This box has the same length , width, and height as the 2 basketballs. Which expression gives the volume of the empty space enci
rcling the basketballs inside the box?
2 answers:
Answer:
Step-by-step explanation:
we know that
The volume of the empty space encircling the basketballs inside the box is equal to the volume of the box minus the volume of the two basketball inside the box
so
<u>The volume of the box is equal to</u>
in this problem we have
substitute
The volume of the two basketball inside the box is equal to
n this problem we have
substitute
The expression is equal to
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To find our quotient we are going to perform long division.
Long division step by step:
Step 1. Write the polynomial (dividend) in descending order (from highest to least exponent). If you encounter a missing term, use zero to fill the space of the term in the descending sequence.
Notice that even tough our polynomial is written in descending form, is missing, so we are going to use
to fill the gap:
Step 2. Divide the first term of the polynomial (dividend) by the first term of the divisor.
In our case the first term of the dividend is and the first term of the divisor is
, so
. Notice that
is the first term of the quotient.
Step 3. Multiply the first term of the quotient by the terms of the divisor and subtract them from the respective term of the dividend.
The first term of our quotient (from the previous step) is and the divisor is
, so
. Now, we are going to subtract them from the respective term (the term with the same power) of the dividend. The respective terms of the dividend are
and
, so
and
Step 4. Bring down the next term in the dividend and repeat the process for the remaining terms.
After finish the process (check the attached picture), we can conclude that the quotient of ÷
is
with a remainder of
, or in a different notation:
I'm going to assume you meant to write fractions (because if are all non-negative integers, the series would clearly diverge), so that
and so on.
a. If the pattern continues as above, we would have the general term
b. Note that we can write as
The series diverges by comparison to the divergent series