The length of a rectangle is represented by the numerical value of 5V^3. If the recrtangle is equal in area to a squae with a side represented by 4V, what is the width of the rectangle in terms of V?
a. 1/80V^5
b. 4/5V
c. 16/5V
d. 16/5V^2
e. 5V/16
please answer and explain
The length of a rectangle is represented by the numerical value of 5V^3. If the recrtangle is equal in area to a square with a side represented by 4V, what is the width of the rectangle in terms of V?
16v^2 / 5v^3 = 16 / 5v
why use 16v^2
4v x 4v ?
exactly (4x)^2 = 16v^2
thank you
To find the width of the rectangle in terms of V, we need to use the formula for the area of a rectangle, which is length multiplied by width.
Given that the length of the rectangle is 5V^3, and the area of the rectangle is equal to the area of a square with a side represented by 4V, we can set up the following equation:
5V^3 * width = (4V)^2
Simplifying the equation, we have:
5V^3 * width = 16V^2
Next, we divide both sides of the equation by 5V^3 to solve for width:
width = 16V^2 / 5V^3
Simplifying further, we can divide the coefficients and subtract the exponents:
width = 16/5 * V^(2-3)
width = 16/5 * V^(-1)
width = 16/5V^1
Finally, we can simplify further by moving V^1 to the denominator:
width = 16/5V
Therefore, the width of the rectangle in terms of V is 16/5V.
So, the correct answer is option c. 16/5V.