Please help me find the value of this angle?
1 answer:
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Ok, so based on a survey - you know that out of 30 students, 11 said that their favourite subject is mathematics. :-)
This means that:
11/30 of these students think mathematics if their favourite subject.
Now, in order to answer your question, we are going to have to change the denominator of the fraction above to 1000. Whatever we do to the denominator of this fraction, we must do to the numerator of this fraction.
Example:
This means that rounded to the nearest ten, theoretically speaking, 370 students out of 1000 would say that mathematics is their favourite subject.
This means that:
11/30 of these students think mathematics if their favourite subject.
Now, in order to answer your question, we are going to have to change the denominator of the fraction above to 1000. Whatever we do to the denominator of this fraction, we must do to the numerator of this fraction.
Example:
This means that rounded to the nearest ten, theoretically speaking, 370 students out of 1000 would say that mathematics is their favourite subject.
A good place to start is to set to y. That would mean we are looking for
to be an integer. Clearly,
, because if y were greater the part under the radical would be a negative, making the radical an imaginary number, not an integer. Also note that since
is a radical, it only outputs values from
, which means y is on the closed interval:
.
With that, we don't really have to consider y anymore, since we know the interval that is on.
Now, we don't even have to find the x values. Note that only 11 perfect squares lie on the interval , which means there are at most 11 numbers that x can be which make the radical an integer. All of the perfect squares are easily constructed. We can say that if k is an arbitrary integer between 0 and 11 then:
Which is strictly positive so we know for sure that all 11 numbers on the closed interval will yield a valid x that makes the radical an integer.