## Question

###### Exploration 16.2:A Parameterization of Movement in the Plane Since you are approximating the vari...

Exploration 16.2:A Parameterization of Movement in the Plane Since you are approximating the various chosen s lengths, it might be helpful to note that 1/8 of an inch is equal to 0.125 inches and thus 1/16 of an inch is approximately equal to Often it is useful to investigate a rule or relation between ordered pairs in the plane as they relate to yet a third variable or parameter. In this investigation, movement of an object in the plane is described by parametric equations. Using a non-standard approach, we will describe the path of an object as it moves around the circumference of a circle. The relationship between circumference arc length s traversed by the object and associated values we will call w(s) and h(s) will be described. Using the origin as our reference point, the value of w(s) will represent the horizontal distance in the plane and h(s) will represent the vertical distance in the plane used to locate the endpoint of the path of our object as it moves in a counter-clockwise direction along the circumference of a unit circle. The assumption will be that the chosen portion of the circumference is measured from the point (1, 0) In addition to recording the chosen circumference s lengths, one needs to also record the ws) and h(s) distances associated with each s length as pictured in Figure 1. Recall that wis) represents the horizontal distance in the plane and h(s) represents the vertical distance in the plane used to locate the endpoint of an arbitrarily chosen length s along the circumference of your circle. It will be helpful to create a table of values in the format of Table 1. Keep in mind that you must denote the positive or negative direction of your recorded ws) and h(s) segment lengths depending on which quadrant you are working in when recording values. It is suggested that you take ten to twelve measurements as you progress around the circumference of the cirele. Table 1 To start, a circle of radius approximately one inch (for simplicity) centered at the origin of your coordinate system has been constructed in Figure 1. A thin piece of string of approximately 13 inches in length will be needed for this exploration. INOTE: The scale on the supplied ruler and "one inch" unit circle can be taken as the same. Please keep in mind that, due to paper copying irregularities, the provided ruler is likely not an accurate representation of a standard inch measurement. 1. Describe any patterns you notice in the relationship between s and w(s) and between s and h(s) respectively 2. Next, use the data recorded in Table 1 to construct two different graphs. The first graph should be a graph of w(s) values as a function of the associated s values, and the second graph should be of h(s) values as a function of the associated s values. The graphs of Figures 2 and 3 are provided for your use. Be sure to label and scale each graph. 1* Figure 1. (Not drawn to scale) h(s) Exploration procedure: Place one end of a string at the point (1,0) and run a length of the string along the circumference of the provided circle. Take approximate measurements of your s lengths at rational multiples of 2r proceeding around the circle in a counter-clockwise fashion Record readings in this manner starting from zero to twice around the circle. Measure your s string lengths using the provided ruler of Figure 2 12345678910111213น15 3. Fully describe the pattern of each of the relationships now that you have graphed them. 4. Can you find the value for s such that w(s) and h(s) are of equal value? 5. Can you find the value for s such that w(s) is half that of s? Also, what is the value of Figure 2. I[Ruler: use inches to measure string h(s) at this point?

## Answers

#### Similar Solved Questions

1 answers

##### Multiple lenses An object is 15 cm to the left of a positive lens of focal...

Multiple lenses An object is 15 cm to the left of a positive lens of focal length 15 cm. A second positive lens of focal length 15 cm is 20 cm to the right of the first length. Where is the final image ? explain please *Question 229: Multiple Lens An object is 15 cm to the left of a positive ...

1 answers

##### Describe a) what you believe to be the most important COSO component; and b) why.

Describe a) what you believe to be the most important COSO component; and b) why....

1 answers

##### Required information E9-9 Demonstrating the Effect of Book Value on Reporting an Asset Disposal [LO 9-5)...

Required information E9-9 Demonstrating the Effect of Book Value on Reporting an Asset Disposal [LO 9-5) [The following information applies to the questions displayed below) Movelt Corporation is the world's leading express-distribution company. In addition to its 643 aircraft, the company has m...

1 answers

##### (References (Review Topics Draw the structure of the major organic product(s) of the reaction NaOH H2O...

(References (Review Topics Draw the structure of the major organic product(s) of the reaction NaOH H2O • You do not have to consider stereochemistry • All carboxyl and amino groups should be drawn in the neutral form. • Draw one structure per sketcher. Add additional sketchers using t...

1 answers

##### Welland Co. shows the following information on its 2016 income statement: sales $155,500; costs = S81,400,...

Welland Co. shows the following information on its 2016 income statement: sales $155,500; costs = S81,400, other expenses-$4,700, depreciation expense $10,400; interest expense $7,900; taxes = $17,885; dividends = $7,450. In addition, you're told that the frm issued $3.100 in new equity during 2...

1 answers

##### How to write a patient note regarding wound care on the sacrum and packing the wound

How to write a patient note regarding wound care on the sacrum and packing the wound...

1 answers

##### Prove that every subset of N is either finite or countable. (Hint: use the ordering of...

Prove that every subset of N is either finite or countable. (Hint: use the ordering of N.) Conclude from this that there is no infinite set with cardinality less than that of N. ...

1 answers

##### 10. The period of a simple pendulum is T = 2.5 s. (a) How long is...

10. The period of a simple pendulum is T = 2.5 s. (a) How long is the pendulum? (b) If this pendulum is taken to another planet, where the free-fall acceleration is 4.5 m/s² what is the period there?...

1 answers

##### 8. A 1500 kg automobile moving at a maximum speed of 26 m/s on a level...

8. A 1500 kg automobile moving at a maximum speed of 26 m/s on a level circular track of radius of 85 m. What is the coefficient of friction? 26 A) 0.6375 B) 0.8115 C) 1.17 D) 0.459 E) 0.42075 2...

1 answers

##### I is the incenter of the triangle AI-3x+7, BI-5x-11, & CI-52-2x X-? ]

I is the incenter of the triangle AI-3x+7, BI-5x-11, & CI-52-2x X-? ]...

1 answers

##### HELLO I AM CURRENTLY IN DIFFERENTIAL EQUATIONS PLEASE EXPLAIN EACH STEP SO I CAN LEARN FROM...

HELLO I AM CURRENTLY IN DIFFERENTIAL EQUATIONS PLEASE EXPLAIN EACH STEP SO I CAN LEARN FROM YOU (I KNOW SOME PEOPLE ONLY CARE ABOUT TEH ANSWER, BUT WILL REALLY APPRECIATE IT) TO SAVE TIME FEEL FREE TO JUST SAY A LAW, THEOREM, OR CONCEPT FOR AN EXPLANATION AND I CAN GO AHEAD AND STUDY IT ON MY OWN. i...

1 answers

##### Question 6 Region Region A Region Region Region The electric potential varies with distance according to...

Question 6 Region Region A Region Region Region The electric potential varies with distance according to the graph shown above. Answer questions 6, 7, and 8 based on the graph. In which region does the electric held point in the negative x-direction? Question 6 Region Region A Region Region Region T...

1 answers

##### How does water affect the concentration of cyanide, caustic and peroxide?

How does water affect the concentration of cyanide, caustic and peroxide?...

1 answers

##### According to the scale on a road map, 3 cm represents 45 kilometers. If two cities measure 10 cm apart on the map, how many kilometers apart are they?

According to the scale on a road map, 3 cm represents 45 kilometers. If two cities measure 10 cm apart on the map, how many kilometers apart are they?...

1 answers

##### A coil of Nichrome wire is 22.0 m long. The wire has a diameter of 0.410...

A coil of Nichrome wire is 22.0 m long. The wire has a diameter of 0.410 mm and is at 20.0°C. Posting this question for the third time. how CAN I report this issue ?...

1 answers

##### The answers must be as a formula Oakdale Fashions, Inc., had $315,000 in 2015 taxable income....

the answers must be as a formula Oakdale Fashions, Inc., had $315,000 in 2015 taxable income. Use the tax schedule in Table 2.3 to calculate the company's 2015 income taxes. What is the average tax rate? (Round your answer to 2 decimal places.) What is the marginal tax rate? Taxable income $ 315...

1 answers

##### As a result of improvements in product engineering, United Automation is able to sell one of...

As a result of improvements in product engineering, United Automation is able to sell one of its two milling machines. Both machines perform the same function but differ in age. The newer machine could be sold today for $63,500. Its operating costs are $21,800 a year, but in five years the machine w...