Chapter 2: Q. 1TF (page 234)

Use algebra to show that the distance of the kth segment can be rewritten as $\sqrt{1 + {(\frac{Δ y_{k}}{Δ x})}^{2}} Δ x$ .

Short Answer

Expert verified

The $k t h$ segment can be written as $\sqrt{1 + {(\frac{Δ y_{k}}{Δ x})}^{2}} Δ x$ .

Step by step solution

Step 1. Given Information.

The given expression is $\sqrt{(Δ x)^{2} + {(Δ y_{k})}^{2}}$ .

Step 2. Conclusion.

The expression can be written as,

$\sqrt{(Δ x)^{2} + {(Δ y_{k})}^{2}} = \frac{∆ x}{∆ x} \sqrt{(Δ x)^{2} + {(Δ y_{k})}^{2}} = ∆ x \sqrt{\frac{(Δ x)^{2} + {(Δ y_{k})}^{2}}{{(∆ x)}^{2}}} = ∆ x \sqrt{\frac{{(∆ x)}^{2}}{{(∆ x)}^{2}} + \frac{{(Δ y_{k})}^{2}}{(Δ x)^{2}}} = ∆ x \sqrt{1 + \frac{{(Δ y_{k})}^{2}}{(Δ x)^{2}}}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Use algebra to show that the distance of the kth segment can be rewritten as $\sqrt{1 + {(\frac{Δ y_{k}}{Δ x})}^{2}} Δ x$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Discrete Mathematics

Applied Mathematics

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

Use algebra to show that the distance of the kth segment can be rewritten as1+ΔykΔx2Δx.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Discrete Mathematics

Applied Mathematics

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

Use algebra to show that the distance of the kth segment can be rewritten as $\sqrt{1 + {(\frac{Δ y_{k}}{Δ x})}^{2}} Δ x$ .