Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 73 and 97 degrees during the day and the average daily temperature first occurs at 10 AM. How many hours after midnight, to two decimal places, does the temperature first reach 82 degrees?

Answer: After about 9.03 hours the temperature first reach 82 degrees.

Step-by-step explanation:

The sinusoidal function is given by :

[tex]y=A\sin[\omega(x-\alpha)]+C[/tex]

where, A =  amplitude; [tex]\omega=\dfrac{2\pi}{period}[/tex] ,  α= phase shift on the Y-axis and C = midline.

As per given,

Average daily temperature= [tex]C=\dfrac{73+97}{2}=85[/tex]   [midline is average of upper and lower limit.]

A=  97-85 = 12

Phase shift: [tex]\alpha=10[/tex]

Period = 24 hours;

[tex]\omega=\dfrac{2\pi}{24}=\dfrac{\pi}{12}[/tex]

Substitute all values in sinusoidal function, we get

[tex]y=12\sin[\dfrac{\pi}{12}(x-10)]+85[/tex]

Put y= 82, we get

[tex]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[/tex]

Hence, After about 9.03 hours the temperature first reach 82 degrees.

There are 3,785 milliliters in 1 gallon, and there are 4 quarts in 1 gallon.

How many milliliters are in 3 gallons?

Wats the answer?Please answer fast

1
Find the missing side
in the similar figures below:
30
15
24
25
.X
Ms. Price
Mr. Clark
Mr. Smith
A) 30
B) 34
C) 36
D) 38
E) 10
Mrs. Wilson
Mrs. White

Which phrase describes how to divide a complex number z by r(cos θ + i sin θ)?

Scale by a factor of StartFraction 1 Over r EndFraction and rotate clockwise by θ.
Scale by a factor of r and rotate clockwise by θ.
Scale by a factor of StartFraction 1 Over r EndFraction and rotate counterclockwise by θ.
Scale by a factor of r and rotate counterclockwise by θ.

point A is located in which quadrant 1 2 3 or 4​

HELP PLEASE!! 100 POINTS
Part A: The sun produces 3.9 ⋅ 1033 ergs of radiant energy per second. How many ergs of radiant energy does the sun produce in 1.55 ⋅ 107 seconds?

Part B: Which is the more reasonable measurement of the distance between the tracks on a CD:
1.6 ⋅ 10−3 mm or 1.6 ⋅ 103 mm? Justify your answer.

A farmer knows that of every 50 what's his chickens lay, only 45 will be marketable. If his chickens lay 2100 eggs in a week, how many will be marketable?

please include an explanation​

please help!!!
For part A I need to put the if/then statement
For part B I have to solve for X

Anybody Know This. ?

If you DIVIDE both sides of an inequality by a POSITIVE number, do you need to flip the direction of the inequality?

Can someone factor f(x)= 2x^4 -12x^3 +6x +20x and please show steps thank you

if 1 dozen bread rolls cost R10, how much will 4 bread rolls cost ​

Two forces are acting on an object, one at 58 Newton's and the other at 83 Newton's.
The resulting force is 105 Newton's. What is the angle between the resulting force and
the larger of the two original forces?

Javier had $305 in his bank account. His bank charges a fee of $7.50 each month that a balance is below $500. If he makes no other deposits or withdraws, how much money is in javier’s account at the end of three months?

Replace the a , b , c , and d with the dighits 2,4,6,8 to form the greatest product. Each digit can only be used once. Explain your substitutions.

a0b
x c d
--------------------------

A rectangular yard has a width that is 10 feet longer than the width . If the the area of the yard is 600 squared feet , find the dimension of the yard

Identify the graph of f(x)=10-10x2/x2

2+2=
A.4
B.2
C.6
D. none of the above

It’s it A B C D please answer

Help

Brainliest in reward

Please name both angles

Can someone help me on this??!??

Select each situation that can represent a proportional relationship

The price of buying x gallons of gas at $3 a gallon.

The total amount of weight a kitten gains in w weeks when it gains 4 ounces per week and started at a weight of 6 ounces.

The price of renting a scooter for m miles when it costs $0.75 per mile plus a base fee of $2.50.

The total amount of money a child earns from doing chores when she earns $10 a week for w weeks.
Plz help!

5/3÷7=_____


plzzzzzz help me ASAP. ​

please help ASAP ;)

The volume of blood pumped from your heart varies directly with your pulse rate. Each time your heart beats it pumps 0.06 liter of blood.
1. Write an equation that relates the volume of blood and pulse.
2. If your pulse is 74 bpm, how much blood is being pumped from your heart each minute?​

A 6-kilogram bag of cat food costs $21.54. What is the unit price?

Please Help!

Gamma ^ 2 + 1

Which expression is equivalent to 5y^-3

The 5th degree polynomial has relative maximum at x=___ and x=___
The 5th degree has relative maximum at x=___ and x=____

Please answer the wrong question