X alpha (y÷z).x = 27 when y = 9 z= 2. (a) Find the relationship between x, y and z. (b) Find x when y =14 and z = 12.
First, let's solve for the value of x when y = 9 and z = 2.
Substituting y = 9 and z = 2 into the equation, we get:
X alpha (9÷2).x = 27
Simplifying the equation:
X alpha (4.5).x = 27
Multiplying 4.5 and x:
4.5x^2 = 27
Dividing both sides by 4.5:
x^2 = 6
Taking the square root of both sides:
x = ±√6
So the relationship between x, y, and z when y = 9 and z = 2 is x = ±√6.
Now, let's find x when y = 14 and z = 12.
Substituting y = 14 and z = 12 into the equation:
x alpha (14÷12).x = 27
Simplifying:
x alpha (7/6).x = 27
Multiplying (7/6) and x:
(7/6)x^2 = 27
Dividing both sides by (7/6):
x^2 = (27 * 6) / 7
x^2 = 162 / 7
Taking the square root of both sides:
x = ±√(162/7)
To find the relationship between x, y, and z, let's substitute the given values y = 9 and z = 2 into the equation X alpha (y÷z).x = 27:
X alpha (9 ÷ 2).x = 27
Simplifying the expression inside the brackets:
X alpha (4.5).x = 27
Noting that alpha represents an unknown operation, let's continue solving the equation.
(a) Find the relationship between x, y, and z:
Multiplying both sides of the equation by (y ÷ z) to eliminate the brackets:
X alpha x = (27) ÷ (4.5)
Simplifying:
X alpha x = 6
This means that the relationship between x, y, and z is that the product of x and an unknown operation (represented by alpha) is equal to 6.
(b) Find x when y = 14 and z = 12:
Substituting the values y = 14 and z = 12 into the equation X alpha x = 6:
X alpha x = 6
To solve for x, we need more information about the operation represented by alpha. If there is no additional information provided, we cannot determine the specific value of x.