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
ankoles [38]
3 years ago
14

The daily average temperature in Santiago, Chile, varies over time in a periodic way that can be modeled approximately by a trig

onometric function.
Assume the length of the year (which is the period of change) is exactly 365days long. The hottest day of the year, on average, is January 777, when the average temperature is about 29 degrees C.

The average temperature at the coolest day of the year is about 14 degrees C.

Find the formula of the trigonometric function that models the daily average temperature T in Santiago t days into the year. (t = 1 on January 1) Define the function using radians.

What is the average temperature in Santiago on January 31? Round your answer, if necessary, to two decimal places.
Mathematics
2 answers:
natali 33 [55]3 years ago
7 0

Answer:

a) the trigonometric function is;

y = 7.5 sin ( \frac{2 \pi}{365}t + \frac{337 \pi}{730})+ 21.5

b) y = 28.36^0 \ C    ( to two decimal places)

Step-by-step explanation:

This data can be represented by the sinusoidal function of the form :

\mathbf{y = A sin (Bt -C)+D}

where A = amplitude and which can be determined via the formula:

A = \dfrac{largest \ temperature -  lowest \ temperature}{2}

A = \dfrac{29-14}{2}

A = \dfrac{15}{2}

A = 7.5° C

where B = the frequency;

Since the data covers a period of 3 days ; then \dfrac{2 \pi}{B } =365

B = \dfrac{2 \pi}{365}   ( where 365 is the time period )

The vertical shift is found by the equation D;

D =  \frac{largest \ temperature + lowest \ temperature}{2}

D = \frac{29+14}{2}

D = 21.5

Replacing the values of A ; B and D into the above sinusoidal function; we have :

y = 7.5 sin (\frac{2 \pi}{365}t -C) + 21.5

From the question; when it is 7th of the year ( i.e January 7);

t =  7 and the temperature (y) = 29° C

replacing that too into the above equation; we have:

29= 7.5 sin (\frac{2 \pi}{365}*7 -C) + 21.5

29= 7.5 sin (\frac{14 \pi}{365} -C) + 21.5

\frac{29-21.5}{7.5}=  sin (\frac{14 \pi}{365} -C)

1=  sin (\frac{14 \pi}{365} -C)

sin^{-1}(1)=   (\frac{14 \pi}{365} -C)

\frac{\pi}{2}=   (\frac{14 \pi}{365} -C)

C=   (\frac{14 \pi}{365} -\frac{\pi}{2})

C=   (\frac{28 \pi- 365 \pi}{730} )

C=  \frac{-337 \pi}{730}

Thus; the trigonometric function is;

y = 7.5 sin ( \frac{2 \pi}{365}t + \frac{337 \pi}{730})+ 21.5

Similarly; to determine the temperature o Jan 31; i.e when t= 31 ; we have :

y = 7.5 sin ( \frac{2 \pi}{365}*31+ \frac{337 \pi}{730})+ 21.5

y = 7.5 sin ( \frac{62 \pi}{365}+ \frac{337 \pi}{730})+ 21.5

y = 7.5 sin ( \frac{124 \pi+ 337 \pi }{730})+ 21.5

y = 7.5 sin ( \frac{461 \pi }{730})+ 21.5

y = 7.5 *( 0.915)+ 21.5

y = 6.8689+ 21.5

y = 28.36^0 \ C    ( to two decimal places)

Lady_Fox [76]3 years ago
3 0

Answer:

7.5cos(2\pi/365(t-7))+21.5

b) 28.37

Step-by-step explanation:

You might be interested in
In the diagram, GH bisects FGI. A. Solve for x and find m FGH. B. Find m HGI. C.find m FGI. A. X=_(simplify your answer)
Sophie [7]

Answer:

Part A) x=9 and m∠FGH=29°

Part B) m∠HGI=29°

Part C) m∠FGI=58°

Step-by-step explanation:

Part A) Solve for x and find m∠FGH

we know that

m∠FGI=m∠FGH+m∠HGI

If GH bisects FGI

then

m∠FGH=m∠HGI

substitute the values

4x-7=5x-16

solve for x

5x-4x=16-7

x=9

m∠FGH=4x-7

m∠FGH=4(9)-7=29°

Part B) Find the measure of angle HGI

m∠HGI=5x-16

Remember that

m∠FGH=m∠HGI

Verify

m∠HGI=5(9)-16=29° -----> is correct

Part C) Find the measure of angle FGI

m∠FGI=m∠FGH+m∠HGI

substitute the values

m∠FGI=29°+29°=58°

8 0
3 years ago
Expand Expression t( 3n + 4)
Free_Kalibri [48]

Answer:

=3tn+4t

hope it helps...

8 0
2 years ago
Read 2 more answers
How many five digit odd numbers are possible if the leftmost digit cannot be zero?
blagie [28]

Answer:

45000 five digit odd numbers are possible if the leftmost digit cannot be zero.

Step-by-step explanation:

Pls mark the brainliest

6 0
3 years ago
The average life of a certain type of small motor is 10 years with a standard deviation of 2 years. The manufacturer replaces fr
Ivenika [448]

Answer:

She should offer a guarantee of 6.24 years.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 10, \sigma = 2

If she is willing to replace 3% of the motors that fail, how long a guarantee (in years) should she offer?

This is the value of X when Z has a pvalue of 0.03. So it is X when Z = -1.88. So

Z = \frac{X - \mu}{\sigma}

-1.88 = \frac{X - 10}{2}

X - 10 = -1.88*2

X = 6.24

She should offer a guarantee of 6.24 years.

8 0
3 years ago
......................,.,................​
Alex787 [66]

a=6, b=2

Step-by-step explanation:

Use simplification into substitution
\frac{a}{3} =1+\frac{2}{b}

a=3(1+\frac{2}{b})

a=3+\frac{6}{b}

We can now plug this value of <em>a</em> into the second equation.

\frac{3+\frac{6}{b} }{4} +\frac{3}{b} =3

Get rid of fractions in the numerators and/or denominators

\frac{3b+6}{4b} +\frac{3}{b} =3

Then we can match the denominators

\frac{3b+6}{4b} +\frac{12}{4b} =3

Combine

\frac{3b+18}{4b} =3

Divide both sides by three

\frac{b+6}{4b} =1

Get rid of fractions

b+6=4b

Single out <em>b</em>

6=3b

b=2

Now we can plug it into the equation

\frac{a}{3} -\frac{2}{2} =1

\frac{a}{3} =2

a=6

Now we can check it;

\frac{6}{3} -\frac{2}{2} =1

↑CORRECT

\frac{6}{4} +\frac{3}{2} =3

↑CORRECT

4 0
2 years ago
Other questions:
  • The focus of a parabola is (0, -3) and the directrix is y = 3. What is the equation of the parabola?
    9·1 answer
  •   ---------------------)Generating Equivalent Expressions
    8·1 answer
  • Find sin(2x), cos(2x), and tan(2x) from the given information.<br> tan(x) = − 1/2 , cos(x) &gt; 0
    9·1 answer
  • PLEASE HELP!!!
    14·2 answers
  • A right triangle has one angle that measures 65°. What is the measure of the other acute angle?
    14·1 answer
  • Suppose it is known that for a given differentiable function y=f(x), its tangent line (local linearization) at the point where a
    10·1 answer
  • (3,-5) (-1,5) you have to find the slope
    8·1 answer
  • The following information was obtained from matched samples taken from two populations. Assume the population of differences is
    6·1 answer
  • 5 times 2/3 is ? For Matthematics please and ty
    13·2 answers
  • HELP FAST! AND NO LINKS! There is a line segment called AB (not pictured). The coordinates of point A are (6, 2), and the coordi
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!