Name:_______________________‌ ‌
Radical‌F
‌ unction‌‌Application‌‌Problems‌ ‌
‌
1.‌‌The‌‌speed‌‌traveled‌‌by‌a‌ ‌ti
‌ dal‌‌wave‌‌can‌‌be‌‌modeled‌‌by‌‌the‌‌equation‌‌
‌ here‌S‌ ‌‌is‌‌the‌s‌ peed‌i‌n‌k‌ ilometers‌‌per‌‌hour,‌‌and‌d
w
‌ ‌‌is‌‌the‌‌
average‌‌depth‌‌of‌‌the‌w
‌ ater‌i‌n‌k‌ ilometers.‌ ‌
‌
a)‌‌‌Solve‌‌the‌‌equation‌‌for‌d
‌ .‌‌ ‌
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b)‌‌‌A‌‌tidal‌‌wave‌‌is‌‌traveling‌‌at‌1
‌ 15‌‌kilometers‌‌per‌‌hour.‌‌What‌‌is‌‌the‌‌average‌‌
depth‌‌of‌‌the‌‌water,‌t‌ o‌t‌ he‌n
‌ earest‌‌thousandths‌‌of‌‌a‌‌kilometer‌.‌ ‌
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2.‌T‌ he‌‌lateral‌‌surface‌‌area‌‌of‌‌a‌‌right‌‌circular‌‌cone,‌s‌ ,‌‌‌is‌‌represented‌‌by‌‌the‌‌
equation‌‌
,‌w
‌ here‌r‌ ‌‌is‌‌the‌r‌ adius‌o
‌ f‌t‌ he‌‌circular‌‌base‌‌and‌h
‌ ‌‌is‌‌
the‌‌height‌‌of‌‌the‌‌cone.‌‌If‌‌the‌l‌ateral‌‌surface‌‌area‌‌of‌‌a‌‌large‌‌cone-shaped‌‌
funnel‌‌is‌‌364.25‌‌square‌c‌ entimeters‌‌and‌‌its‌‌radius‌‌is‌‌5.75‌‌centimeters,‌‌find‌‌
its‌‌height,‌‌to‌‌the‌n
‌ earest‌‌hundredth‌‌of‌‌a‌‌centimeter‌.‌ ‌
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3.A‌r‌ ectangle‌‌has‌‌a‌‌perimeter‌o
‌ f‌‌24‌‌inches‌‌with‌‌a‌‌length‌‌of‌‌4‌‌inches‌‌and‌‌a‌‌
width‌‌of‌‌
‌inches.‌‌Find‌x‌ .‌ ‌
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4.‌‌A‌‌wrecking‌‌ball,‌‌when‌s‌ uspended‌‌from‌‌a‌‌crane,‌‌models‌‌the‌‌movement‌‌of‌‌
a‌‌pendulum.‌‌The‌‌relationship‌b
‌ etween‌R
‌ ‌‌(the‌‌rate‌‌of‌‌speed‌‌of‌‌the‌‌ball),‌m
‌ ‌‌
(the‌‌mass‌‌of‌‌the‌‌ball),‌L‌ ‌‌(the‌‌length‌‌of‌‌the‌c‌ hain),‌‌and‌F‌ ,‌‌‌(the‌‌force)‌‌is‌‌
represented‌‌by‌‌of‌‌the‌‌
.‌‌Determine‌F‌ ‌‌when‌L‌ ‌‌=‌‌15,‌m
‌ ‌‌=‌‌60‌‌and‌ ‌
R‌‌‌=‌0
‌ .7.‌(‌Express‌a‌ nswer‌t‌ o‌t‌ he‌‌nearest‌t‌ enth.‌)‌ ‌
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5.‌‌The‌‌horizon‌‌(skyline)‌‌is‌‌an‌a
‌ pparent‌‌line‌‌that‌‌separates‌‌the‌‌earth‌‌from‌‌the‌‌
sky.‌‌The‌‌distance‌‌to‌‌the‌h
‌ orizon‌‌from‌‌an‌‌observer‌‌close‌‌to‌‌the‌‌Earth's‌‌surface‌‌
(ignoring‌‌atmospheric‌r‌ efraction)‌‌can‌‌be‌‌approximated‌‌by:‌ ‌
‌
where‌d
‌ ‌i‌s‌‌the‌‌distance‌‌in‌‌kilometers‌a‌ nd‌h
‌ ‌‌is‌‌the‌h
‌ eight‌‌above‌‌ground‌‌level‌‌
in‌‌meters.‌ ‌
Express‌‌answers‌‌to‌‌the‌n
‌ earest‌‌‌tenth.‌ ‌
‌
a)‌What‌‌is‌‌the‌‌distance‌‌to‌‌the‌h
‌ orizon‌‌at‌‌an‌‌average‌‌eye-level‌‌height‌‌of‌‌5‌‌ft.‌‌7‌‌
in.‌‌(1.7‌‌meters)?‌‌Express‌a‌ nswer‌‌in‌‌kilometers.‌ ‌
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b)‌‌‌What‌‌is‌‌the‌‌distance‌t‌ o‌t‌ he‌‌horizon‌‌from‌‌the‌‌top‌‌of‌‌Mount‌‌Everest‌ ‌
‌8,848‌‌meters‌‌in‌‌altitude?‌‌ ‌
‌