Pre-Calculus
U12N2: Day 2 Parabolas (Applications)
Examples: You will need a calculator!!!
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1)Asate11itedishi"@.Thesigna1sthatemanatefromasate1lite
strike the surface of the dish and are reflected to a si
int, where the receiver is
iocated. If the dish is 1O feet across at its widest opening andlis 4 feet deep at its
center, at what position should the receiver by placed? (Hint: t\here should the focus
r:oint be placed?)
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2) A TV receiving dish is in the shape of a parabola. Find the location of the rec
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uvhich is placed at the focus, if the dish is 6 feet across at its opening and 2 feet deep.
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3) The cables of a suspension bridge are in the shape of a parabola. The towers
sr-ipporting the cable are 60O feet apart and 8O feet high. If the cables touch the road
i.t trface midway between the towers, what is the height ol_thc-tab-ls at a point 150 feet
f,rom a tower?
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a) The fuel efficiency of a vehicle can be modeled with a quadratic function over a
limited span of typical highway speeds. Suppose that a certain car has its best
efficiency, 34 miles per gallon , at a speed of 42 miles per hour. At 70 miles per hour
the efficiency is reduced to 20 miles per gallon.
a) Find a quadratic function that models the car's efficiency
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b) What speed(s) result in an efficiency of 25 miles per gallon?
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sounds from a distance. The sound waves enter the reflector and are concentrated
toward the microphone.
a) How far from the reflector should a microphone be placed if the reflector has a width
of 3 feet and a depth of i.25 feet?
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b) Write an eqrration to model a different parabolic reflector that is 4 feet wide and 2 feet
the left.
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