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Anuta_ua [19.1K]

2 years ago

11

What is the slope of the line that passes through the points (-10, -4)(−10,−4) and (10, -29) ?(10,−29)? Write your answer in sim

plest form

1 answer:

irga5000 [103]2 years ago

3 0

Answer:

The answer is -1.25

Hope that helps. x

Step-by-step explanation:

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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

Read 2 more answers

Mr. Jackson invested a sum of money at 6% per year, and 3 times as much at 4%

bogdanovich [222]

Mr. Jackson invested $800 at 6% per year and $ 2400 at 4 % per year

<h3><u>Solution:</u></h3>

Mr. Jackson invested a sum of money at 6% per year, and 3 times as much at 4% per year.

Let the sum invested be ‘a’ and ‘3a’ at 6% per year and 4 % per year respectively

Also, his annual return totaled $144

We can form following equation on the basis of question:-

$\begin{array}{l}{\text { Then, } \frac{a \times 6 \times 1}{100}+\frac{3 a \times 4 \times 1}{100}=\$ 144} \\\\ {\frac{6 a}{100}+\frac{12 a}{100}=144} \\\\ {\frac{6 a+12 a}{100}=144} \\\\ {\frac{18 a}{100}=144} \\\\ {18 a=14400} \\\\ {a=14400 \div 18}\end{array}$

a = $800

The amount of money invested at 6% = a = 800

The amount of money invested at 4 % = 3a = 3(800) = 2400

So, the amount of money invested at 6% is $800 and the amount of money invested at 4% is $ 2400

4 0

2 years ago

NOTE: Angles not necessarily drawn to scale.

Alina [70]

Answer:

x = 56°

Step-by-step explanation:

DAF is a straight line so it has a measurement of 180°

180° - 64° - 60° = x

x = 56°

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

7 0

2 years ago

Solve The Following Expression..<br><br>#No Spam..

Rainbow [258]

$\\ \sf\longmapsto \dfrac{x+0.25}{3}-0.5=x$

$\\ \sf\longmapsto \dfrac{x+0.25-1.5}{3}=x$

$\\ \sf\longmapsto x-1.25=3x$

$\\ \sf\longmapsto x-3x=1.25$

$\\ \sf\longmapsto -2x=1.25$

$\\ \sf\longmapsto x=\dfrac{1.25}{-2}=-0.625$

4 0

2 years ago

Read 2 more answers

Class is made up of 8 boys and 12 girls. Half of the girls wear glasses. A student is selected at random from the class. What is

Norma-Jean [14]

8/20(2/5) are boys
12/20(3/5) are girls
6/20(3/10) are girls with glasses
You have a 3/10 chance of the student is being a girl with glasses.

5 0

3 years ago

Read 2 more answers