Vector bought 15.6 pounds of paintballs. All together, the balls cost $35.99. About how much did the paintballs cost per pound?
2 answers:
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They're not equivalent.
(vertical bars) represents the absolute value of x. How it works is that it turns negative numbers positive but leaves 0 and positive numbers alone (hence it gets a number's distance from 0 on the number line).
(square brackets) usually represents the floor function, which returns the largest integer that is less than or equal to x. (The floor of x can also be written as
--- it depends on what your textbook/source says).
To solve , you first transform it into the equivalent equation
. Then by definition of absolute value, there are only two solutions for the first equation: x = 10 or x = -10.
[x] = 10 has infinitely many solutions. For example, the floor of 10 is 10, so , thus a solution for the second equation is x = 10
The floor of 10.1 is 10, so , thus another solution for the second equation is x = 10.1.
The two equations do not have the same solution set (as x = 10.1 does not solve |x| - 3 = 7 but solves [x] = 10), so they're not equivalent.
First, we expand the equation:
Then, we combine certain terms in order to simplify them using trigonometry identities.
Note these identities:
Pythagoran relation:
Sum and Difference Formula/Identities:
Thus, if we apply these identities, the simplified equation would be:
Simplying further, the answer would be
![2[cos(A-B)+1]](https://tex.z-dn.net/?f=2%5Bcos%28A-B%29%2B1%5D)
Then, we combine certain terms in order to simplify them using trigonometry identities.
Note these identities:
Pythagoran relation:
Sum and Difference Formula/Identities:
Thus, if we apply these identities, the simplified equation would be:
Simplying further, the answer would be