Multiplying both sides of a rational equation by a variable expression introduces the possibility of extraneous solutions. Therefore, we must check the solutions against the set of restrictions. If a solution is a restriction, then it is not part of the domain and is extraneous.
6x^4-17x^3-7x^2+13x=3
6x^4-17x^3-7x^2+13x-3=3-3
6x^4-17x^3-7x^2+13x-3=0
y=6x^4-17x^3-7x^2+13x-3
y=0
The solutions are: x=-1, 1/2, 1/3 and 3
21 + p = 44
Subtract 21 from both sides;
21 + p - 21 = 44 - 21
p = 23
It is often easiest to use "military time". That is, add 12 to all the afternoon numbers and do the subtraction in the usual way. Of course, 1 hour = 60 minutes, so 10 minutes = 10/60 hour = 1/6 hour.
Mon: 15:10 -8:00 = 7:10 = 7 1/6
Tue: 15:25 -8:05 = 7:20 = 7 1/3
Wed: 14:30 -8:00 = 6:30 = 6 1/2
Thur: 14:45 -7:55 = 7:(-10) = 6:50 = 6 5/6
Fri: 15:38 -7:58 = 8:(-20) = 7:40 = 7 2/3
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Some calculators have nice features for working with degrees, minutes, and seconds. In this context, degrees and hours are the same thing. That is, the base-60 arithmetic is the same whether you consider the numbers to be hours or degrees. Similarly, some calculators convert nicely between decimal fractions and mixed numbers. In short, a suitable calculator will almost do this math for you. (You just need to add 12 to all the numbers in the column on the right.)
1680 is the PERMUTATION answer.
