The sum of two consecutive integers is 57. If x is the integer what are the two numbers

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

natali 33 [55]

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)

7 0

2 years ago

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(13 points) asap!! please help!!!!

kenny6666 [7]

Answer:

(-1,4)(1,4)

2

Step-by-step explanation:

6 0

2 years ago

What is 1/2 plus 1/3

Dafna11 [192]

Answer:

1/2 + 1/3 = 5/6

Step-by-step explanation:

1/2 + 1/3 = 5/6

3 0

2 years ago

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A school did a survey among 100 students to find their sports preferences. The students were asked about their preferences for s

Helen [10]

Part a)
we know that

Total number of students = 100
80 students like soccer.
So
this means 20 students do not like soccer.

Out of 80 who liked soccer, 30 liked volleyball
so
this means remaining 50 do not like volleyball.

Out of 45 students who likes volleyball, 30 likes soccer (mentioned in previous statement),
so
15 did not like soccer.

Based on this data, we can complete the table
see the attached picture.

Part b)
Number of students who do not like soccer = 20
Number of students who do not like volleyball = 55
This is also include 5 students who do not like both games.
So
number of students who do not like either soccer or volleyball
= 20 + 55 - 5 = 70 students

Percentage of students who do not like either soccer or volleyball
= 70/100 = 70 %

the answer part b) is
70%

Part c)
The survey reveals a greater dislike for volleyball.
80 students like soccer and only 45 students like volleyball.
Only 20 students do not like soccer, while 55 students do not like volleyball.

the answer part c) is
This shows a greater dislike for volleyball as compared to soccer.

4 0

3 years ago

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PLEASE HELP ASAP..! I REALLY NEED IT

SpyIntel [72]

Answer:

lINEAR

Step-by-step explanation:

4 0

2 years ago

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