Rosalie sleeps 8 hours the first night of finals week. Each night after, she stays up later to study and sleeps 75% as much as she did the previous night. How many total hours of sleep does she receive during the 4 nights of finals week? Do this without finding each night and adding for a total

she received 21.875 hours of sleep during the 4 nights.

Step-by-step explanation:

Rosalie is following a geometric sequence(GP) by having a common rate of sleep .

as 75% or 0.75%.

Formula for a sum in GP= , where a= first term, r = common ratio, n= number of terms.

Put a= 8, r=0.75 and n =4, we get

On simplifying we get

Sum =21.875 hours

Hence, she received 21.875 hours of sleep during the 4 nights.

step-by-step explanation:

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x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)