Answer:
305 °F
Step-by-step explanation:
The core temperature of the object after 4 hours can be found using an exponential decay formula to model the decay of the difference between core temperature and ambient.
<h3>Cooling Model</h3>
The solution to the differential equation described by Newton's law of cooling is the exponential equation ...
y = ab^t +c
where 'a' is the initial core temperature difference from ambient, 'b' is the decay factor of that difference in 1 unit of time period t. 'c' is the ambient temperature.
For this problem, the ambient temperature is c=80, and the differences of interest are ...
a = 1200 -80 = 1120
b = (830 -80)/1120 = 75/112
Using these values in the model gives ...
y = 1120(75/112)^t +80 . . . . . . where y(t) is the core temperature at time t
Note that units of time are hours.
<h3>Application</h3>
We want y when t=4.
y = 1120(75/112)^4 +80 ≈ 1120(0.20108) +80 ≈ 305.212
The core temperature after 4 hours is about 305 °F.
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<em>Additional comment</em>
The differential equation will have a solution of the form ...
where k = ln(75/112) ≈ -0.40101
In the above, we defined b = e^k = 75/112. Accuracy with this fraction can be better than using a truncated value of k.
Answer:
D. 5
Step-by-step explanation:
Mean: (50+60)/2
110/2
55
Margin of error:
60 - 55
5
Answer: 17.68
Step-by-step explanation: just add the taxes, this is your final sale price.
Answer: Integers and Rational Numbers
Explanation: -2 is an integer because integers include positive an negative numbers. It would not be a whole number or a Naural number because both of those sets only include positive numbers. Here’s a better explanation:
Natural numbers: Natural Numbers are like (1,2,3....). They only include positive numbers. Therefore, -2 does not belong in this category.
Whole Numbers: Whole Numbers are like (0,1,2,3....). They include all the natural numbers with 0. Therefore, -2 does not belong in this set.
Integers: Integers include both positive and negative numbers. They are like (-3,-2,-1,0,1,2,3....). Since they both have positive and negative numbers, -2 would belong in this set.
Rational Numbers: Rational Numbers include ALL the sets that were described. (Natural, Whole, Integer). Since this set also includes positive and negative numbers, -2 would belong in this set.
So, -2 belongs in Integers and Rational Numbers
Hope this helps!
<span>tan(15) =
sin(15) / cos(15) =
sin(45 - 30) / cos(45 - 30) =
[ sin(45)cos(30) - sin(30)cos(45) ] / [ cos(45)cos(30) + sin(45)sin(30)]
Since sin(45) = cos(45) = √2/2, you can just factor that out from the top and bottom
[ cos(30) - sin(30) ] / [ cos(30) + sin(30)]
[ √3/2 - 1/2 ] / [ √3/2 + 1/2]
(√3 - 1) / (√3 + 1)
(√3 - 1)^2 / (√3+1)(√3 - 1)
(√3 - 1)^2 / (3 - 1)
(3 - 2√3 +1) / 2
2 - √3
There's also a formula for tan(a-b), but I couldn't remember it off hand.</span>
