A wire with a length of 100 cm is cut into three parts. The length of wire of the first and second parts are the same. The length of the third part of the wire exceeds the sum of the first two parts by 4 cm. Calculate the length of each part.

The first two pieces are the same, let each of those equal x, so you have x + x = 2x

The 3rd piece is the sum of the first two + 4, so this would be 2x + 4

Now you have 2x + 2x + 4 = 100 cm

Combine like terms:

4x +4 = 100

Subtract 4 from both sides

4x = 96

Divide both sides by 4

X = 24

First piece is 24 cm

Second piece is 24 cm

Third piece is 52 cm

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step-by-step explanation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt