After sitting on a shelf for a while, a can of soda at a room temperature ( 6 9 ∘ 69 ∘ F) is placed inside a refrigerator and slowly cools. The temperature of the refrigerator is 3 7 ∘ 37 ∘ F. Newton's Law of Cooling explains that the temperature of the can of soda will decrease proportionally to the difference between the temperature of the can of soda and the temperature of the refrigerator, as given by the formula below: T = T a + ( T 0 − T a ) e − k t T=T a ​ +(T 0 ​ −T a ​ )e −kt T a = T a ​ = the temperature surrounding the object T 0 = T 0 ​ = the initial temperature of the object t = t= the time in minutes T = T= the temperature of the object after t t minutes k = k= decay constant The can of soda reaches the temperature of 5 2 ∘ 52 ∘ F after 20 minutes. Using this information, find the value of k k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the can of soda, to the nearest degree, after 95 minutes. Enter only the final temperature into the input box.

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation:

english maybe i can ..

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.