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

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