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Darina [25.2K]
3 years ago
5

Use inductive reasoning to describe the pattern. then find the next two numbers in the pattern. –3, 9, –27, 81, . . .

Mathematics
2 answers:
erastovalidia [21]3 years ago
6 0
Tmes -3 each times so next 2 numbers are -243 then 729
miv72 [106K]3 years ago
5 0

Answer:

-243 and 729.

Step-by-step explanation:

We have been given a pattern –3, 9, –27, 81, . . . We are asked to find the next two numbers of our given pattern.

We can see that our given pattern is in form of geometric sequence. We need to find the common ratio of our given sequence by dividing any term of sequence by its previous term.

r=\frac{9}{-3}=-\frac{9}{3}=-3.

So the next number of our given term would be 81\times -3=-243.

The next number would be  -243\times -3=729.

Therefore, the next two numbers of our given sequence are -243 and 729.

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Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 73 and 9
Naddika [18.5K]

Answer: After about 9.03 hours the temperature first reach 82 degrees.

Step-by-step explanation:

The sinusoidal function is given by :

y=A\sin[\omega(x-\alpha)]+C

where, A =  amplitude; \omega=\dfrac{2\pi}{period} ,  α= phase shift on the Y-axis and C = midline.

As per given,

Average daily temperature= C=\dfrac{73+97}{2}=85   [midline is average of upper and lower limit.]

A=  97-85 = 12

Phase shift: \alpha=10

Period = 24 hours;

\omega=\dfrac{2\pi}{24}=\dfrac{\pi}{12}

Substitute all values in sinusoidal function, we get

y=12\sin[\dfrac{\pi}{12}(x-10)]+85

Put y= 82, we get

82=12\sin[\dfrac{\pi}{12}(x-10)]+85\\\\\Rightarrow\ -3= 12\sin[\dfrac{\pi}{12}(x-10)]\\\\=\dfrac{-1}{4}= \sin[\dfrac{\pi}{12}(x-10)]\\\\\Rightarrow\ \dfrac{\pi}{12}(x-10)=\sin^{-1}(\dfrac{-1}{4})\\\\\Rightarrow\ x-10=\dfrac{12}{\pi}(\sin^{-1}(\dfrac{-1}{4}))\\\\\Rightarrow\ x=\dfrac{12}{\pi}(\sin^{-1}(\dfrac{-1}{4}))+10\\\Rightarrow\ x\approx9.03

Hence, After about 9.03 hours the temperature first reach 82 degrees.

3 0
3 years ago
ABC is an isosceles triangle with
12345 [234]
Https://brainly.in/question/16189033?referrer=searchResults
5 0
2 years ago
Helppp this is chemistry not math though
Scorpion4ik [409]

Answer:

It is balance she need to use. Answer is B.

7 0
3 years ago
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Select the slope-intercept form of an equation for a line with y-intercept -2 and slope 6.<br>​
ozzi

Answer:

y = 6x - 2

Step-by-step explanation:

slope intercept form is y = mx + b

m = slope

b = y-intercept

They give us the slope (m) which is 6 and the y-intercept (b) which is -2. PLug it into the equation

y = mx + b

y = 6x - 2

3 0
3 years ago
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sergey [27]
The answer is v=25.
5 0
3 years ago
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