Answer:
53.3324
Step-by-step explanation:
given that a thermometer is removed from a room where the temperature is 70° F and is taken outside, where the air temperature is 40° F.
By Newton law of cooling we have
T(t) = ![T+(T_0-T)e^{-kt}](https://tex.z-dn.net/?f=T%2B%28T_0-T%29e%5E%7B-kt%7D)
where T (t) is temperature at time t,T =surrounding temperature = 40, T0 =70 = initial temperature
After half minute thermometer reads 60° F. Using this we can find k
![T(0,5) = 40+(70-40)e^{-k/2} = 60\\e^{-k/2} =2/3\\-k/2 = -0.4055\\k = 0.8110](https://tex.z-dn.net/?f=T%280%2C5%29%20%3D%2040%2B%2870-40%29e%5E%7B-k%2F2%7D%20%3D%2060%5C%5Ce%5E%7B-k%2F2%7D%20%3D2%2F3%5C%5C-k%2F2%20%3D%20-0.4055%5C%5Ck%20%3D%200.8110)
So equation is
![T(t) = 40+(30)e^{-0.8110t}\\](https://tex.z-dn.net/?f=T%28t%29%20%3D%2040%2B%2830%29e%5E%7B-0.8110t%7D%5C%5C)
When t=1,
we get
![T(1) = 40+(30)e^{-0.8110}\\\\=53.3324](https://tex.z-dn.net/?f=T%281%29%20%3D%2040%2B%2830%29e%5E%7B-0.8110%7D%5C%5C%5C%5C%3D53.3324)
Answer:
<u>96 cm ²</u>
Step-by-step explanation:
A = bh (12 x 8)
12 x 8 = 96
Answer:
What's the question lol ?
Step-by-step explanation:
The answer to your question is A
Answer:
Ben must wait more than 4.2 years
Step-by-step explanation:
step 1
we know that
The simple interest formula is equal to
![A=P(1+rt)](https://tex.z-dn.net/?f=A%3DP%281%2Brt%29)
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
![t=?\ years\\ P=\$1,200\\r=6\%=6/100=0.06\\A>\$1,500](https://tex.z-dn.net/?f=t%3D%3F%5C%20years%5C%5C%20P%3D%5C%241%2C200%5C%5Cr%3D6%5C%25%3D6%2F100%3D0.06%5C%5CA%3E%5C%241%2C500)
substitute the values
![1,200(1+0.06t)>1,500](https://tex.z-dn.net/?f=1%2C200%281%2B0.06t%29%3E1%2C500)
Solve for t
Divide by 1,200 both sides
![(1+0.06t)>1.25](https://tex.z-dn.net/?f=%281%2B0.06t%29%3E1.25)
Subtract 1 both sides
![0.06t>1.25-1](https://tex.z-dn.net/?f=0.06t%3E1.25-1)
![0.06t>0.25](https://tex.z-dn.net/?f=0.06t%3E0.25)
Divide by 0.06 both sides
![t>4.2\ years](https://tex.z-dn.net/?f=t%3E4.2%5C%20years)
therefore
Ben must wait more than 4.2 years