Suppose we let 
, so that 
.
Also, recall the double angle identity for cosine:
So, we can rewrite and compute the integral using the substitution, as
Answer: 8000
Step-by-step explanation:
From the question, we are informed that the expression 10³ × 2^w models the population of the bacteria after w weeks.
The number of bacteria that will be present in 3 weeks will then be:
= 10³ × 2^w
= 10³ × 2³
= 1000 × 8
= 8000 bacterias
1 mile = 5,280 feet.
Convert the 0.25 mile to feet:
0.25 miles = 0.25 x 5,280 = 1,320 feet.
Add the soda shop distance to this:
1,320 + 900 = 2,220 feet.
Total distance is 3 miles and 2,220 feet
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