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DENIUS [597]
3 years ago
13

Complete the recursive formula of the arithmetic sequence 14, 30, 46, 62, ....

Mathematics
1 answer:
Sauron [17]3 years ago
5 0

Answer:

They are adding 16 to the number each time. So the next number in the sequence would be 78.

Step-by-step explanation:

d(1) = 14

d(n) = d (n-1) + 16

14 + 16 = 30

30 + 16 = 46

46 + 16 = 62

62 + 16 = 78 and so on...

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Solve the following ODE's: c) y* - 9y' + 18y = t^2
Nastasia [14]

Answer:

y = C_1e^{3t}+C_2e^{6t} + \dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})

Step-by-step explanation:

y''- 9 y' + 18 y = t²

solution of ordinary differential equation

using characteristics equation

m² - 9 m + 18 = 0

m² - 3 m - 6 m+ 18 = 0

(m-3)(m-6) = 0

m = 3,6

C.F. = C_1e^{3t}+C_2e^{6t}

now calculating P.I.

P.I. = \frac{t^2}{D^2 - 9D +18}

P.I. = \dfrac{t^2}{(D-3)(D-6)}\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(1-\frac{D}{6})^{-1}(t^2)\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(1+\frac{D}{6}+\frac{D^2}{36}+....)(t^2)\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(t^2+\frac{2t}{6} + \frac{2}{36})\\P.I. =\dfrac{1}{18}(1+\frac{D}{3}+\frac{D^2}{9}+....)(t^2+\frac{2t}{6} + \frac{2}{36})\\P.I. =\dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})

hence the complete solution

y = C.F. + P.I.

y = C_1e^{3t}+C_2e^{6t} + \dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})

7 0
2 years ago
5 times 5 grggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggrfgrrrrrrrrrrrrrrrrrrrrrrr
Bezzdna [24]

Answer:

25

Step-by-step explanation:

5 0
2 years ago
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Rationalize the denominator and simplify.<br><br> 5 / 4 - sqrt 3
Whitepunk [10]

Answer:\frac{20+5\sqrt[]{3} }{13}

Step-by-step explanation:

4 0
3 years ago
I’m about to take the test please hurry! I will give brianliest.
scZoUnD [109]

Answer:

i think its 358

Step-by-step explanation:

5 0
2 years ago
HELP ME PLEASE ASAP
Paha777 [63]

Answer:

33

Step-by-step explanation:

angles on a straight line sum up to 180°

104+x+x+10=180

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3 0
3 years ago
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