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Quiz 4NAMES_World's Best _Student____________________________ 1) Let t(h) be the temperature in degrees Celsius at a height h (in meters) above the surface of the earth. What do each of the following quantities mean to a sky diver? Explain using complete sentences. Give units for the quantities. (a) t(1000) =22.1 At 1000 meters the temp is 22.1 degrees (b) t ' (20)=2.18 (Perhaps the decimal place Is misplaced-fix it to make this a more reasonable value) t'(20)=-0.0218 deg/meter. Since temps decrease as altitude increases this should be negative.Expecting 2.18 degrees each meter seems pretty extreme. (c) t(h) + 20 SKIPPED! (d) h such that t ' (h) = 20 h represents the height at which the temp is changing at the rate of 20 degrees per meter of increased altitude (e) Make up a reasonable value for t(1000) and t ' (1000) and use your value to estimate t(900) and t(1100) t(1000)=22.1 degrees and let t'(1000)=-.02 degrees/meter. ie every additional meter of height reduces the temp by .02 degrees. Thus going up to 1100 meters means a decrease of 100(-.02) degrees=-2 degrees. So t(1100)=20.1. Similarly t(900)= 24.1 degrees. 2) Let L(r) be the amount of lumber, in board-feet, produced from a tree of radius r (measured in inches). Interpret the following in practical terms, giving units. Use complete sentences. (a) L(6) =1200 A tree of radius 6" produces 1200 board feet of lumber (b) L ' (24)=82 If a tree has radius 24 inches each additional Inch produces 82 more board feet (c) r such that L(r) = 100 The radius of tree that produces 100 board feet (d) r such that L ' (r) = 10 The radius of tree at whichh each additional inch produces 10 additional board feet. (e) Use L(24)=1200 and L ' (24)=82 to find the equation of the line tangent to the curve y=L(r) at the point y=1200, r=24 y-1200=82(r-24)