What’s the measure of angle B? It’s not 64.

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

3 years ago

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What is the purpose of scientific notation? How is scientific notation represented? Explain.

Anit [1.1K]

Answer:

Step-by-step explanation: The purpose of scientific notation is to make the numbers and quantities used easier to comprehend, to read and to write.

Express both numbers with the same power of ten.

Add the base numbers.

Bring the power of ten down to represent the new power of ten for the sum.

Simplify so that the base number is between 1 and 10.

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What's 17 times 1764

Gnoma [55]

Answer:

1764 x 17 = 29,988

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3 years ago

Which questions best describes: A tire manufacturer has a 60,000 mile warranty for tread life. The manufacturer considers the ov

seropon [69]

This question is incomplete because the answer choices were not provided. The complete question was obtained from google as:

A tire manufacturer has a 60,000 mile warranty for tread life. The manufacturer considers the overall tire quality to be acceptable if less than 5% are worn out at 60,000 miles. The manufacturer tests 250 tires that have been used for 60,000 miles. They find that 3.6% of them are worn out. With this data, we test the following hypotheses.

H0: The proportion of tires that are worn out after 60,000 miles is equal to 0.05.

Ha: The proportion of tires that are worn out after 60,000 miles is less than 0.05.

In order to assess the evidence, which question best describes what we need to determine?

a. If we examine a sample of tires used for 60,000 miles and determine the proportion that are worn out, how likely is that proportion to be 3.6% or less?

b. If we examine the proportion of worn out tires in the population of tires used for 60,000 miles, how likely is that proportion to be 5%?

c. If we examine the proportion of worn out tires in the population of tires used for 60,000 miles, how likely is that proportion to be less than 5%?

d. If we examine the proportion of worn out tires in the population of tires used for 60,000 miles, how likely is that proportion to be 3.6%?

e. If we examine a sample of tires used for 60,000 miles and determine the proportion that are worn out, how likely is that proportion to be less than 5%?

Answer:

Option A is the correct question - If we examine a sample of tires used for 60,000 miles and determine the proportion that is worn out, how likely is that proportion to be 3.6% or less?

Step-by-step explanation:

The correct question that describes what needs to be determined is expressed in option A as this will give us p-value and we will guide us in deciding whether to keep or reject the null hypothesis

Thus option A is the correct question - If we examine a sample of tires used for 60,000 miles and determine the proportion that is worn out, how likely is that proportion to be 3.6% or less?

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3 years ago

Slope is 8: y-intercept is -7

erma4kov [3.2K]

Answer:

If you are looking for the coordinates they land on it would be (1,1).

Step-by-step explanation:

If the slope is 8 that would be 8/1. So first you start of at -7 on the y-axis then you move upwards 8 spaces so that your new y-axis is 1, then you move right 1 so that your new x-axis is 1.

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3 years ago