Matter is in a liquid state when its temperature is between its melting point and its boiling point. Suppose that some substance
has a melting point of negative 37.57 degrees Upper C and a boiling point of 389.96 degrees Upper C. What is the range of temperatures in degrees Fahrenheit for which this substance is not in a liquid state? (Hint: Upper C equals five ninths left parenthesis Upper F minus 32 right parenthesis ) Express the range as an inequality and in interval notation.
1 answer:
Answer:
-35.626 < temperature < 733.928 . . . . degrees F
(-35.626, 733.928)
Step-by-step explanation:
It is convenient to let a calculator evaluate the expression for converting °C to °F.
-35.626 < temperature < 733.928 . . . . degrees F
(-35.626, 733.928) . . . . . . . . . . . . . . . . . in interval notation
_____
The given relation is C = 5/9(F -32). The inverse relation is F = 9/5C +32. That is the relation we need to use to answer this question.
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Answer:
- See the graphs attached and the explanation below
Explanation:
The most simple sine function, considered the parent function, is:
That function has:
- Midline, also known as rest or equilibrium position: y = 0
- Minimum: - 1
- Maximum: 1
- Amplitude: the distance between a minimum or a maximum and the midline = 1
- period: the interval of repetition of the function = 2π
The more general sine function is:
That function has:
- Midline: y = D (it is a vertical shift from the parent function)
- Minimum: - A + D
- Maximum: A + D
- Amplitude: A
- period: 2π/B
- phase shift: C (it is a horizontal shift of the from the parent function)
Now, you have to draw the sine function with the given key features:
- Period = 4 ⇒ 2π/B = 4 ⇒ B = π/2
- Amplitude, A = 3
- midline y = - 1 ⇒ D = - 1
- y-intercept = (0, -1)
Substitute the know values and use the y-intercept to find C:
Substitute (0, -1)
Hence, the function to graph is:
To draw that function use this:
- Maxima: 3(1) - 1 = 3 - 1 = 2, at x = 1 ± 4n (n = 0, 1, 2, 3, ...)
- Minima: 3(-1) - 1 = - 3 - 1 = -4
- y-intercept: (0, - 1)
- x-intercepts: the solutions to 0 = 3sin(πx/2) = - 1
- first point of the midline: (0, -1) it is the same y-intercept
With that you can understand the graphs attached.
See attached graph: v is on the y-axis and t is on the x-axis
