Ok so I'm reviewing algebra since it was the only math class I didn't do well in and thought I would work out all the problems in the Schaum's Outline. I have ran across 3 problems I'm not sure how to do.
a)Two numbers have the ratio 3:4. If 4 is added to each of the numbers the resluting ratio is 4:5. Find the two numbers.
b) Determine whether the graph of each relation is symmetric with respect to the y axis, x axis, or origin.
I want to work this one out rather than look at the graph.
So it is symmetric with respect to the origin but is there a faster way of showing that. I tried going this route but got stuck
and then got stuck.
c)Find the largest rectangle which can be inscribed in a right triangle whose legs are 6 and 8 inches repectively.
I know
and
Thanks in advance
The relation you posted is not symmetric to the origin.
This is where you went wrong. For a lack of a better explanation, you "counted" the negatives twice. Look at the binomial cubic expansion in the general case:
????
If you're saying that a = -x and b = -3, then you follow the first rule:
But, if you're saying that a = -x and b = 3, then you follow the second rule:
You were combining both rules.
In either case,
.
And since
,
the two polynomials are not equal, so this relation is not symmetric at the origin.
In fact, this relation is not symmetric to the x-axis, y-axis, or the origin. You'll now have to show algebraically that the first two are not the case.
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