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Fishing Rod Guides

Fishing Rod Guides
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Question: Math Help??!!?

The rod has a fishing rod with eight guides, plus a guide at the tip of the rod.

Leo has a fishing rod with overall length 230 cm. The table shown below gives the distances for each of the line guides from the tip of his fishing rod.

Guide number(from tip) = 1,2,3,4,5,6,7,8
Distance from tip(cm) = 10, 23, 38, 55, 74, 96, 120, 149

Find a polynomial function which passes through every data point. Explain your choice of function, and discuss its reasonablenesss. On a new set of axes, draw this model function and the original data points. Comment on any differences.

Answer: Let f(x) be the distance from the rod's tip as a function of guide number.

f(1) = 10
f(2) = 23
f(3) = 38

etc.

look at the differences between these: f(2) - f(1) = 15, f(3)-f(2) = 17, f(4) - f(3) = 19, etc.

Now look at the differences between THESE. They're all two. Since after two steps of looking at the differences we've reached a repeating answer, we know that f(x) is a quadratic. (this is explained better at http://www.purplemath.com/modules/nextnumb.htm )

We now know that f(x) is of the form aX^2 + bX + c

We know 1^2A + 1B + C = 10 and 2^2A + 2B + C = 23 and 3^2A + 3B + C = 38. This gives us a system of equations, so we can solve for A, B, and C

A + B + C = 10
4A + 2B + C = 23
9A + 3B + C = 38

Solve this and find that A = 1, B = 10, C = -1

So our function is X^2 + 10X -1

Edit:

Also, the guide at the tip of the rod will not necessarily fit the model (and it doesn't) because it isn't placed according to the function.

Another thing, I think 95 and 118 were intended in the original problem statement instead of 96 and 120. With 96 and 120 in there you would get a complicated fifth degree polynomial, which I doubt was the intention.

Here are the very best Fishing Rod Guides products on Ebay right now:

50 Fishing Rod Single Roller Guide 1 Size Medium NEW
50 Fishing Rod Single Roller Guide 1 Size Medium NEW
Paypal   US $21.99
18 Fishing Rod Single Roller Guide 6 Roller Tips NEW
18 Fishing Rod Single Roller Guide 6 Roller Tips NEW
Paypal   US $19.99
FISHING ROD FUJI GUIDES ORANGE 30 PCS NEW SIZES
FISHING ROD FUJI GUIDES ORANGE 30 PCS NEW SIZES
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FISHING ROD FUJI GUIDES ORANGE 10 SETS 60 PCS NEW SIZES
FISHING ROD FUJI GUIDES ORANGE 10 SETS 60 PCS NEW SIZES
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10 Spools Silk Thread For Wrapping Fishing Rod Guides
10 Spools Silk Thread For Wrapping Fishing Rod Guides
Paypal   US $9.99
Heavy Duty Roller Fishing Guides set Rod Making
Heavy Duty Roller Fishing Guides set Rod Making
Paypal   US $24.99
Fishing Rod Guides 100 Mixed Size Gold Plated NEW
Fishing Rod Guides 100 Mixed Size Gold Plated NEW
Paypal   US $15.99
20 CHROME STAMPED FISHING ROD GUIDE TIP TOPS SIZE 55
20 CHROME STAMPED FISHING ROD GUIDE TIP TOPS SIZE 55
Paypal   US $8.00
20 CHROME WIRED FISHING ROD GUIDE TIP TOPS SIZE 7 NOS
20 CHROME WIRED FISHING ROD GUIDE TIP TOPS SIZE 7 NOS
Paypal   US $6.00
FUJI FISHING ROD GUIDE EYE ID 14mm OD 21mm 5B20
FUJI FISHING ROD GUIDE EYE ID 14mm OD 21mm 5B20
Paypal   US $1.00
FISHING ROD FUJI GUIDES ORANGE 140 PCS NEW SIZES
FISHING ROD FUJI GUIDES ORANGE 140 PCS NEW SIZES
Paypal   US $65.00
Heavy Duty Boat Fishing Guides set Rod Making
Heavy Duty Boat Fishing Guides set Rod Making
Paypal   US $22.99
Concept Casting Fishing Rod Guides by Dblue Rod Making
Concept Casting Fishing Rod Guides by Dblue Rod Making
Paypal   US $22.99
FUJI FISHING ROD GUIDE EYE ID 23mm OD 33mm 6B20
FUJI FISHING ROD GUIDE EYE ID 23mm OD 33mm 6B20
Paypal   US $1.00
Concept SIC Casting Fishing Rod Guides Titanium Frame
Concept SIC Casting Fishing Rod Guides Titanium Frame
Paypal   US $29.99
Concept Casting Fishing Rod Tip Top Guides by Dblue
Concept Casting Fishing Rod Tip Top Guides by Dblue
Paypal   US $9.99
Concept SIC Casting Fishing Rod Guides by Dblue
Concept SIC Casting Fishing Rod Guides by Dblue
Paypal   US $34.99
Concept Spinning Fishing Rod Guides by Dblue Rod Making
Concept Spinning Fishing Rod Guides by Dblue Rod Making
Paypal   US $22.99
Concept SIC Spinning Fishing Rod Guides by Dblue
Concept SIC Spinning Fishing Rod Guides by Dblue
Paypal   US $34.99
FUJI FISHING ROD GUIDE EYE ID 7mm OD 12mm 3B20
FUJI FISHING ROD GUIDE EYE ID 7mm OD 12mm 3B20
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FUJI FISHING ROD GUIDE EYE ID 85mm OD 135mm 4B20
FUJI FISHING ROD GUIDE EYE ID 85mm OD 135mm 4B20
Paypal   US $1.00
FUJI FISHING ROD GUIDE EYE ID 5mm OD 95mm 2B20
FUJI FISHING ROD GUIDE EYE ID 5mm OD 95mm 2B20
Paypal   US $1.00
12 Spinning Fishing Rod Tip Top Guides Rod Making
12 Spinning Fishing Rod Tip Top Guides Rod Making
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6 FISHING ROD GUIDES EYES TITANIUM NITRIDE F2F50
6 FISHING ROD GUIDES EYES TITANIUM NITRIDE F2F50
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FISHING ROD FUJI GUIDES ORANGE 3 SETS 18 PCS NEW SIZES
FISHING ROD FUJI GUIDES ORANGE 3 SETS 18 PCS NEW SIZES
Paypal   US $13.00
Complete Fishing Rod Guide Finish Kit
Complete Fishing Rod Guide Finish Kit
Paypal   US $15.95
20 CHROME SPINNING FISHING ROD GUIDE TIP TOPS 16 NOS H
20 CHROME SPINNING FISHING ROD GUIDE TIP TOPS 16 NOS H
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20 CHROME FISHING ROD GUIDE TIP TOPS SIZE 20 NOS R
20 CHROME FISHING ROD GUIDE TIP TOPS SIZE 20 NOS R
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10 Titanium Oxide Spinning Fishing Rod Tip Top Guides
10 Titanium Oxide Spinning Fishing Rod Tip Top Guides
Paypal   US $11.99
20 CHROME WIRED FISHING ROD GUIDE TIP TOPS SIZE 6 NOS
20 CHROME WIRED FISHING ROD GUIDE TIP TOPS SIZE 6 NOS
Paypal   US $8.00
Spinning Fishing Rod Guide Set Black Frame Halide Ring
Spinning Fishing Rod Guide Set Black Frame Halide Ring
Paypal   US $11.00
Fly Rod Fishing Guide Set Gold Zirconia TiCh 9 10ft rod
Fly Rod Fishing Guide Set Gold Zirconia TiCh 9 10ft rod
Paypal   US $41.99
Fly Rod Fishing Guide Set BLUE Zirconia TiCh 8 9 ft rod
Fly Rod Fishing Guide Set BLUE Zirconia TiCh 8 9 ft rod
Paypal   US $38.10
6 Fishing Rod Guide Sets 4 Guides Per Set Stainless
6 Fishing Rod Guide Sets 4 Guides Per Set Stainless
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Question: How are the guides on a fishing rod positioned?

The guide on the fishing rod is positioned so that between the ones closer to the tip has a shorter distance than those between the ones further away from the rod. The distance between 2 guides are getting bigger and bigger from the tip of the fishing rod.
1)Why are they position that way and how does it help fishing?
2)Does the length of the fishing rod affect fishing? How?
3)What is the purpose of having guides?

Thank you for your time =)

Answer: 1. The guides are spaced so the line doesn't go around an especially sharp corner when it goes through each of them when the rod is bent. This reduces wear on the line (as well as wear on the guides), and reduces friction which adds to the drag if a fish is taking line.

In addition, on a saltwater conventional rod (which is used with the reel and the guides on top) the guides are positioned to keep the line from rubbing on the rod between the guides.

2. The length of the fishing rod affects casting distance and the leverage you use when pulling on a heavy fish. Longer rods will cast further, while shorter rods will make it easier to lift heavy fish. So surf fishing rods tend to be long (sometimes 12 feet or more) while big game rods tend to be short (6 feet or less at times).

3. The purpose of having guides -- I assume you're thinking of a rod with only a tip guide. The guides keep the line from flying out of control when casting -- especially with a spinning reel (I tried this once when building a rod as a kid -- I put on the tip guide and a reel, and tried casting, and got a mess with line wrapping around the rod blank about halfway up). They also, as described in #1 above, keep the line from going around tight corners and wearing out quickly, as well as keeping the line coming into the reel from (pretty much) directly in front of it.

If you're thinking of running the line through the center of a hollow fishing rod -- even if the inside was smooth, there would be so much friction the outfit would be nearly unusable.

Spinning rods tend to have fewer guides, since they don't have to keep the line from rubbing on the blank, and larger ones (especially the first guide) to reduce friction when casting, as the line spins off the reel. Casting and conventional rods usually have more, and smaller, guides.

One other great place to find Fishing Rod Guides products is at Amazon:

Guide Gear® 8' 5-Rod / Reel Case Guide Gear® 8' 5-Rod / Reel Case
List Price: $30.00
Sale Price: $24.97
Average Rating:

Carry / store up to Five fully rigged rods and reels in this 8' Case. SAVE BIG! Adjustable to fit up to 8' rods; Full-length, sewn-in sleeve dividers keep reels, lines and lures separated and tangle-free; Compartments are lined with soft, synthetic lamb's wool protection; Durable, fade-resistant 200-denier polyester fabric; Sewn-on D-ring and shoulder strap...

Crystal River Fly and Spinning Combo Travel Kit Crystal River Fly and Spinning Combo Travel Kit
List Price: $44.99
Sale Price: $23.59
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Up the creek without your tackle? NOT with this Travel Fly and Spinning Rod! For the man on the go... who loves fishing along the way! Be ready, with this sweet graphite Rod, with both Fly and Spinning Reels for river or lake...

Berkley Cherrywood 2 Piece Fly Rod (7'6 Berkley Cherrywood 2 Piece Fly Rod (7'6", 6 Guide, 4-5 lb. Line Wt.)
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Sale Price: $41.14
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Berkley Cherrywood Fly Rod Graphite Technology, Remarkable Value Lightweight, responsive graphite blank construction delivers exceptional fish fighting performance characteristics. Blank-through handle construction with custom contoured cork grips

Fenwick Eagle GT 2 Piece Fly Rod (7'6 Fenwick Eagle GT 2 Piece Fly Rod (7'6", 8 Guides, 4 lb. Line Wt.)
List Price: $109.95
Sale Price: $64.99

Eagle GT Fly Rod Classic Fenwick Performance at an Entry-Level Price. The high energy, fast actioned high modulus graphite Eagle GT is within the reach of every angler. Cork grips and black anodized reel seats with resin-impregnated walnut inserts...

Guide Gear® 8' 3-Rod / Reel Case Guide Gear® 8' 3-Rod / Reel Case
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Carry / store up to Five fully rigged rods and reels in this 8' Case. SAVE BIG! Adjustable to fit up to 8' rods; Full-length, sewn-in sleeve dividers keep reels, lines and lures separated and tangle-free; Compartments are lined with soft, synthetic lamb's wool protection; Durable, fade-resistant 200-denier polyester fabric; Sewn-on D-ring and shoulder strap...

Custom Saltwater Offshore Trolling Fishing Rod Pole ALL ROLLER GUIDES FREE SHIPPING AND 20% CUSTOMER APPRECIATION DISCOUNT! Custom Saltwater Offshore Trolling Fishing Rod Pole ALL ROLLER GUIDES FREE SHIPPING AND 20% CUSTOMER APPRECIATION DISCOUNT!
Sale Price: $135.00

Up for sale is a 5'6" 20-40 lb, custom saltwater fishing rod. Ideal length for stand-up battle. Designed and built for Eatmetackle.com, this rod is perfect for offshore trolling in search of Dolphin, Wahoo, and Kingfish, yet has a sensative enough tip to feel snapper bites while bottom fishing...

Martin 3 - Pc. 8' Fly Fishing Kit Martin 3 - Pc. 8' Fly Fishing Kit
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Sale Price: $27.97
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Martin Fly Fishing Kit has everything you need to get started. At a great price, too! Perfect for giving fly fishing a try. My guess is you'll love it. But if not, heck you're only a few bucks into it, so no worries Includes: 5/6 rim control fly reel pre-rigged with backing, fly line and leader; 3-Pc...

Fenwick HMX 2 Piece Fly Rod (8 Fenwick HMX 2 Piece Fly Rod (8"0", 8 Guides, 5 lb. Line Wt.)
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Sale Price: $169.95
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HMX® Fly Rod Fast-Tapered, Fast-Actioned Cross-Scrim Grpahite Performance. IM7 graphite blank material offers smooth, dependable and sensitive performance. Durable Cross-Scrim construction utilizes overlapping layers to achieve exceptional strength and action...


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