The expression x/6 ÷ 4/3x simplifies to 2/3, which represents the effective data transmission speed in a technological system, taking bandwidth and other transmission components into account.
To simplify the expression x/6 ÷ 4/3x, we apply the rule a/b ÷ c/d = a · d / b · c. Substituting our expression into this rule, we get:
x/6 ÷ 4/3x = (x · 3x) / (6 · 4) = 3x2 / 24
After simplifying, we divide both the numerator and the denominator by 3x:
3x2 / 24 = 3x · x / (3 · 8) = 2/3
So the simplified expression is 2/3, which indicates the effective data transmission speed given the factors affecting it. In technological terms, this expresses that the transmission speed is proportional to the bandwidth (x) adjusted for the influence of transmission components.
The probable question may be:
In a technological system, data transmission speed is crucial for efficient communication. If we represent the data transmission speed in terms of the expression x/6÷4/3x, simplify the expression using the fact that a/b÷c/d=a⋅d/b⋅c. Express the simplified form in terms of x.
Additional Information:
Consider a scenario where x represents the bandwidth, and the expression x/6÷4/3x models the effective data transmission speed. The numerator, x, denotes the available bandwidth, while the denominators 6 and 4 represent factors affecting the transmission speed.
Table:
+--------------+-------------------------+----------------------+
| Bandwidth | Transmission Component 1| Transmission Component 2|
+--------------+-------------------------+----------------------+
| x | 6 | 4 |
+--------------+-------------------------+----------------------+
In this context, simplifying the expression is essential for assessing the overall data transmission efficiency. What is the simplified expression, and how does it relate to the technological aspects of data transmission speed?
Options:
A) 3/2
B) 2/3
C) x/4
D) 4/x