The base of a box is a rectangle. the width of the box is half its length. the height of the box is 0.5m. find the volume of the box if the area of the base is 1.08m² less than the combined area of the sides.

We assume the box is open-top.

If the width of the box is represented by w, then its length is 2w. The area of the base is then w·2w = 2w².

The combined area of the sides is the product of the perimeter of the base, 2(w+2w) = 6w and the height, 0.5, so is 3w.

Since the base area is 1.08 m² less than the lateral area, we have ...

... 2w² = 3w -1.08

... 2w² -3w +1.08 = 0 . . . . rearrange to standard form

... w² -1.5w +0.54 = 0 . . . make the leading coefficient 1 (divide by 2)

... (w -0.9)(w -0.6) = 0 . . . factor

The width of the box may be either 0.6 meters or 0.9 meters.

The volume is the product of width, length, and height, so is ...

... V = w·2w·0.5 = w²

... V = 0.36 m³ . . . or . . . 0.81 m³. . . . . . (there are two possible answers)

Check

For width 0.6 m, the length is 1.2 m and the perimeter is 2(0.6+1.2) = 3.6 m. The lateral area is then (0.5 m)(3.6 m) = 1.8 m². Subtracting 1.08 m² from this, we get 0.72 m². The area of the base is (0.6 m)(1.2 m) = 0.72 m², so this answer checks.

For width 0.9 m, the length is 1.8 m and the perimeter is 2(0.9+1.8) = 5.4 m. The lateral area is then (0.5m)(5.4 m) = 2.7 m². Subtracting 1.08 m² from this, we get 1.62 m². The area of the base is (0.9 m)(1.8 m) = 1.62 m², so this answer checks, too.

the degrees would remain the same ( the number to the left of the decimal point.

the multiply the decimal by 60 to get the minutes and use the numbers to the left of the decimal point.

then multiply the decimal portion of that by 60 for the seconds and round off as needed.

39 .956652

the 39 remains the degrees.

the minutes = 0.956652 x 60 = 57.39912

the minutes = 57

the seconds = 0.39912 x 60 = 23.95 = 24 ( rounded to nearest tenth)

so 39.956652 = 39 degrees, 57 minutes and 24 seconds

-75.159809

the -75 remains the degrees

the minutes = 0.159809 x 60 = 9.58854

the minutes = 9

the seconds = 0.58854 x 60 = 35.31, rounded to nearest tenth = 35.3 seconds

so -75.159809 = -75 degrees, 9 minutes and 35.3 seconds.

the first coordinate is north or south, since it it positive it is north.

the second number is east or west, because it is negative it is west.

39 degrees, 57 minutes and 24 seconds n

-75 degrees, 9 minutes and 35.3 seconds w

i think it’s c i believe