# Algebra Feedback

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 15 letters

### Country

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

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

Newton method very nice Square Root Approximation India

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

Find the perimeter of a triangle General USA

Trouble understanding math and science General USA

Next 15 letters

First 15 letters

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

December 10, 2008

### Question

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

December 10, 2008

### Question

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

January 15, 2008

### Question

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?

October 20, 2007

### Question

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

March 6, 2007

### Question

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

January 31, 2004

### Question

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.

## Misc

Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. I will try to get back to you as soon as possible.

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