Consider the equation v = (1/6)zxt2. the dimensions of the variables v, x, and t are [l/t], [l], and [t] respectively. the numerical factor 6 is dimensionless. what must be the dimensions of the variable z, such that both sides of the equation have the same dimensions?

The dimension of the variable will be:  

Step-by-step explanation:

Given equation is:  

The dimensions of the variables and are   and respectively.

Replacing all variables by their dimensions, we will get......

So, the dimension of the variable will be:  

The dimension of z is .

Step-by-step explanation:

We have been given the dimension of  , and

We need to find the dimension of z

Here, l denotes the length and t denotes the time:

We will put the values of the dimension of the variables given to find the dimension of z. and 1/6 is dimensionless.So, neglect it.

Now, we will simplify the above expression so, as to get the value of z

Hence, the dimension of z is

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x