Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 181.5 square centimeters

The base and height of the solid is 5.5cm

Step-by-step explanation:

Given

Required

Determine the dimensions that maximizes the volume

Let the base dimension be x and the height be h

The volume is calculated as:

181.5 =x^2h

The surface area (S) is calculated as this:

Substitute 181.5 for S

Make h the subject:

Substitute in

To get the maximum, we differentiate V with respect to t and set the differentiation to 0

Set to 0

Multiply through by 4

Recall that:

So, we have:

Hence, the base and height of the solid is 5.5cm

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.

b

step-by-step explanation: