# Feedback Q&A on Algebra

by Ron Kurtus

Readers have sent in a total of 66 comments and questions on Algebra issues. They are listed according to date.

## List of next 10 letters

### Country

General Why is derivative of e^x = e^x? Australia

General Antiderivative of sin(3x+1)dx Australia

Square Root Approximation Newton method very nice India

Fractals What is self-similarity and what is fractal? USA

General Find the perimeter of a triangle USA

General Trouble understanding math and science USA

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First 10 letters

## Why is derivative of e^x = e^x?

Topic: General

### Question

December 10, 2008

why does the Derivative of e^x is still e^x?
Why does the derivative of sinx=cosx?<

String - Australia

16927

e^x is one of the unusual expressions that equals its derivative. de^x/dx = e^x
A simple derivation can be seen at: http://math2.org/math/derivatives/more/e^x.htm, but it is difficult to understand.

Although you can prove sinx = cosx through the use of the derivative of a series, most sources say sinx = cosx by definition.

Typically, you simple have to memorize these relationships or use a reference table.

## Antiderivative of sin(3x+1)dx

Topic: General

### Question

December 10, 2008

why does an antiderivative of sin(3x+1)dx=(-cos(3x+1)+C)/3
Why it has to be devided by 3?
Can you give a ful detail as many you can Please?

String - Australia

16928

The anti-derivative of sin(nx)dx = -[cos(nx)]/n
Thus sin(3x)dx = - [cos(3x)]/3

Also sin(a+b) = sin(a)cos(b) - cos(a)sin(b)

But I'm at a loss where they get (-cos(3x+1)+C)/3. I assume that C is some constant?

Sorry, that is the best I can do without knowing what your teacher was getting at.

## Newton method very nice

Topic: Square Root Approximation

### Question

January 15, 2008

The method to calculate the square root for any number using newton method is very nice.

siva - India

15137

Thanks for the feedback. I'm glad you found the method useful.

## What is self-similarity and what is fractal?

Topic: Fractals

### Question

October 20, 2007

What is self-similarity and what is fractal? I not sure I completely understand what the two are and what the difference is between them.

Denise - USA

14592

A fractal is a design or fragmented geometric shape that repeats the same design in smaller and smaller patterns. It is like taking a triangle and putting a smaller triangle on each side, and then putting even smaller triangle on each side of those triangles, and so on.

Self-similarity is a property of fractals, where an object is exactly or approximately similar to a part of itself,.

## Find the perimeter of a triangle

Topic: General

### Question

March 6, 2007

How do I find the total length of the perimeter of a right triangle, when the angles are known and the length of one side is known.

Example: angles 90, 60, 30 adjacent side = 12 inches.

Dan - USA

13319

If, by the adjacent side you mean they hypotenuse of the triangle, you can find the length of the sides by using the sine of the angles.

The sine of 30° is 1/2 times 12 or 6 inches. That is the side opposite 30°. The sine of 60° is 0.866 time 12 = 10.39.

As a double-check, you can use Pythagorean Theory 12 squared = 6 squared + 10.39 squared. 144 = 36 + 108.

## Trouble understanding math and science

Topic: General

### Question

January 31, 2004

How can I understand math and science?

Laura - USA

2196

Our lessons in Physical Science can help you understand that topic for your class. I also have Algebra lessons for you to use. Hopefully, your teachers will do a good job in helping you learn.

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