1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Murrr4er [49]
3 years ago
10

The temperature of a chemical reaction ranges between 20 degrees Celsius and 160 degrees Celsius. The temperature is at its lowe

st point when t = 0, and the reaction completes 1 cycle during an 8-hour period. What is a cosine function that models this reaction?
Mathematics
1 answer:
Crank3 years ago
3 0

Answer:

The cosine function that models this reaction is:

y=-70cos(\frac{1}{4}\pi x) +90

Step-by-step explanation:

The general cosine function has the following form

y = Acos(bx) + k

Where A is the amplitude: half the vertical distance between the highest peak and the lowest peak of the wave.

\frac{2\pi}{b} is the period: time it takes the wave to complete a cycle.

k is the vertical displacement.

The maximum temperature is 160 and the minimum is 20. Then the amplitude A is:

A =\frac{160-20}{2}\\\\A= 70

The reaction completes a cycle in 8 hours

Then the period is 8 hours.

Thus:

\frac{2\pi}{b}=8\\\\ b=\frac{2\pi}{8}\\\\ b=\frac{1}{4}\pi

The function is:

y = 70cos(\frac{1}{4}\pi x)+k

when t=0 y is minumum therefore y=-cos(x)

So

y = -70cos(\frac{1}{4}\pi x)+k

Now we substitute t = 0 in the function and solve for k

20 = -70cos(0)+k\\\\k=20+70\\\\k=90

Finally

y=-70cos(\frac{1}{4}\pi x) +90

You might be interested in
How can i find the volume of this figure help please
valentinak56 [21]

Answer:

The answer is 463 inch cubed

Step-by-step explanation:

you do 8 x 8 x 7 which will give you 448 volume for just the cube.

then you do 5 x 3 x 1 = 15

you add 448 with 15 you will get 463

6 0
3 years ago
Nathan had an infection, and his doctor wanted him to take penicillin. Because Nathan’s father and paternal grandfather were all
Sergio039 [100]
Let events
A=Nathan has allergy
~A=Nathan does not have allergy
T=Nathan tests positive
~T=Nathan does not test positive

We are given
P(A)=0.75  [ probability that Nathan is allergic ]
P(T|A)=0.98  [probability of testing positive given Nathan is allergic to Penicillin]

We want to calculate probability that Nathan is allergic AND tests positive
P(T n A)

From definition of conditional probability,
P(T|A)=P(T n A)/P(A)
substitute known values,
0.98 = P(T n A) / 0.75
solving for P(T n A)
P(T n A) = 0.75*0.98 = 0.735

Hope this helps!!
3 0
3 years ago
What is the first numbers of pi?
kirza4 [7]
3,141......
_____________________________
5 0
3 years ago
Read 2 more answers
Describe how you could represent the fraction 4/10 using a model or number line. Dont make the answer huge thank you
Rzqust [24]

Answer:

As a model for representing fractions, the number line differs from other models (e.g., sets, regions) in several important ways. First, a length represents the unit, and the number line model suggests not only iteration of the unit but also simultaneous subdivisions of all iterated units. That is, the number line can be treated as a ruler.

Step-by-step explanation:

3 0
2 years ago
How do you do inequalities
fgiga [73]
So some quick tips for inequalities:
**What you do to one side you HAVE TO do it to the other 2**
**If you ever divide a negative number past the inequality signs, the signs FLIP!!**
(e.g. 2>-5x>25)
-2/5 <x < -5

I hope that this has helped!
8 0
2 years ago
Other questions:
  • Saul makes green paint by mixing blue paint and yellow paint. For every 4 gallons of green paint, he uses 3 gallons of blue pain
    10·2 answers
  • Express 45 = x as a logarithmic equation.
    14·2 answers
  • Graph the system of equations. <br> −x+2y=−8 <br> 3x−y=−6
    15·2 answers
  • What digits can be in one's place of a number that has 5 as a factor
    13·1 answer
  • How do you determine the range and median of a Box And Whisker Plot??
    13·1 answer
  • Question: 1) Hi how are you?
    12·1 answer
  • The domain of the following relation R{(6,-2), (1, 2), (-3,-4), (-3,2)} is<br> (1 point)
    6·1 answer
  • Can I get help with this please ????
    10·1 answer
  • This holiday weekend, Sue is going to Chicago to shop and to see a baseball game. To avoid traffic, Sue decides to take the trai
    6·1 answer
  • Meghan sells handmade sweaters and hats at her store. Let A represent the event that a randomly selected customer buys hat, and
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!