Log(2)/log(1.064) ≈ 11.17 . . . . hours
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The population can be given by
p(n) = p₀×1.064ⁿ . . . . where n is the number of hours
You want to find n whe p(n) = 2*p₀.
2p₀ = p₀×1.064ⁿ . . . . . . . . . . . . substitute the given information
2 = 1.064ⁿ . . . . . . . . . . . . . . . . . divide by p₀
log(2) = n×log(1.064) . . . . . . . . take logs to make it a linear equation
log(2)/log(1.064) = n . . . . . . . . divide by the coefficient of n
Answer:
15 hours.
Step-by-step explanation:
Suppose the time taken to catch Mike is t hours and the distance ran by Mike is x miles then
5.5 = x/ t (Mike) --- ...(1)
6 = (x +7.5 )/ t (Julia ).......(2)
From equation (1):
x = 5.5t ..............(3).
From equation (2):
x + 7.5 = 6t
x = 6t - 7.5............(4).
Eliminating x from equations 3 and 4:
6t - 7.5 = 5.5t
0.5t = 7.5
t = 15 hours.
Answer:
The remainder theorem
Step-by-step explanation:
The remainder theorem states that given a polynomial f(x) and a linear factor x - k as in the question, then if f(x) is divided by x - k, then remainder is obtained at the value of x - k = 0 ⇒ x = k. That is, the remainder is f(k) when x = k.
For example, if we have a polynomial f(x) = x³ + 3x² -2x + 1 and a linear factor x - 1. The remainder theorem states that the remainder when f(x) is divided by x - 1 is obtained by equating the factor to zero and finding the value of x.
So, x - 1 = 0 ⇒ x = 1
Substituting x = 1 into f(x), we have
f(x) = x³ + 3x² -2x + 1
f(1) = 1³ + 3(1)² -2(1) + 1
= 1 + 3 - 2 + 1
= 3.
So, the remainder is 3.
Answer:
*dies of boredom*
Step-by-step explanation:
EH, MWAH