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° ?
148
likes740 views
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° ?
Gene
4.5108 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.
(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.
Frequently asked questions (FAQs)
What is the mode of the following dataset: 2, 5, 5, 8, 10
+
What is the equation for finding the volume of a sphere?
+
What is the degree and end behavior of the cubic function f(x) = x^3? Define its symmetry and the number of real zeros.
+
New questions in Mathematics