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Question

The temperature of water in a heating tea ket- tle rises according to the equation y = 30x + 72, where y is the temperature (in degrees Fahrenheit) x minutes after the kettle was put on the burner. (a) Whatphysicalinterpretationcanbegiventothey-intercept of the graph? (b) What will the temperature of the water be after 3 minutes? (c) After how many minutes will the water be at its boiling point of 212° ?

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Answer to a math question The temperature of water in a heating tea ket- tle rises according to the equation y = 30x + 72, where y is the temperature (in degrees Fahrenheit) x minutes after the kettle was put on the burner. (a) Whatphysicalinterpretationcanbegiventothey-intercept of the graph? (b) What will the temperature of the water be after 3 minutes? (c) After how many minutes will the water be at its boiling point of 212° ?

Expert avatar
Gene
4.5
107 Answers
To find the physical interpretation of the y-intercept of the graph, we need to analyze the equation y = 30x + 72.

(a) The y-intercept represents the initial temperature of the water in the tea kettle. In this case, the y-intercept is 72. Therefore, the physical interpretation of the y-intercept is that the initial temperature of the water in the tea kettle is 72 degrees Fahrenheit.

To find the temperature of the water after 3 minutes, we can substitute x = 3 into the equation y = 30x + 72.

(b) y = 30(3) + 72
= 90 + 72
= 162

After 3 minutes, the temperature of the water will be 162 degrees Fahrenheit.

To find the number of minutes it takes for the water to reach its boiling point of 212°, we set the temperature (y) equal to 212 and solve for x.

(c) 212 = 30x + 72
30x = 212 - 72
30x = 140
x = 140 / 30
x = 4.6667

After approximately 4.67 minutes, the water will reach its boiling point of 212 degrees Fahrenheit.

Answer:
(a) The physical interpretation of the y-intercept is that the initial temperature of the water in the tea kettle is 72 degrees Fahrenheit.
(b) After 3 minutes, the temperature of the water will be 162 degrees Fahrenheit.
(c) After approximately 4.67 minutes, the water will reach its boiling point of 212 degrees Fahrenheit.

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