Answer:
120960
Step-by-step explanation:
Given that a librarian has a set of ten different books, including four different books about Abraham Lincoln.
The librarian wants to put the ten books on a shelf with the four Lincoln books next to each other, somewhere on the shelf among the other six different books.
First arrnage the 6 other books in the shelf.
This can be done in 
Now arrange the 4 books of Lincoln
This can be done in 
Now we have 7 places to insert Lincoln books including two corners and in between.
Thus this can be done in 7 ways
Total no of ways = 
H1 (t) = 196 - 16 t-squared. / / / H2 (t) = 271-16t-squared. / / / In each function, 't' is the number of seconds after that ball is dropped. / / / Each function is only true until the first time that H=0, that is, until the first bounce. Each function becomes very complicated after that, and we would need more information in order to write it.
Answer:
222.86
Step-by-step explanation:
<h2><u>in order to solve this question you can create an equation :</u></h2>
35% * x = 78
where x is the original amount
in order to get x , you have to say :
78/ 35% = x
hence x = 222.8571...
to 2dp = 222.86
The question is somewhat poorly posed because the equation doesn't involve <em>θ</em> at all. I assume the author meant to use <em>x</em>.
sec(<em>x</em>) = csc(<em>x</em>)
By definition of secant and cosecant,
1/cos(<em>x</em>) = 1/sin(<em>x</em>)
Multiply both sides by sin(<em>x</em>) :
sin(<em>x</em>)/cos(<em>x</em>) = sin(<em>x</em>)/sin(<em>x</em>)
As long as sin(<em>x</em>) ≠ 0, this reduces to
sin(<em>x</em>)/cos(<em>x</em>) = 1
By definition of tangent,
tan(<em>x</em>) = 1
Solve for <em>x</em> :
<em>x</em> = arctan(1) + <em>nπ</em>
<em>x</em> = <em>π</em>/4 + <em>nπ</em>
(where <em>n</em> is any integer)
In the interval 0 ≤ <em>x</em> ≤ 2<em>π</em>, you get 2 solutions when <em>n</em> = 0 and <em>n</em> = 1 of
<em>x</em> = <em>π</em>/4 <u>or</u> <em>x</em> = 5<em>π</em>/4
You can determine if things are parallel if the lines will eventually meet or not. M and N are one line while P and Q are also a line. Therefore, we can say P is one line while M is also one line. The answer would be is that they are parallel, the two lines will not crash with one another. To show your work as if they are parallel, you can continue the lines down and write a note saying they won't collide or you just say they won't collide and are parallel lines.
