I just need help with the "_", since each "_" needs to be a whole number from 1-9, and each number can only be used once.
Equation: _ = _ sin((pi/_)(_-_))+_
9=2sin((pi)/(4)(5-3))+7. I dont know if this works so a tutor should double check
works for me.
To solve for the blank space, we need to start by simplifying the given equation.
Let's break it down step by step:
1. First, let's focus on the expression inside the sine function: (pi/_)(_-_). Since each "_" represents a whole number from 1 to 9, we have 9 possible values to consider.
2. Now, let's go through the possible values for "_" and evaluate the expression (pi/_)(_-_):
a) If "_" equals 1, then the expression becomes (pi/1)(1-_). Simplifying further, we get pi(1-_), which simplifies to pi-pi_.
b) If "_" equals 2, the expression becomes (pi/2)(2-_). Simplifying further, we get (pi/2)(2-_), which is equal to pi-pi_/2.
c) If we continue this process for "_" values of 3, 4, 5, 6, 7, 8, and 9, we will get similar expressions.
3. Now let's analyze the full equation: _ = _ sin((pi/_)(_-_))+_
Assuming "_sin((pi/_)(_-_))" has a non-zero value, we have two options:
a) If _ is equal to zero, then the equation becomes 0 = _ sin((pi/_)(_-_))+_. This means that "_" cannot be zero, as it will lead to a contradiction.
b) If _ is not equal to zero, then we can divide both sides of the equation by _ to isolate the sine function, giving us 1 = sin((pi/_)(_-_))+(_/_)_.
c) Since the sine function is bound between -1 and 1, there is only one possible value for _ that satisfies the equation: _ must be equal to the reciprocal of the remaining term on the right side.
Therefore, the solution for "_" depends on the value of the expression (pi/_)(_-_). By evaluating this expression for each potential value of "_", we can determine the valid and unique solution for the blank space.