An industrial model builder need several pieces of wire that are 7 3/8 inches long. How many whole pieces of wire of this length
1 answer:
Answer: 13 whole pieces of wire can be cut from that spool and of wire is left over.
Step-by-step explanation:
Convert from mixed number to improper fraction. To do it you must multiply the whole numbe part by the denominator of the fraction and then add the product to the numerator. The denominator does not change. Then:
Since the spool contains 100 inches of wire, you must divide this lenght by :
Convert from improper fraction to mixed number:
- When you divide the numerator 800 by the denominator 59, the quotient is 13 (this is the whole number part)
- The remainder is 33 (This is the numerator of the fraction).
- The denominator does not change.
Then:
Therefore 13 whole pieces can be cut from that spool.
The amount of wire left over is:
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Okay, this is my proof. I'm not exactly sure if this is a viable proof, but I think it works.
Hence, from x > 0, it is always increasing (gradient > 0)
y = lnx crosses the x-axis only once, so there is only one root.
Since x cannot be less than zero, as well as a monotonic increasing function for x > 0, and the fact that it crosses the x-axis once, then as x approaches 0 from the positive side, f(x) has to be approaching negative infinity.
Hence, from x > 0, it is always increasing (gradient > 0)
y = lnx crosses the x-axis only once, so there is only one root.
Since x cannot be less than zero, as well as a monotonic increasing function for x > 0, and the fact that it crosses the x-axis once, then as x approaches 0 from the positive side, f(x) has to be approaching negative infinity.