Question 151340This question is from textbook elementary and intermediate algebra concepts and applications
: Hello Everyone I just need a refresher.
List any four situations where variables can be used to replace numbers; convert each situation into an algebraic expression.
This question is from textbook elementary and intermediate algebra concepts and applications
Answer by nabla(475)   (Show Source):
You can put this solution on YOUR website! I'm not entirely certain what is meant by 'situations.' I will list real world happenstances from which we can utilize algebra:
1) Larry has $20. He wants to buy as many nails as he can with his money. Each nail costs $.05. How many nails can he buy?
20=.05x
400=x
Here x stands for the amount of nails Larry can buy with his $20.
2) Suppose I want to add up all the numbers from 1 to 100. Perhaps you wonder why anyone would do such a thing. To that I have no answer.
consider: S=100+99+98+...+3+2+1
and P=1+2+3+...+98+99+100
Would you agree that S=P?
Since S=P, (S+P)/2=S=P
Now, the Guassian method is to have (S+P)/2= (100 pairs of 101)/2=50(101)=5050.
In any case, although our symbols for S and P stand for something, that is, they can potentially vary, we have something more substantial:
The sum from any number from 1 to n is
S=n(n+1)/2
3) We have so far dealt with a purchasing question and a general number theory question. Now it is time to deal with a triangle.
Consider triangle ABC. Angle B measures 90 degrees. Side BA measures 5 units. Side BC measures 12 units. Find the measure of the side opposite angle B, which is to say the hypotenuse, which is moreover to say the side AC.
Using the Pythagorean Theorem, we know a^2+b^2=c^2. c is the hypotenuse.
Thus we can just plug in numbers in order to find the value of the variable c (dependent on a and b).
5^2+12^2=25+144=169
Sqrt(169)=13. Thus, c=13.
4) Last, let's consider a standard parabolic function. If you ask me why parabolas are important, I will just point to curves in the road, the motion of objects, among other things.
f(x)=x^2+2x+1
factors as f(x)=(x+1)^2
An interesting thing to note about this function is that, if we choose a number, the function will give us the value of the next number after that's square. Implications are heavy and rather beautiful, but I'll leave this to you to sort out. If you have anymore questions, or if you'd like this answer done differently, send me an E-mail at enabla@gmail.com .
|
|
|
