![f(n)\in\mathcal O(g(n))](https://tex.z-dn.net/?f=f%28n%29%5Cin%5Cmathcal%20O%28g%28n%29%29)
is to say
![|f(n)|\le M_1|g(n)|](https://tex.z-dn.net/?f=%7Cf%28n%29%7C%5Cle%20M_1%7Cg%28n%29%7C)
for all
![n](https://tex.z-dn.net/?f=n)
beyond some fixed
![n_1](https://tex.z-dn.net/?f=n_1)
.
Similarly,
![d(n)\in\mathcal O(h(n))](https://tex.z-dn.net/?f=d%28n%29%5Cin%5Cmathcal%20O%28h%28n%29%29)
is to say
![|d(n)|\le M_2|h(n)|](https://tex.z-dn.net/?f=%7Cd%28n%29%7C%5Cle%20M_2%7Ch%28n%29%7C)
for all
![n\ge n_2](https://tex.z-dn.net/?f=n%5Cge%20n_2)
.
From this we can gather that
![|f(n)+d(n)|\le|f(n)|+|d(n)|\le M_1|g(n)|+M_2|h(n)|\le M(|g(n)|+|h(n)|)](https://tex.z-dn.net/?f=%7Cf%28n%29%2Bd%28n%29%7C%5Cle%7Cf%28n%29%7C%2B%7Cd%28n%29%7C%5Cle%20M_1%7Cg%28n%29%7C%2BM_2%7Ch%28n%29%7C%5Cle%20M%28%7Cg%28n%29%7C%2B%7Ch%28n%29%7C%29)
where
![M](https://tex.z-dn.net/?f=M)
is the larger of the two values
![M_1](https://tex.z-dn.net/?f=M_1)
and
![M_2](https://tex.z-dn.net/?f=M_2)
, or
![M=\max\{M_1,M_2\}](https://tex.z-dn.net/?f=M%3D%5Cmax%5C%7BM_1%2CM_2%5C%7D)
. Then the last term is bounded above by
![M(|g(n)|+|h(n)|)\le2M\max\{|g(n)|,|h(n)|\}](https://tex.z-dn.net/?f=M%28%7Cg%28n%29%7C%2B%7Ch%28n%29%7C%29%5Cle2M%5Cmax%5C%7B%7Cg%28n%29%7C%2C%7Ch%28n%29%7C%5C%7D)
from which it follows that
That number is the ratio of 578,778,777 to 100,000,000 , so it's rational.
Here's a surprising factoid:
ANY number that you can completely write down on paper with digits...
and a decimal point or a fraction bar if you need them ... is rational.
If you can write it down ... without saying "repeating" or using symbols ...
it's rational.
The mass of brick is 2478 gram
<em><u>Solution:</u></em>
A brick is in the shape of a rectangular prism with a length of 8 inches, a width of 3.5 inches, and a height of 2 inches
Length = 8 inches
Width = 3.5 inches
Height = 2 inches
<em><u>The volume of rectangular prism is given as:</u></em>
![volume = length \times width \times height](https://tex.z-dn.net/?f=volume%20%3D%20length%20%5Ctimes%20width%20%5Ctimes%20height)
![volume = 8 \times 3.5 \times 2\\\\volume = 56](https://tex.z-dn.net/?f=volume%20%3D%208%20%5Ctimes%203.5%20%5Ctimes%202%5C%5C%5C%5Cvolume%20%3D%2056)
Thus volume of brick is 56 cubic inches
<em><u>Convert inches to centimeter</u></em>
1 inch = 2.54 centimeter
Therefore,
56 cubic inches = 56 x 2.54 x 2.54 x 2.54 cubic centimeter
56 cubic inches = 917.676 cubic centimeter
Thus, we get,
volume = 917.676 cubic centimeter
The brick has a density of 2.7 grams per cubic centimeter
Density = 2.7 grams
<em><u>The mass of brick is given by formula:</u></em>
![mass = density \times volume](https://tex.z-dn.net/?f=mass%20%3D%20density%20%5Ctimes%20volume)
<em><u>Substituting the values we get,</u></em>
![mass = 2.7 \times 917.676\\\\mass = 2477.724 \approx 2478](https://tex.z-dn.net/?f=mass%20%3D%202.7%20%5Ctimes%20917.676%5C%5C%5C%5Cmass%20%3D%202477.724%20%5Capprox%202478)
Thus mass of brick is 2478 gram
True. If there is a point in the middle that is false, we have two create 2 solutions.
Hope this helps!
Answer:
x =76.45 degrees
Step-by-step explanation:
72 + 252 – 2(7)(25)cos _x__=242
combine like terms
324-350cosx = 242
subtract 324 from each side
-350x = -82
divide by -350
cos x = -82/-350
cos x = 82/350
take the arccos of each side
arccos (cos x) = arccos (82/350)
x =76.45 degrees