A Parabolic Trough A water runoff collector is built in the shape of a parabolic trough as shown below. 12 in 18 in 3ft We are tasked with writing an equation for the surface area of the water in the trough as a function of the depth of the water. This means that we need to find a function where • the input variable is the depth of the water in the trough, and • the output variable is the surface area of the water in the trough. We begin by writing the equation for the parabolic cross-sectional shape of the trough. To do this, we impose a coordinate system at the cross-section with -6 • a measured horizontally, . y measured vertically, and • the origin at the vertex of the parabola. 18 6 x In the next activity, you will need to find an equation for this parabolic shape and show your work. Hint: use the equation y = az², identify a point on the graph, substitute the a and y values into the equation, and solve for the stretch factor a.
A Parabolic Trough A water runoff collector is built in the shape of a parabolic trough as shown below. 12 in 18 in 3ft We are tasked with writing an equation for the surface area of the water in the trough as a function of the depth of the water. This means that we need to find a function where • the input variable is the depth of the water in the trough, and • the output variable is the surface area of the water in the trough. We begin by writing the equation for the parabolic cross-sectional shape of the trough. To do this, we impose a coordinate system at the cross-section with -6 • a measured horizontally, . y measured vertically, and • the origin at the vertex of the parabola. 18 6 x In the next activity, you will need to find an equation for this parabolic shape and show your work. Hint: use the equation y = az², identify a point on the graph, substitute the a and y values into the equation, and solve for the stretch factor a.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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I attached the previous page also here plz look that and do this question 1 plz
Transcribed Image Text:A Parabolic Trough
A water runoff collector is built in the shape of a parabolic trough as shown below.
12 in
18 in
3ft
We are tasked with writing an equation for the surface area of the water in the trough as a
function of the depth of the water.
This means that we need to find a function where
• the input variable is the depth of the water in the trough, and
• the output variable is the surface area of the water in the trough.
We begin by writing the equation for the parabolic cross-sectional shape of the trough. To
do this, we impose a coordinate system at the cross-section with
-6
• measured horizontally,
• y measured vertically, and
• the origin at the vertex of the parabola.
18-
6 x
In the next activity, you will need to find an equation for this parabolic shape and show
your work. Hint: use the equation y = az², identify a point on the graph, substitute the a
and y values into the equation, and solve for the stretch factor a.
Transcribed Image Text:Question 1
On the previous page, we learned that we need to begin by writing the equation for the
parabolic cross-sectional shape of the trough. Repeat the work here.
• Impose a coordinate system at the cross-section with a measured horizontally, y
measured vertically, and the origin at the vertex of the parabola.
• Sketch a graph of the parabolic cross-section and include all relevant information
from the diagram of the trough above.
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