. The height, hcm, of mercury in a thermometer varies directly with the Temperature, T:C, of the mercury. when T=45, h=6.75. Find h when T=76
Question
The height, hcm, of mercury in a thermometer varies directly with the Temperature, T:C, of the mercury.
When
T = 45,h = 6.75.
Find h when T = 76.
Solution
Sure, let's solve this step by step.
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First, we need to understand that "varies directly" means that the relationship between the height of mercury (h) and the temperature (T) can be expressed as h = kT, where k is the constant of variation.
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We know that when T = 45, h = 6.75. We can substitute these values into the equation to find the constant of variation (k). So, 6.75 = k * 45.
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To find k, we divide 6.75 by 45. k = 6.75 / 45 = 0.15.
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Now that we have the constant of variation, we can find the height of mercury (h) when T = 76. We substitute these values into the equation h = kT. So, h = 0.15 * 76.
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After doing the multiplication, we find that h = 11.4 cm.
So, when the temperature is 76 degrees Celsius, the height of the mercury in the thermometer is 11.4 cm.
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