The wavelength of the color red is about 6.5 × 10−9 m. The wavelength of the color blue is about 4.75 × 10−9 m. Show that the wavelength of red is longer than the wavelength of blue.

2.5 x 10^-7 m

Explanation:

We can substract the wavength of the violet light to the wavelength of the red light:

(6.5 x 10^-7 m) - (4.0 x 10^-7 m) = 2.5 x 10^-7 m

This is the difference between this two values of wavelength.

So the wavelength of red light is 2.5 x 10^-7 m longer than violet light.

here is a big fat

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