$z=\frac{(\sqrt{3}+1)+(\sqrt{3}-1)}{4}
Answer (2)
The value of z simplifies to 2 3 . This is achieved by combining terms in the numerator and simplifying the fraction. The final answer is 2 3 .
;
Simplify the numerator: ( 3 + 1 ) + ( 3 − 1 ) = 2 3 .
Divide by 4: z = 4 2 3 .
Simplify the fraction: z = 2 3 .
The final answer is 2 3 .
Explanation
Understanding the problem We are given the expression z = 4 ( 3 + 1 ) + ( 3 − 1 ) and we need to find the value of z .
Simplifying the numerator First, let's simplify the numerator by combining like terms: ( 3 + 1 ) + ( 3 − 1 ) = 3 + 1 + 3 − 1 = 2 3 So, the expression becomes: z = 4 2 3 .
Simplifying the fraction Now, we simplify the fraction by dividing both the numerator and the denominator by 2: z = 4 2 3 = 2 3 Thus, the value of z is 2 3 .
Final answer Therefore, the final answer is 2 3 .
Examples
Imagine you are building a ramp that needs to have a specific slope. The slope is related to the angle of the ramp, and trigonometric functions like sine, cosine, and tangent are used to calculate these angles. If you know that the sine of the angle is 2 3 , you can determine the angle of the ramp, which is 60 degrees. This helps you ensure the ramp is safe and easy to use.
