GCF of 32 and 48 = 16
32 - 48
16(2 - 3) <==
Answer:7
7
Step-by-step explanation:
<span>the dimensions of a door are variable, for effects of this problem we will assume a door height of 210 cm and a door width of 80 cm
Step 1
</span><span>convert the dimensions of the door in cm to inches
</span>we know that
1 in-------------> 2.54 cm
X----------------> 210 cm
X=210/2.54=82.67 in (height)
1 in-------------> 2.54 cm
X----------------> 80 cm
X=80/2.54=31.50 in (width)
the dimensions of a door are 31.50 in x 82.67 in
Step 2
calculate the amount of rules of 12-inches necessary to measure the height of the door
82.67 in (height)
if one rule-------------> measure 12 in
X----------------------> 82.67 in
X=82.67/12=6.8-----------> 7 rules
Step 3
calculate the amount of rules of 12-inches necessary to measure the width of the door
31.50 in (width)
if one rule-------------> measure 12 in
X----------------------> 31.50 in
X=31.50/12=6.8-----------> 2.62 ------------> 3 rules
the answer is
to measure a door are needed about 7 rules of 12-inches for the height and about 3 rules of 12-inches for the width
First, notice every term has a common factor of 2, so factor out a 2.


Now we need two numbers that multiply to 5 and two numbers that multiply to -4.
For the 5, it is a single possibility, 5 and 1, so we will have

Pairs of numbers that multiply to -4 are:
-4, 1
4, -1
2, -2
We need to choose the correct pair and place it in the correct order.
To do that, we place the numbers as guesses and multiply out the factors to see if we get the correct middle term.
First guess: -4, 1

The middle term would be: 5x - 4x = x, which is what we want, so we lucked out and we have the answer with just one guess.
Answer:
Looks like the series is

Split up the summand into partial fractions:

The series has <em>k</em>th partial sum


Several intermediate terms cancel to leave us with

As
, the last two terms converge to 0, so that
