Mr. Murphy is designing a rectangular concrete fire pit. The concrete sides and bottom will be 5 inches thick. The interior length will be 3 times the interior height, and the interior width will be 2 times the interior height. What should the outer dimensions of the fire pit be if the inner volume is to be 6000 cubic inches

For the outer dimensions: length = 35 inches, width = 25 inches, and height = 15 inches.

Step-by-step explanation:

For the interior;

volume = 6000

length, l = 3h

width, w = 2h

height = h

But,

Volume of a cuboid = length x width x height

So that;

6000 = 3h x 2h x h

6000 = 6

Divide through by 6 to have;

1000 =

h =

  = 10

Thus, the height is 10 inches. Thus;

length, l = 3h = 3 x 10 = 30 inches

width, w = 2h = 2 x 10 = 20 inches

For the outer dimension, since the concrete sides and bottom would be 5 inches thick. Then its dimension are;

length, l = 30 + 5 = 35 inches

width, w = 20 + 5 = 25 inches

height = 10 + 5 = 15 inches

The image will be the point (6,5)

Step-by-step explanation:

Here, we want to get the image of the point (-5,-6) after the reflection

Mathematically if we reflected a point with the pre-image coordinates (x,y) over the line y = -x; its image becomes (-y, -x)

So, (-5,-6) becomes (6,5)