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2 years ago

7

Find the distance between the pair of points: (4,0) and (2,-1)

1 answer:

Marysya12 [62]2 years ago

6 0

The distance is 2.23606 (2.24 rounded)

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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

(2x-1)^2=<br><br> Some one plz help.....

Arlecino [84]

Answer: 4x^2−4x+1

Step-by-step explanation:

(2x-1)^2

Square of Difference: (a−b)^2=a^2−2ab+b^2.

(2x)^2−2*2x+1

Multiplication Distributive Property: (xy)^a= $x^{a} y^{a}$

2^2x^2−2*2x+1

4x^2−2*2x+1

4x^2−4x+1

Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! As well as a great Valentines Day! :-)

- Cutiepatutie ☺❀❤

3 0

3 years ago

A jar contains chocolate candies. There are 12 red, 17 blue, 5 green and 6 orange. What is the probability of picking either a g

nataly862011 [7]

Answer:

Step-by-step explanation:

If you sum everything, you'll get 50 candies. Now you know that 50 candies is 100%.

Now you'll calculate the probability:

12 on 50 : 24.00 %

17 on 50 : 34.00 %

5 on 50 : 10.00 %

6 on 50 : 12.00 %

Hope I was helpful :)

Edit :

12/50 17/50 6/50 5/50

7 0

3 years ago

Answers plz help. imma fail.

Zarrin [17]

Answer:

Try your best and never give up take a deep breath and focus on it

5 0

3 years ago

Read 2 more answers

HELP, 50 POINTS!!

Contact [7]

Answer:

d. f opens upward with a y-intercept at (0, 2); h opens downward with a y-intercept at (0, -2)

5 0

3 years ago