Question 109727: I need some help with my daughters homework as I don't know what I'm doing, hope you can help.
Thermal expansion problem: Bridges on expressways often have expansion joints which are small gaps in the roadway between one bridge section and the next. The gaps are put there so that the bridge will have room to expand when the weather gets hot. Suppose that a bridge has a gap of 1.3 cm when the temp is 15 degrees C, and the gap narrows to 0.7 cm when the temp warms to 25 degrees C. Assume that the gap width varies linearly with the temp.
a) Write the particular equation for gap width as a function of temp.
b) How wide would the gap be at 35 degrees C? At -10 C
c) At what temp would the gap close completely? What mathematical name is given to this temp?
d) Would the temp ever be likely to get hot enough to close the gap?
e) Sketch the graph using an appropriate domain.
Thank you for any help you can give me
Brian
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Thermal expansion problem: Bridges on expressways often have expansion joints which are small gaps in the roadway between one bridge section and the next. The gaps are put there so that the bridge will have room to expand when the weather gets hot. Suppose that a bridge has a gap of 1.3 cm when the temp is 15 degrees C, and the gap narrows to 0.7 cm when the temp warms to 25 degrees C. Assume that the gap width varies linearly with the temp.
:
a) Write the particular equation for gap width as a function of temp.
Let x = temp, and y = gap
:
Determine the slope from the given information, translated to:
x1 = 15; y1 = 1.3; x2 = 25, y2 = .7
The slope (m) =  =  = -.06
:
Use the point/slope formula to determine the equation:
y - 1.3 = -.06(x - 15)
y - 1.3 = -.06x + .9
y = -.06x + .9 + 1.3
y = -.06x + 2.2, is our particular equation
:
:
b) How wide would the gap be at 35 degrees C? At -10 C
:
Substitute -10 for x in our equation, find y
y = -.06(-10) + 2.2
y = +.6 + 2.2
y = 2.8 cm at -10 degrees
:
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c) At what temp would the gap close completely?
:
When the gap is closed, y = 0, therefore we can find x:
-.06x + 2.2 = 0
-.06x = -2.2
x = -2.2/-,06
x = +36.67 degrees
:
What mathematical name is given to this temp? The x intercept
:
:
d) Would the temp ever be likely to get hot enough to close the gap?
:
I think it would. Steel in the hot sun can get well over 100 degrees F, which
is about 37 degree C
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e) Sketch the graph using an appropriate domain.
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Note the x intercept occurs at about 37 degrees
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Any questions about this?
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