96/38n X 25/45 (multiplying rational expressions .simplify.)
2 answers:
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If you're just starting calculus, perhaps you're asking about using the definition of the derivative to differentiate .
We have
Expand the numerator using the binomial theorem, then simplify and compute the limit.
In general, the derivative of a power function is
. (This is the aptly-named "power rule" for differentiation.)
Answer:
2 3/4 in
Step-by-step explanation:
The sum of the marked distances is equal to the total distances shown:
... (1 5/8) + ? + (1 5/8) = 6
... ? = 6 - (1 5/8 + 1 5/8) . . . . . subtract the constants on the left
... ? = 6 - (2 5/4) . . . . . . . . . . . add the numbers in parentheses
... ? = 6 - 3 1/4 . . . . . . . . . . . . rewrite the number in parentheses (2+5/4 = 2 + 1 1/4)
... ? = (6 -3) -1/4 = 3 -1/4 . . . . . see below
... ? = 2 3/4
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<em>Comment on subtacting mixed numbers</em>
Some folks find it convenient to subtract by adding. To find the difference between 3 1/4 and 6, they would start by adding 3/4 to make 4, then add 2 to make 6. Then they see the difference is 3/4 + 2 = 2 3/4.
Here, I chose to subtract 3 1/4 by subtracting 3, then subtracting 1/4. After subtracting 3 from 6, I get 3, from which I now need to subtract 1/4. It should be clear that taking 1/4 away from 3 will leave 2 3/4. (One of the units has been converted to 4/4 to make the subtraction of 1/4 possible.)
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<em>Comment on doubling a fraction</em>
As part of this problem, we needed to add 1 5/8 to itself. We did that by doubling the integer part, and doubling the fraction. When a fraction has an even denominator, it is easy to double it: replace the denominator with half its value — 2×(5/8) = 5/4, where the denominator 4 is half the denominator 8.
