In 1/8 of an hour, Ms. Wolf can grade 1/3 of a stack of papers. How many hours will it take her to grade 2 stacks?
2 answers:
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Answer is below.
<em>(Note to asker: Lack of explanations can get my answer deleted)</em>
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<u><em>Step 1</em></u>
We'll to isolate the variable, but to do that, get rid of the coefficient that multiplies it.
To do that, divide both sides by 22.
<em><u>Step 2.</u></em>
Now we have divided both sides by 22, but we'll need to reduce the fraction .
We can reduce the fraction by dividing the factors that are in the numerator and denominator.
That being said, 22 appears both in the numerator and denominator.
<u><em>Step 3</em></u>
Now, for , we'll need to reduce it to the lowest terms. Like in the 2nd step, we'll divide factors that are in the numerator and denominator.
That being said, 2 appears both in the numerator and denominator.
Hence, M = 5/11
1. If AB is tangent to the circle, then
We have
so AB is indeed tangent to the circle.
2. The unlabeled leg is another radius of the circle so it has length 8. Then if AB is tangent to the circle,
but we have
so that cannot be a right triangle and AB is not tangent to the circle.
Let F be the primitive of f, i.e.
Then, we have
So, we have
As for the sine, we can spare the integral: the sine is an odd function, which means that it is symmetrical with respect to the origin. Any odd function integrated over a symmetrical neighborhood of zero (i.e. any interval of the form [-n,n]) returns zero: by symmetry, there is an equal amount of positive and negative area. So, we have