What is the 10th 53rd & 200th Figure if the constant difference is +4

Mathematics

1 answer:

natulia [17]3 years ago

7 0

Answer:

Step-by-step explanation:

Assuming we are doing an arithmetic sequence

It depends on where you start

If the first term is a₁ and the term number is n

each subsequent term is

aₙ = a₁ + 4(n - 1)

a₁₀ = a₁ + 4(10 - 1) = a₁ + 36

a₅₃ = a₁ + 4(53 - 1) = a₁ + 208

a₂₀₀ = a₁ + 4(200 - 1) = a₁ + 796

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$y=2\text{cos}((\frac{2\pi}{3})t)$

Step-by-step explanation:

We have been given that an object oscillates 4 feet from its minimum height to its maximum height. The object is back at the maximum height every 3 seconds. We are asked to find the cosine function that can be used to model the height of the object.

We know that standard form of cosine function is $y = A\cdot \text{cos}(Bt-C)+D$ , where,

|A| = Amplitude,

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C = Phase shift,

D = Vertical shift.

Since distance between maximum and minimum is 4, therefore, amplitude will be half of it, that is, $A = 2$ .

Since objects gets back to its maximum value in every 3 seconds, therefore, period of the function is 3 seconds. We know that period is given by $\frac{2\pi}{|B|}$ , therefore, we can write $\frac{2\pi}{|B|}=3$ , therefore, $B = \frac{2\pi}{3}$ .