This problem can also be done without resorting to complex numbers.
Complete the square on the denominator:
s2 + 2s + 5 = (s+1)2 + 4
Since the denominator is now expressed in terms of s+1, express the numerator the same way:
2s + 2 = 2(s+1)
Now the whole fraction...
Both of the previous answers give the result as 4%. However, that's the percentage of the cake
that has been eaten. The question asks what percentage of the cake
is left, which is the remaining 96%.
Sorry, but this answer is wrong. The exponent (cx+d) applies only to the b; the a is not part of the base. So taking the base (ab) logarithm is the wrong move. George C's answer, complicated as it is, is correct.
1000/2 is one very easy way. But the real answer is, get a new calculator! You can get a simple calculator as cheap as a buck (at a Dollar Tree or someplace similar). Why waste your time fooling around with one with broken keys?
I don't see any reason to do this in decimal form. Like many fraction problems, it's done most easily as a common fraction.
Begin by putting the .21 over the .33. Now you have .21/.33. Get rid of the decimals by multiplying by 100/100. that gives you 21/33. 21 and 33 are both multiples...
This is a partial fractions problem. But notice that it's an improper fraction (because the highest power in the numerator is as large as the highest power in the denominator), so before you can apply the partial fractions technique, you need to use long
polynomial division to break it down...
The number 8 is the correct number, and so is the process you described for how you got it. However, what the 8 represents is not f(x)dx, but what you stated in your question, namely, the definite integral from 1 to 2 of (4x3 - 3x2).
So if you answered the question by saying "f(x)dx = 8", you...