 according to the inequality, at what rate does the airplane consume fuel while flying through clear skies, and how much fuel does it have before takeoff? the airplane consumes fuel at a rate of gallons per minute while flying through clear skies, and it has gallons of fuel before takeoff. does the airplane have enough fuel to fly for 60 minutes through clear skies and 90 minutes through rain clouds?

Need solving this second acceleration problem.