They help scientists explain concepts that are difficult to observe.
Explanation:
First we will convert the given mass from lb to kg as follows.
157 lb = 
= 71.215 kg
Now, mass of caffeine required for a person of that mass at the LD50 is as follows.

= 12818.7 mg
Convert the % of (w/w) into % (w/v) as follows.
0.65% (w/w) = 
= 
= 
Therefore, calculate the volume which contains the amount of caffeine as follows.
12818.7 mg = 12.8187 g = 
= 1972 ml
Thus, we can conclude that 1972 ml of the drink would be required to reach an LD50 of 180 mg/kg body mass if the person weighed 157 lb.
A wind turbine turns wind energy into electricity using the aerodynamic force
Answer:
6.77 minutes
Explanation:
172 degree - 78 degree = (185 degree - 78 degree)e−2 k
=> 94 = 107
e−2 k => 94 ÷ 107
k => ln (94÷107) / 2
147 - 78 = (185 - 78)e ^[ln (94÷107) / 2]
=> 69 = 107 e^ [ln (94÷107) / 2]
e^[ln (94÷107) / 2] =69 ÷ 107
=> t = [ln (69 ÷ 107)] ÷ [ln (94÷107) / 2]
t=> -0.4387 ÷ -0.0648
t => 6.77 minutes.
Therefore, the final answer to the question is 6.77 minutes.
Why do teachers give such hard questions? anyways hopefully your question will get answered! (btw i also need the points but yeah gl!!!)