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4 years ago

11

How do I know if a sequence is arithmetic ,geometric ,or neither

1 answer:

Mekhanik [1.2K]4 years ago

8 0

Answer:

Step-by-step explanation:

Let's assume that you have a sequence written out in always increasing or always decreasing order.

If each new term is equal to the previous term, plus a certain constant, then the sequence is arithmetic. Example: 2, 7, 12, 17, 22, ... (the additive constant is 5).

If each new term is equal to the previous term, multiplied by a certain constant, then the sequence is geometric. Example: 2, 8, 32, 128, ... (the multiplicative constant is 4).

If the spacing between terms is not a constant, then the sequence is neither arith. nor geom.

If all new adjacent terms are not found by multiplying the previous term by the same constant, the sequence is not geometric (and not arithmetic).

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c2*sin(wt)+c1*cos(wt)= A*Sin(wt+phi), where c2=Acos(Phi) and c1=Asin(Phi). They ask me to find the amplitude of the function 2 s

Iteru [2.4K]

The amplitude of $A\sin(\omega t+\phi)$ is the absolute value of $A$ . So first you need to condense the given function into one sine expression.

Recall that

$A\sin(\omega t+\phi)=A\sin(\omega t)\cos\phi+A\cos(\omega t)\sin\phi$

so you need to choose $\phi$ and $\omega$ accordingly.

If we line up the terms of the given function with the expanded one above, we should have

$2\sin(4\pi t)+5\cos(4\pi t)\implies\begin{cases}A\cos\phi=2\\A\sin\phi=5\\\omega=4\pi\end{cases}$

Now, using the Pythagorean identity,

$(A\sin\phi)^2+(A\cos\phi)^2=2^2+5^2\implies A^2=29\implies A=\pm\sqrt{29}$

so the amplitude is √29.

Just for completeness, we also get

$\tan\phi=\dfrac{\sin\phi}{\cos\phi}=\dfrac52\implies\phi=\tan^{-1}\left(\dfrac52\right)+n\pi$

where $n$ is any integer.

7 0

3 years ago

2) Macle grew from 5 feet to 5.5 feet. What was the percent change in her

givi [52]

Answer:

The answer is C.

Step-by-step explanation:

5×1.1=5.5.

8 0

3 years ago

many years ago, some doctors administered medication to patients themselves, as opposed to using a pharmacist. One curious yet u

IrinaVladis [17]

Answer:

They are now dead

Step-by-step explanation:

Jake Paul

5 0

3 years ago

Which statement is true regarding the graphed functions? Can someone help me out?

lozanna [386]

f(2) = 0

g(2) = 0

you can see in graph f and g are 0 at x= 2 and x = -2 respectively

6 0

4 years ago

How do you work out 2/3 of 15? 4/5? of 20? 1/5 of 85? 1/8 of 96 2/5 of 65? 3/5 135? 4/5 of 200? 3/10 of 30? 3/10 of 25?

solniwko [45]

Answer:

Take your numerator times the whole number, then divide by the denominator. For example,

2x15= 30

30/3= 10

2/3 of 15 would be 10

8 0

3 years ago