Renaldo will write 3/20 as a decimal. Which of the following methods should he use?
2 answers:
Answer:
1. Multiply the fraction by 5/5 to get a denominator of 100 and then write the numerator as hundredths using a decimal point.
Step-by-step explanation:
Renaldo must use a method that does not alter the value of the original fraction. This means that by multiplying the fraction by a number, the result obtained remains the same as the initial number.
Then the fraction must be multiplied by the same number in the denominator and the numerator. For example:
If we multiply the result is:
To write this fraction in decimal form, we move the comma 2 digits to the left in the following way:
15.0 --------> 0.15.
Then
The answer is Option 1.
ANSWER
1. Multiply the fraction by 5/5 to get a denominator of 100 and then write the numerator as hundredths using a decimal point.
EXPLANATION
Renaldo wants to write
as a decimal.
He needs a denominator of 100, so he can multiply by
to obtain:
This will be
He can now obtain the decimal equivalent as
The correct choice is option 1.
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The half-range sine series is the expansion for 
with the assumption that is considered to be an odd function over its full range, 
. So for (a), you're essentially finding the full range expansion of the function
with period 2 so that
for 
and integers 
.
Now, since is odd, there is no cosine series (you find the cosine series coefficients would vanish), leaving you with
where
In this case,
, so
The half-range sine series expansion for is then
which can be further simplified by considering the even/odd cases of, but there's no need for that here.
The half-range cosine series is computed similarly, this time assuming is even/symmetric across its full range. In other words, you are finding the full range series expansion for
Now the sine series expansion vanishes, leaving you with
where
for
. Again, . You should find that
Here, splitting into even/odd cases actually reduces this further. Notice that when is even, the expression above simplifies to
while for odd, you have
So the half-range cosine series expansion would be
Attached are plots of the first few terms of each series overlaid onto plots of. In the half-range sine series (right), I use 
terms, and in the half-range cosine series (left), I use 
or 
terms. (It's a bit more difficult to distinguish from the latter because the cosine series converges so much faster.)
with period 2 so that
Now, since
where
In this case,
The half-range sine series expansion for
which can be further simplified by considering the even/odd cases of
The half-range cosine series is computed similarly, this time assuming
Now the sine series expansion vanishes, leaving you with
where
for
Here, splitting into even/odd cases actually reduces this further. Notice that when
while for odd
So the half-range cosine series expansion would be
Attached are plots of the first few terms of each series overlaid onto plots of
Answer:
(C)c= f
Step-by-step explanation:
Clare uses cups of flour to make 4 cakes.
It means she uses 1 cup of flour to make cakes.
Let us simplify that expression first for future use.
Therefore, Clare uses 1 cup of flour to make cakes.
If Noah follows the same recipe,
He uses f cups of flour to make c cakes
Using Ratio Method
→ Name : Cup : Cake
→ Clare : 1 :
→ Noah : f : c
By using cross multiplication
c X 1 = f
c= f
The equation c= f represents the relationship between c and f