Gby cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box can be made. if the cardboard is 17 in. long and 10 in. wide and the square cutaways have dimensions of x in. by x in., find a function giving the volume v(x) of the resulting box.

We find the function by starting from the formula of the volume of a rectangular box.

Volume of a rectangular box = length x width x height

From the problem statement,
length = 17 - 2x
width = 10 - 2x
height = x

where x is the height of the box or the side of the equal squares from each corner and turning up the sides

V = (17-2x) (10-2x) (x)
V = (17 - 2x) (10x - 2x^2)
V = 170x - 34x^2 - 20x^2 + 4x^3

V = 4x^3 - 54x^2 + 170x <THE FUNCTION V(x)

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation:

a

step-by-step explanation: