I need help with a math assignment

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ZeArjmIN

Mathematics

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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?

Unformatted Attachment Preview

fe 4 GHI 7 PORS * 5 JKL JKL 6 MNO 8 των 9wXYZ 0 # 3. Sums and Differences of Functions What can be said about the sum and difference of each pair of functions? (a) Two even functions (b) Two odd functions (c) An odd function and an even function 4. Inverse Functions The functions = f(x) = x and g(x) are their own inverse functions. Graph each function and explain why this is true. Graph other linear functions that are their own inverse functions. Find a formula for a family of linear functions that are their own inverse functions. 5. Proof Prove that a function of the form y = a,r2n + a2n-2121–2 + + a2x2 + ao is an even function. 6. Miniature Golf A golfer is trying to make a hole-in-one on the miniature golf green shown. The golf ball is at the point (2.5, 2) and the hole is at the point (9.5, 2). The golfer wants to bank the ball off the side wall of the green at the point (x, y). Find the coordinates of the point (x, y). Then write an equation for the path of the ball. y у (x, y) 8 ft х 12 ft Figure for 6 At 2:00 P.M. on April 11, 1912, the Ireland, on her voyage to New Y P.M. on April 14, the Titanic struck ar having covered only about 2100 mil tely 3400-mile trip. ar the total di 10. Trip Time You are in a boat 2 miles from the nearest point on the coast (see figure). You plan to travel to point Q, 3 miles down the coast and 1 mile inland. You row at 2 miles per hour and walk at 4 miles per hour. 2 mi 3 - r 1 mi Nor drawn to scale 3 mi (a) Write the total time T (in hours) of the trip as a function of the distance x (in miles). (b) Determine the domain of the function. (c) Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. (d) Find the value of x that minimizes T. (e) Write a brief paragraph interpreting these values. 11. Heaviside Function The Heaviside function 1, x > 0 H(x) lo, x < 0 is widely used in engineering applications. (See figure.) To print an enlarged copy of the graph, go to MathGraphs.com. 3 H(x) 2 1 X -3 -2 -1 1 2 2 3
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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 ...


Anonymous
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