Reader questions and feedback on Algebra. Also refer to mathematics, math, maths, Ron Kurtus, School for Champions. Copyright © Restrictions
Answers to Readers' Questions on Algebra:
General Algebra Topics
The following 8 comments and questions have been sent in. They are listed according to date.
List of first 10 items
- Quotients that equal 4 to the negative 5 power
- Direct variation or inverse variation equation?
- Antiderivative of sin(3x+1)dx
- Why is derivative of e^x = e^x?
- How much math I need for physics?
- Need help in Chemistry and Physics
- Problem of a man rowing a boat across a river
- Need help with matrices
Quotients that equal 4 to the negative 5 power
Question
November 19, 2009
On my homework it says that I have to write THREE different quotients that equal 4 to the negative 5 power. I don't know ho to do it except for writing it one way only!:(
Tiffany - USA
18705
Answer
4^-5 (4 to the negative 5 power) = 1/4^5 = 1/4*4*4*4*4 = 1/2^10 = 2^-10
I hope that is what your teacher is looking for.
Direct variation or inverse variation equation?
Question
May 11, 2009
The equation lw=a is the area of a rectangle. Does this model represent direct variation, inverse variation, or neither?
- USA
17731
Answer
If the length was constant as you varied the width, then the area would be a direct variation of the width. A = kw, where k is a constant.
Since neither the length or width is a constant, the answer is "neither".
Antiderivative of sin(3x+1)dx
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
Answer
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.
Why is derivative of e^x = e^x?
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
Answer
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.
How much math I need for physics?
Question
December 7, 2008
Math is a good thing, how much math I need for physics?
String - Australia
16913
Answer
Much of Physics concerned solving problems with mathematics. At the very least, you need Algebra and Trigonometry for Basics Physics. Intermediate and Advanced Physics usually requires knowledge of Calculus.
Need help in Chemistry and Physics
Question
September 19, 2008
Will you help me. I am currently sudying A Level science and i really need to improve on my chemistry,maths and physics. can you help me.
Ben - UK
16523
Answer
We are adding more Algebra and Maths lessons. Check out our Chemistry and Physical Science areas for help in those subjects.
Problem of a man rowing a boat across a river
Question
April 26, 2008
A man row a boat in still water at 6 knots. he wishes to row due north across a river 3km wide which is flowing due west at 2 knots. find the direction in which he must head the boat.
mirza - Saudi Arabia
15812
Answer
The solution is found by using vectors or geometry. Draw an arrow 6 cm long in the north direction to represent the normal motion of the boat. From the beginning of that arrow, draw another arrow 2 cm long in the west direction. Now draw a line from the end of the 2 cm arrow to the end of the 6 cm arrow. That represents the direction and speed he will have to row.
He will have to row north-east at the measured angle. His speed will be 6.3 knots in that direction.
Need help with matrices
Question
March 25, 2008
I need help adding subtracting multipying matrices
- USA
15592
Answer
Working with matrices can be difficult.
When you multiply a number times a matrix, you multiply that number time each element in the matrix. For a very simple matrix: 2 * | 1 -2 | = |2 -4|.
To add or subtract matrices, they must both be the same dimensions. Like both are 2x2 or both are 3x4. Then you add or subtract corresponding numbers. For example: subtract |2 3| matrix from |2 5| matrix: |2 5| - |2 3| = |0 2|.
Multiplying two matrices together is complex. See:
http://library.thinkquest.org/20991/alg2/matrices.html for some examples and further instructions.
Best wishes in your test.
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Answers to Readers' Questions on Algebra