Answer: After about 9.03 hours the temperature first reach 82 degrees.
Step-by-step explanation:
The sinusoidal function is given by :
![y=A\sin[\omega(x-\alpha)]+C](https://tex.z-dn.net/?f=y%3DA%5Csin%5B%5Comega%28x-%5Calpha%29%5D%2BC)
where, A = amplitude; 
, α= phase shift on the Y-axis and C = midline.
As per given,
Average daily temperature= 
[midline is average of upper and lower limit.]
A= 97-85 = 12
Phase shift: 
Period = 24 hours;
Substitute all values in sinusoidal function, we get
![y=12\sin[\dfrac{\pi}{12}(x-10)]+85](https://tex.z-dn.net/?f=y%3D12%5Csin%5B%5Cdfrac%7B%5Cpi%7D%7B12%7D%28x-10%29%5D%2B85)
Put y= 82, we get
![82=12\sin[\dfrac{\pi}{12}(x-10)]+85\\\\\Rightarrow\ -3= 12\sin[\dfrac{\pi}{12}(x-10)]\\\\=\dfrac{-1}{4}= \sin[\dfrac{\pi}{12}(x-10)]\\\\\Rightarrow\ \dfrac{\pi}{12}(x-10)=\sin^{-1}(\dfrac{-1}{4})\\\\\Rightarrow\ x-10=\dfrac{12}{\pi}(\sin^{-1}(\dfrac{-1}{4}))\\\\\Rightarrow\ x=\dfrac{12}{\pi}(\sin^{-1}(\dfrac{-1}{4}))+10\\\Rightarrow\ x\approx9.03](https://tex.z-dn.net/?f=82%3D12%5Csin%5B%5Cdfrac%7B%5Cpi%7D%7B12%7D%28x-10%29%5D%2B85%5C%5C%5C%5C%5CRightarrow%5C%20-3%3D%2012%5Csin%5B%5Cdfrac%7B%5Cpi%7D%7B12%7D%28x-10%29%5D%5C%5C%5C%5C%3D%5Cdfrac%7B-1%7D%7B4%7D%3D%20%5Csin%5B%5Cdfrac%7B%5Cpi%7D%7B12%7D%28x-10%29%5D%5C%5C%5C%5C%5CRightarrow%5C%20%5Cdfrac%7B%5Cpi%7D%7B12%7D%28x-10%29%3D%5Csin%5E%7B-1%7D%28%5Cdfrac%7B-1%7D%7B4%7D%29%5C%5C%5C%5C%5CRightarrow%5C%20x-10%3D%5Cdfrac%7B12%7D%7B%5Cpi%7D%28%5Csin%5E%7B-1%7D%28%5Cdfrac%7B-1%7D%7B4%7D%29%29%5C%5C%5C%5C%5CRightarrow%5C%20x%3D%5Cdfrac%7B12%7D%7B%5Cpi%7D%28%5Csin%5E%7B-1%7D%28%5Cdfrac%7B-1%7D%7B4%7D%29%29%2B10%5C%5C%5CRightarrow%5C%20x%5Capprox9.03)
Hence, After about 9.03 hours the temperature first reach 82 degrees.
Answer:
Step-by-step explanation:
1. 6.96 in
2. 2.6 in
3. 8.1 in
4. 5.6 m
5. 1.89 cm
6. 6 in
20x^2+50 = -40x^2+110x [ Taking x as the unknown positive integer ]
Answer:
155.25= 12
Step-by-step explanation:
17/2*2*1/2 = 12
17*1/2 = 12
8 1/2 17/1* 1/2
8*2+1 17*1/1*2
2 17*1/1*2
16+1 17/1*2
2 17/2
17 8.5=12
2
Answer:
Plant C is <u>0.64</u> times as tall as Plant B
Plant C is <u>2.4 inches</u> shorter than Plant B
Step-by-step explanation:
Plant B is 6 2/3 inches tall. Plant B is 20/3 inches tall.
Plant C 4 4/15 inches tall. Plant C is 64/15 inches tall.
a.) Plant C is shorter than Plant B 
= 0.64 times.
b.) Plant C is shorter than Plant B by = 
inches
