Scientists plan to release a space probe that will enter the atmosphere of a gaseous planet. The temperature of the gaseous plan
et increases linearly with the height of the atmosphere as measured from the top of a visible boundary layer, defined as 0 kilometers in altitude. The instruments on board can withstand a temperature of 601 K. At what altitude will the probe's instruments fail?
1 answer:
Based on my analysis, the image aligns well with the inquiry. From the provided graph, we can derive the equation of the line through the two-point formula. Knowing the temperature at 601 K allows us to calculate the corresponding altitude.
y - y1 = [(y2 - y1)/(x2 - x1)](x - x1)
y - 147.52 = [ (567 - 147.54)/(78.11 - 18.4) ](x - 18.4)
By substituting y = 601, we can solve for x:
601 - 147.52 = [ (567 - 147.54)/(78.11 - 18.4) ](x - 18.4<span>)
</span>x = 83
Hence, the instruments on the probe will fail at an altitude of 83 kilometers.
y - y1 = [(y2 - y1)/(x2 - x1)](x - x1)
y - 147.52 = [ (567 - 147.54)/(78.11 - 18.4) ](x - 18.4)
By substituting y = 601, we can solve for x:
601 - 147.52 = [ (567 - 147.54)/(78.11 - 18.4) ](x - 18.4<span>)
</span>x = 83
Hence, the instruments on the probe will fail at an altitude of 83 kilometers.
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