I have a fair variety of problems that I am having some issues with--most I have worked out but need confirmation on, others I have no real idea what to do with.
The ones I need to double check are:
(1)
Assuming that none of the solutions are undefined,simplify each of the following:
(a)
My answer: Either abc or ab(I'm not too sure which, though I am leaning towards "ab")
(b)
My answer: or
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(2)
Simplify:
(a)
My answer:
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(3)
If you are h feet above the earth's surface, the distance, d, that you can see is approximately d (in miles)= .
Suppose you are on the roof of a building 900 ft. tall. how far can you see?(calculate to two decimal places)
My answer: so Thus, I can see for 36.74 Mi.
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(4)
According to Descartes' Rule of Signs, (a) how many positive real roots does each of the following have? (b) how many negative roots?
(1)
My answer:
(a):1
(b):0
(2)
My answer:
(a):0
(b):1
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Now for the ones I have no idea about.
(1)
Solve the equation , if -2 is a root.
(I have tried to solve this one but when I do synthetic division on it I get the equation: which I don't think will work)
(2)
Find the dimensions of a rectangle a with the greatest area whose perimeter is 30 feet.
(I got nothing--I'm totally confused as to what to do with this one.)
Thank you!
This can be done in two ways.
The algebraic approach is as follows,
Let and be the sides of the rectangle in feet.
Therefore, the perimeter of the rectangle P =
Now, the area of the rectangle A =
Now, since the Arithmetic mean of two numbers>= Their geometric mean,
>=
Thus
Hope you can proceed from here.
Thank you!
Just so I'm clear: because .
So: since and then if and , and .
How do I make sure that the area I found is the greatest possible?
Thank you muchly!
1.Thank You!! I felt like something was off.....
2.Ah..... .
3.More oil? I haven't even gotten over the deep fryer I'm in right now......