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Mathquestions.150points.Thenumberofhours,H,ofdaylightinMadridatpariculartimeofyearmaybeapproximatebyH(t)=12+2.4sin[0.0172(t-80)]wheretisthenumberofdayssincethestartoftheyear.Findtheaveragenumberofhoursofdaylight
题目详情
Math questions.150 points.
The number of hours,H,of daylight in Madrid at paricular time of year may be approximate by H(t)=12+2.4sin[0.0172(t-80)] where t is the number of days since the start of the year.Find the average number of hours of daylight in Madrid [you may use your calculator to carry out your calculations]:a in January B in June c over a whole year d comment on the relative magnitudes of your answers to part a,b,c.why are they reasonable.
process is very important.
The number of hours,H,of daylight in Madrid at paricular time of year may be approximate by H(t)=12+2.4sin[0.0172(t-80)] where t is the number of days since the start of the year.Find the average number of hours of daylight in Madrid [you may use your calculator to carry out your calculations]:a in January B in June c over a whole year d comment on the relative magnitudes of your answers to part a,b,c.why are they reasonable.
process is very important.
▼优质解答
答案和解析
t\x05sin(0.0172*(t-80))\x05H(t)\x05\x05\x05t\x05sin(0.0172*(t-80))\x05H(t)
A\x051\x05-0.977612812\x059.653729251\x05\x05B\x05152\x050.945263115\x0514.26863148
\x05365\x05-0.982077623\x059.643013704\x05\x05\x05153\x050.950735535\x0514.28176528
\x053\x05-0.969797691\x059.672485541\x05\x05\x05154\x050.955926697\x0514.29422407
\x054\x05-0.965459185\x059.682897956\x05\x05\x05155\x050.960835064\x0514.30600415
\x055\x05-0.960835064\x059.693995846\x05\x05\x05156\x050.965459185\x0514.31710204
\x056\x05-0.955926697\x059.705775927\x05\x05\x05157\x050.969797691\x0514.32751446
\x057\x05-0.950735535\x059.718234715\x05\x05\x05158\x050.9738493\x0514.33723832
\x058\x05-0.945263115\x059.731368524\x05\x05\x05159\x050.977612812\x0514.34627075
\x059\x05-0.939511055\x059.745173468\x05\x05\x05160\x050.981087114\x0514.35460907
\x0510\x05-0.933481057\x059.759645464\x05\x05\x05161\x050.984271179\x0514.36225083
\x0511\x05-0.927174904\x059.774780229\x05\x05\x05162\x050.987164064\x0514.36919375
\x0512\x05-0.920594463\x059.790573288\x05\x05\x05163\x050.989764913\x0514.37543579
\x0513\x05-0.91374168\x059.807019967\x05\x05\x05164\x050.992072958\x0514.3809751
\x0514\x05-0.906618583\x059.824115401\x05\x05\x05165\x050.994087515\x0514.38581004
\x0515\x05-0.899227278\x059.841854534\x05\x05\x05166\x050.995807989\x0514.38993917
\x0516\x05-0.891569952\x059.860232116\x05\x05\x05167\x050.997233869\x0514.39336129
\x0517\x05-0.88364887\x059.879242711\x05\x05\x05168\x050.998364736\x0514.39607537
\x0518\x05-0.875466377\x059.898880696\x05\x05\x05169\x050.999200254\x0514.39808061
\x0519\x05-0.867024891\x059.919140261\x05\x05\x05170\x050.999740175\x0514.39937642
\x0520\x05-0.858326912\x059.940015412\x05\x05\x05171\x050.999984341\x0514.39996242
\x0521\x05-0.849375011\x059.961499974\x05\x05\x05172\x050.999932678\x0514.39983843
\x0522\x05-0.840171837\x059.983587591\x05\x05\x05173\x050.999585203\x0514.39900449
\x0523\x05-0.830720113\x0510.00627173\x05\x05\x05174\x050.998942018\x0514.39746084
\x0524\x05-0.821022635\x0510.02954568\x05\x05\x05175\x050.998003313\x0514.39520795
\x0525\x05-0.811082271\x0510.05340255\x05\x05\x05176\x050.996769366\x0514.39224648
\x0526\x05-0.800901963\x0510.07783529\x05\x05\x05177\x050.995240542\x0514.3885773
\x0527\x05-0.790484722\x0510.10283667\x05\x05\x05178\x050.993417293\x0514.3842015
\x0528\x05-0.779833629\x0510.12839929\x05\x05\x05179\x050.991300159\x0514.37912038
\x0529\x05-0.768951837\x0510.15451559\x05\x05\x05180\x050.988889766\x0514.37333544
\x0530\x05-0.757842563\x0510.18117785\x05\x05\x05181\x050.986186827\x0514.36684838
\x0531\x05-0.746509094\x0510.20837817\x05\x05\x05\x05averageH(t)of JUN\x0514.31773993
\x05\x05averageH(t)of JAN\x059.931053712\x05\x05\x05\x05\x05
answer of A and B as data above,I calculatd with excel.
quantion C's answer is 12 hours.
question D.because the function H(t) is a trigonometric function with period 2pie/0.0172=
365.3 and mean value 12,I believe it is reasionable.
A\x051\x05-0.977612812\x059.653729251\x05\x05B\x05152\x050.945263115\x0514.26863148
\x05365\x05-0.982077623\x059.643013704\x05\x05\x05153\x050.950735535\x0514.28176528
\x053\x05-0.969797691\x059.672485541\x05\x05\x05154\x050.955926697\x0514.29422407
\x054\x05-0.965459185\x059.682897956\x05\x05\x05155\x050.960835064\x0514.30600415
\x055\x05-0.960835064\x059.693995846\x05\x05\x05156\x050.965459185\x0514.31710204
\x056\x05-0.955926697\x059.705775927\x05\x05\x05157\x050.969797691\x0514.32751446
\x057\x05-0.950735535\x059.718234715\x05\x05\x05158\x050.9738493\x0514.33723832
\x058\x05-0.945263115\x059.731368524\x05\x05\x05159\x050.977612812\x0514.34627075
\x059\x05-0.939511055\x059.745173468\x05\x05\x05160\x050.981087114\x0514.35460907
\x0510\x05-0.933481057\x059.759645464\x05\x05\x05161\x050.984271179\x0514.36225083
\x0511\x05-0.927174904\x059.774780229\x05\x05\x05162\x050.987164064\x0514.36919375
\x0512\x05-0.920594463\x059.790573288\x05\x05\x05163\x050.989764913\x0514.37543579
\x0513\x05-0.91374168\x059.807019967\x05\x05\x05164\x050.992072958\x0514.3809751
\x0514\x05-0.906618583\x059.824115401\x05\x05\x05165\x050.994087515\x0514.38581004
\x0515\x05-0.899227278\x059.841854534\x05\x05\x05166\x050.995807989\x0514.38993917
\x0516\x05-0.891569952\x059.860232116\x05\x05\x05167\x050.997233869\x0514.39336129
\x0517\x05-0.88364887\x059.879242711\x05\x05\x05168\x050.998364736\x0514.39607537
\x0518\x05-0.875466377\x059.898880696\x05\x05\x05169\x050.999200254\x0514.39808061
\x0519\x05-0.867024891\x059.919140261\x05\x05\x05170\x050.999740175\x0514.39937642
\x0520\x05-0.858326912\x059.940015412\x05\x05\x05171\x050.999984341\x0514.39996242
\x0521\x05-0.849375011\x059.961499974\x05\x05\x05172\x050.999932678\x0514.39983843
\x0522\x05-0.840171837\x059.983587591\x05\x05\x05173\x050.999585203\x0514.39900449
\x0523\x05-0.830720113\x0510.00627173\x05\x05\x05174\x050.998942018\x0514.39746084
\x0524\x05-0.821022635\x0510.02954568\x05\x05\x05175\x050.998003313\x0514.39520795
\x0525\x05-0.811082271\x0510.05340255\x05\x05\x05176\x050.996769366\x0514.39224648
\x0526\x05-0.800901963\x0510.07783529\x05\x05\x05177\x050.995240542\x0514.3885773
\x0527\x05-0.790484722\x0510.10283667\x05\x05\x05178\x050.993417293\x0514.3842015
\x0528\x05-0.779833629\x0510.12839929\x05\x05\x05179\x050.991300159\x0514.37912038
\x0529\x05-0.768951837\x0510.15451559\x05\x05\x05180\x050.988889766\x0514.37333544
\x0530\x05-0.757842563\x0510.18117785\x05\x05\x05181\x050.986186827\x0514.36684838
\x0531\x05-0.746509094\x0510.20837817\x05\x05\x05\x05averageH(t)of JUN\x0514.31773993
\x05\x05averageH(t)of JAN\x059.931053712\x05\x05\x05\x05\x05
answer of A and B as data above,I calculatd with excel.
quantion C's answer is 12 hours.
question D.because the function H(t) is a trigonometric function with period 2pie/0.0172=
365.3 and mean value 12,I believe it is reasionable.
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