Recall that
sin(<em>a</em> + <em>b</em>) = sin(<em>a</em>) cos(<em>b</em>) + cos(<em>a</em>) sin(<em>b</em>)
sin(<em>a</em> - <em>b</em>) = sin(<em>a</em>) cos(<em>b</em>) - cos(<em>a</em>) sin(<em>b</em>)
Adding these together gives
sin(<em>a</em> + <em>b</em>) + sin(<em>a</em> - <em>b</em>) = 2 sin(<em>a</em>) cos(<em>b</em>)
To get 14 cos(39<em>x</em>) sin(19<em>x</em>) on the right side, multiply both sides by 7 and replace <em>a</em> = 19<em>x</em> and <em>b</em> = 39<em>x</em> :
7 (sin(19<em>x</em> + 39<em>x</em>) + sin(19<em>x</em> - 39<em>x</em>)) = 14 cos(39<em>x</em>) sin(19<em>x</em>)
7 (sin(58<em>x</em>) + sin(-20<em>x</em>)) = 14 cos(39<em>x</em>) sin(19<em>x</em>)
7 (sin(58<em>x</em>) - sin(20<em>x</em>)) = 14 cos(39<em>x</em>) sin(19<em>x</em>)
Answer:
5000 particles of size 10 nanometer should be stacked
Step-by-step explanation:
Average diameter of the of the human hair = 50 micron = 50 × 10⁻⁶ m
Now,
let the number of 10 nanometer i.e 10 × 10⁻⁹ m particle be 'n'
thus,
n × 10 × 10⁻⁹ m = 50 × 10⁻⁶ m
Therefore to find the number of 10 nanometer i.e 10 × 10⁻⁹ m particle,
n = 
or
n = 5000
Hence,
5000 particles of size 10 nanometer should be stacked
Answer:
number 20
Step-by-step explanation:
Answer:
22.81
Step-by-step explanation:
The distance formula can be used to find the distances between pairs of vertices. The perimeter is the sum of those distances.
<h3>Side lengths</h3>
The distance formula is ...
d = √((x2 -x1)^2 +(y2 -y1)^2)
Using this formula the triangle side lengths are ...
AB = √((6 -(-2))^2 +(2 -2)^2) = √(8^2) = 8
BC = √((0 -6)^2 +(8 -2)^2) = √(6^2 +6^2) = 6√2
CA = √((-2 -0)^2 +(2 -8)^2) = √(4 +36) = √40
The perimeter of the triangle is the sum of these lengths:
P = 8 +6√2 +2√10 ≈ 22.8098
The perimeter is about 22.81 units.
If you add up all of the digits in the number, and if that number you get is able to be divided by 3, the original number is good to divide by 3.
For example: 618
You add 6+1+8 and get 15
Take 15 and divide by 3
You get a whole number, 5
Therefore, 618 can be divided by 3