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A solar farm records its power output (in kilowatt-hours) once every hour from 10 a.m. to 2 p.m. The data are shown below, where t is hours after 10 a.m. and P(t) is the power generated in that hour.
Use the trapezoidal rule with an interval width of 1 to estimate the total energy generated between 10 a.m. and 2 p.m..
A high-precision meter later shows the true total was 325 kWh.
Calculate the percentage error of your estimate from part (a).
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A pollutant’s concentration in a river (in mg/L) at time t hours after a spill can be estimated by the following table:
Estimate the total pollutant exposure with a step size h=1 by using the trapezoidal rule.
It is known that the total exposure is actually 39Lmg⋅h.
Find the percent error of your estimate from part (a).
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The total market value of all the gold in the world is 2.7×1013 US dollars.
Given that a kilogram of gold costs $110000, calculate the mass of all the gold in the world.
Olympic swimming pools have dimensions 50m by 25m by 2m. It is given that 1cm3 of gold weighs 19g.
Find the number of olympic swimming pools needed to store all the world's gold.
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A spherical raindrop has a diameter of 2mm.
Find the volume of the raindrop in cm3.
In the following parts of the problem, give all your answers in the form a×10k where 1≤a<10 and k∈Z.
During a large thunderstorm, 7000m3 of water falls.
Estimate the number of raindrops that fell.
The number of HX2O molecules in 1mL is 3.34×1022.
Calculate the number of HX2O molecules that fell during the storm.
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