# The base and sides of a container is made of wood panels. The container does not have a lid. The base and sides are rectangular. The width of the container is x cm . The length is double the width. The volume of the container is 54cm3 . Determine the minimum surface area that this container will have.

Minimum surface area =

Step-by-step explanation:

We are given that

Width of container=x cm

Length of container=2x cm

Volume of container=

We have to find the minimum surface areas that this container will have.

Volume of container=

Surface area of container=

Because the container does not have lid

Surface area of container=

Differentiate w.r.t x

Substitute

Again differentiate w.r.t x

Substitute x=3.4

0" alt="\frac{d^2S}{dx^2}=\frac{324}{(3.4)^3}+4=12.24>0" align="absmiddle" class="latex-formula">

Hence, function is minimum at x=3.4

Substitute x=3.4

Then, we get

Minimum surface area =

## Related Questions

Twelve friends share 4 bread rolls equally what fraction of a bread roll does each friend get

Step-by-step explanation:

There are 12 people, and 4 bread rolls. Each person would therefore get

4 bread rolls/ 12 people, so each person would get 1/3 of a bread roll.

Each friend will get 1/3 of a bread roll.

4 bread rolls. and 12 friends.

So 4/12 = 1/3.

Hope it helps..........

Step-by-step explanation:

What is the remainder when 2 is synthetically divided into the polynomial -3x2 + 7x - 9?

-7

Step-by-step explanation:

When you divide a polynomial f(x) by (x-c), the remainder r will be f(c).

hence you will get the remainder by putting the 2 as value of x:

f(x) = -3x² + 7x - 9

f(2) = -3(2)² +7(2) - 9

= -3(4) + 14 - 9

= -12 + 5

remainder = -7

What are the intercepts of f(x)=5x-45

The y-intercept of f(x) = 5x - 45 would be -45, as that is what is represented in the equation. The way to find the x-intercept would be to solve the equation when f(x) = 0.

0 = 5x - 45
+ 45         + 45

45 = 5x
/5     /5
9 = x

And there we have it.
The intercepts of f(x) = 5x - 45 are as follows:

y-intercept = -45
x-intercept = 9

Hope that helped =)

You are facing North. Turn 90 degrees left. Turn 180 degrees right. Reverse direction. Turn 45 degrees left. Reverse direction. In which direction are you now facing?

Northeast.

Explanation:

From a north facing, turning 90° left would result in facing west.

While facing west, turning 180° east would result in facing east.

Reversing direction would put us back facing west.

Turning 45° left will put us halfway between west and south; this is southwest.

Reversing direction from southwest puts us northeast.

In this exercise we have to use the directions of a compass to orient ourselves, like this:

Northeast.

We have to assume that we are in a circle, where when we turn 90 degrees to the left we will be in west.  Following this way of thinking by turning 180 degrees, we are making two 90 degree turns and we will meet at east.

Reversing this last position we return to west and finally turn 45 degrees which puts us between west and south the would be southwest. But we reversed that position, so we are between north and east, that is, northeast.

See more about directions at brainly.com/question/989117