Answer:
For numbers between 0.1 and 0.2, there is a 1 in the tenths' place: 0.11, 0.12, 0.13, and so on. For numbers between 0.2 and 0.3, there is a 2 in the tenths' place: 0.21, 0.22, 0.23, and so forth. For example, the number “seven and forty-two hundredths” can be written as 7.42.
Step-by-step explanation:
Ummmmmmmmm that is a mixed number already
That is true because the square root of 32 is about 5.66, so 4.65 IS less than it.
-I5I=-5 vs. I-5I= 5
The absolute value will stay the same for both negative and positive. The result will change depending on where you put your absolute value signs.
Setting
, you have
. Then the integral becomes
Now,
in general. But since we want our substitution
to be invertible, we are tacitly assuming that we're working over a restricted domain. In particular, this means
, which implies that
, or equivalently that
. Over this domain,
, so
.
Long story short, this allows us to go from
to
Computing the remaining integral isn't difficult. Expand the numerator with the Pythagorean identity to get
Then integrate term-by-term to get
Now undo the substitution to get the antiderivative back in terms of
.
and using basic trigonometric properties (e.g. Pythagorean theorem) this reduces to
