Description
Read through the two problems and try to come up with a plan for solving these problems. Will you be using technology, and if so, what will it be? Do you have different ideas on how to approach the problems?
At the end of week 5, you must submit in the W5 Assignment dropbox a Microsoft Word document addressing the following items.
Problem solving plan (problems found on page 239-240 in textbook) Please see attachment
Problem 6
What parent function does it look like you need to use to fit the shape in Figure 6?
Share your ideas of how you will go about figuring out the equation. There are multiple methods, so if you have more than one idea, share them all!
Problem 10
In order to find the distance for the red marked paths, does it make more sense to use the Pythagorean Theorem, distance formula, slope, or equation of the line? Could it be possible to use any of them? Explain your answer.
What concept or formula will you need to use in order to create the equation that gives time as a function of distance?
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Explanation & Answer
Attached.
6. Parent function for this plot is linear function. Using linear functions, this can be modeled as
a piece wise function.
f(x)
2.5 ≤ 𝑥 ≤ 6
g(x)
6 ≤ 𝑥 ≤ 9.5
y
This problem can be solved manually. Two equations of the lines can be found using their
slopes as coordinates of the ball and hole is known.
Coordinates of the ball
= (2.5, 2)
Coordinates of the hole
= (9.5, 2)
To bank the ball, x coordinate should be the mid-point of the line from ball to hole.
x coordinate of the (x, y) point,
=
2.5 + 9.5
2
=6
y coordinate of the (x, y) point is 8ft as maximum limit of side wall.
So, the coordinates of the point (x, y)
= (6, 8)
When we know the coordinates of the banked point, two equations of the paths of the ball can be
found.
Path consist of the line passing through (2.5, 2), (6, 8) and (9.5, 2), (6, 8)
We have to find equations of these two lines
Line passing through (2.5, 2) and (6, 8)
Slope of the line
slope =
y2 − y1
x2 − x1
=
8−2
6
12
=
=
6 − 2.5 3.5
7
Equation =
y − 8 12
=
x−6
7
y − 8 12
=
x−6
7
Simplify this
7(y − 8) = 12(x − 6)
7y − 56 = 12x − 72
7y = 12x − 72 + 56
7y = 12x − 72 ...