An art exhibit at a local museum features several similarly shaped metal cubes welded together to make a sculpture. The smallest cube has a edge length of 6 inches. What are the edge lengths of the other cubes if the ratios of similarity to the smallest cube are 1.25, 43 , 1.5, 74 , and 2 respectively?

Given:

The smallest cube has a edge length of 6 inches.

The ratios of similarity to the smallest cube are 1.25, 43 , 1.5, 74 , and 2 respectively.

To find:

The edge lengths of the other cubes.

Solution:

If two figures are similar, then the ratios of similarity is equal to the ratio of their corresponding sides.

Let the edge of other cube be x.

It means, the edges of other cubes are 6 times of the ratio of similarity to the smallest cube.

Now,

Therefore, the edges of other cubes are 7.5, 8, 9, 10.5 and 12 respectively.

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

-2 is the right