Answer:
110.5348 minutes
Step-by-step explanation:
The difference from room temperature changes from 103 to 59 in 46 minutes, so that difference can be modeled by the exponential equation ...
Δt = 103×(59/103)^(t/46)
We want to find t for the temperature difference Δt = 91 -64 = 27.
27 = 103×(59/103)^(t/46)
27/103 = (59/103)^(t/46) . . . . . divide by 103
Taking logs gives the linear equation ...
log(27/103) = (t/46)log(59/103)
Multiplying by the inverse of the coefficient of t, we get ...
t = 46·log(27/103)/log(59/103) ≈ 46·(-0.58147346)/(-0.24198521)
≈ 110.5347
It will take about 110.5347 minutes for the turkey to cool to 91 °F internally.
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<em>Comment on 4 decimal places</em>
An answer correct to 4 decimal places (7 significant digits) is a pretty good indication that the problem was worked correctly. However, that level of precision in the timing makes little sense in this context. Most thermometers will take at least a few seconds to register the temperature to within a tenth of a degree or so. This problem is asking for an answer that is within 6 milliseconds and 30 micro-degrees. Neither of these is anywhere near realistic for a kitchen meat thermometer.
More realistic would be an answer to 4 <em>significant figures</em>, a tenth of a minute and a few hundredths of a degree.
(The rate of change at the time of interest is about -0.33 degrees per minute.)
Answer:
x = 3
Step-by-step explanation:
Answer: -4x²z²y + 12xz²y
Step-by-step explanation:-------------
The picture isn’t loading but 12 is the answer to everything
Answer: Boat A should travel 152.8° to reach B
Step-by-step explanation:
The diagram illustrating the scenario is shown in the attached photo. Triangle ABP is formed. A represents the position of boat A. B represents the position of boat B. P represents the position of the port.
We would determine AB by applying the law of cosines
AB² = AP² + BP² - 2AP×BPCosP
AB² = 20² + 25² - 2 × 20 × 25 × Cos45
AB² = 1025 - 707.10678 = 317.89322
AB = √317.89322 = 17.83
We would determine the bearing of B from A by finding angle A. We would apply the sine rule.
AB/SinP = AP/Sin A
17.83/Sin45 = 20/SinA
Cross multiplying, it becomes
17.83 × SinA = 20Sin45 = 14.14
SinA = 14.14/17.83 = 0.79
A = Sin^-1(0.79) = 52.2°
The total angle at A is 65 + 52.2 = 117.2°
The angle formed outside the third quadrant is 117.2 - 90 = 27.2°
Therefore, bearing B from A is
180 - 27/2 = 152.8°