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:
69
Step-by-step explanation:
If every 175th person gets free admission, that means
175th
175 * 2 = 350th
175 * 3 = 525th
person gets free admission and so on...
This basically means <em><u>"how many 175s are there is 6742 (for first day) and 5487 (for 2nd day)?"</u></em>
<em><u /></em>
We would need to divide and see the WHOLE number, not the fractional(decimal) amount remaining. So
<u>1st Day:</u>
6742/175 = 38.53
This means 38 people will get free admission
<u>2nd Day:</u>
5487/175 = 31.35
This means 31 people will get free admission
In the 2 days, total of 38 + 31 = 69 people will get free admission
Answer: I think it would be 285.
Step-by-step explanation:
A circle is 360* so I did 360-75. Hope this helps!!!
Answer:
f(-3) = 9
Step-by-step explanation:
Lets define f(a) first where a is any integer,
f(a) is found out by putting the integer in the function in place of the variable
So for the given question
In order to find f(-3) we will put -3 in place of x
So putting -3,
So, the value of function at -3 is 9 ..
60% of 20 quizzes = 60/100*20 quizzes = 12 quizzes
Amount of quizzes remaining = 50 quizzes - 20 quizzes = 30 quizzes
He passes 80% of those 30 quizzes, so
80/100 * 30 quizzes = 24 quizzes
So, he passed 12 quizzes from the initial bunch and 24 quizzes from the rest, which totals to 12 quizzes + 24 quizzes = 36 quizzes.
Then, you see that he passed 36 quizzes, out of the total 50 quizzes, so the ratio is 36 quizzes / 50 quizzes = 36/50, which when converted as a percentage is 36/50 * 100% = 72%.
Therefore, he passed 72% of the quizzes for the entire year.
