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

likes
740 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° ?

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.

Frequently asked questions (FAQs)
Question: What is the area of a square when the length of each side is represented by 'a'?
+
Math question: What is the equation of a logarithmic function whose graph passes through points A(1, 4) and B(3, 6)?
+
Math Question: What is the sine value of an angle corresponding to π/3 radians on the unit circle chart?
+
New questions in Mathematics
How many percent is one second out a 24 hour?
x/20*100
1. Suppose we have a good whose quantity supplied changed from 100 to 120 units when the price increased from $10 to $12 per unit. Compute the price elasticity of supply using the midpoint method
The sum of two numbers is equal to 58 and the largest exceeds by at least 12. Find the two numbers
∫ √9x + 1 dx
Calculate the value of a so that the vectors (2,2,−1),(3,4,2) and(a,2,3) are coplanar.
The question is using rule 72 determine Kari wants to save 10,000 for a down payment on a house. Illustrate the difference in years it will take her to double her current 5,000 savings based on 6%, 12% and 18% interest rate .
Congratulations, you have saved well and are ready to begin your retirement. If you have $1,750,000.00 saved for your retirement and want it to last for 40 years, and will earn 10.8% compounded monthly: What is the amount of the monthly distribuion? 216.50 How much interest is earned in retirement?
List the remaining zeros of the polynomial with the given zeros Zeros are: 2, 3i, and 3 + i
How to factorise 5y^2 -7y -52
Log0
A given initial capital in simple interest at the annual rate and for 27 months produced the accumulated capital of 6600 um if the same capital had been invested at the same rate but during 28 months the said accumulated capital would be increased in an amount corresponding to 0.75% of the initial capital Calculate the initial capital and the annual rate at which it was invested
A salesperson earns a base salary of $600 per month plus a commission of 10% of the sales she makes. You discover that on average, it takes you an hour and a half to make $100 worth of sales. How many hours will you have to work on average each month for your income to be $2000?
X^3 - x^2 - 4 = 0, what are the values of x?
The average undergraduate cost per tuition, fees, room, and board for all institutions last year was $26,025. A random sample of 40 institutions of higher learning this year indicated that the mean tuition, fees, room, and board for the sample was $27,690, and the population standard deviation is $5492. At the 0.05 level of significance, is there sufficient evidence that the cost has increased? (Remember to follow the steps in hypothesis testing)
A factory produces glass for windows. The thickness X of an arbitrarily selected pane of glass is assumed to be Normally distributed with expectation μ = 4.10 and standard deviation σ = 0.04. Expectation and Standard deviation is measured in millimeters. What is the probability that an arbitrary route has a thickness less than 4.00 mm?
Solve for z: 2z-6=10z+2
How many moles are there in 235 grams of potassium thiosulfate pentahydrate? K2S2O3*5(H2O)
Find the symmetric point to a point P = (2,-7,10) with respect to a plane containing a point Po = (3, 2, 2) and perpendicular to a vector u = [1, -3, 2].
The domain of the function f(x)=x+7x2−144 is (−∞,), ( ,), and ( , ∞).