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dT Avalanche forecasters measure the temperature gradient which is the rate at which the temperature...

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Calculus

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dT Avalanche forecasters measure the temperature gradient which is the rate at which the temperature in a snowpack T changes with dh respect to its depth h A large temperature gradient may lead to a weak layer in the snowpack When these weak layers collapse avalanches occur Avalanche forecasters use the rule of thumb that if exceeds 10 C m anywhere in the snowpack conditions are dh dT favorable for weak layer formation and the risk of avalanche increases Assume the temperature function is continuous and differentiable Complete parts a through d below a An avalanche forecaster digs a snow pit and takes two temperature measurements At the surface h 0 the temperature is 14 C At a depth of 1 1 m the temperature is 2 C Using the Mean Value Theorem what can he conclude about the temperature gradient The average temperature gradient from h 0 to h 1 1 is C m Simplify your answer Round to the nearest tenth as needed

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