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PtichkaEL [24]
3 years ago
6

What is the rule for the following sequence: 2, 9, 21, 65

Mathematics
1 answer:
Helga [31]3 years ago
5 0

There is no common ratio or common difference. The first three terms increases more slowly than a cubic, but the last three increase more quickly than the cube of n. The pattern is not obvious to me. When the sequence is cast in recursive terms, you get

... a[n] = (48/13)a[n-2] + (59/39)a[n-1] . . . . a[1] = 2, a[2] = 9

The next term using this rule is 174 34/39, not an integer.

The coefficients p and q for a[n-2] and a[n-1] can be found from

2p+9q=21\\9p+21q=65

_____

Any sequence of 4 numbers can be matched by a polynomial of degree 3 or less. Here, a calculator's polynomial regression function tells us the rule could be

... a[n] = 4.5n³ -24.5n² +49n -27

Using this rule, the next two terms are 168 and 357.

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Help! i will give brainliest!!!
melisa1 [442]
I am assuming the angle is given in degrees.

Answer:

12.71

or in terms of Pi

182π / 45

Steps:
Formula for the arc length:
L = 2πr(θ/360)
We are given r and θ. Let’s solve for L.

L = 2* π * 8 * (92/360)

The answer is 12.71

or in terms of Pi
182π / 45
8 0
2 years ago
A 45 foot ladder is leaning against a building. If the bottom of the ladder is 27 feet from the base of the building, how tall i
taurus [48]

Answer:

The height of building to the nearest foot is h = 36 foot

Step-by-step explanation:

We have given,

Length of ladder leaning against a building, l = 45 foot

Bottom length between ladder and the building , b = 27

Now, we need to find the height of building to the nearest foot.

Let the height of building be h.

Using Pythagoras theorem,

l^{2} = b^{2} +h^{2}

Here, l = 45 , b = 27 and h =?

So,

45^{2} = 27^{2} +h^{2}

h² = 45² - 27²

h = √(45² - 27²)

h = 36

The height of building to the nearest foot is h = 36 foot

8 0
3 years ago
Read 2 more answers
A new episode of Charlie's favorite TV series will be aired 25 minutes after Charlie gets home from school. Which method should
Tresset [83]

Answer:

Charlie should use a stopwatch with minutes and seconds

Step-by-step explanation:

charlie should not count in his head as it is not accurate, he could count too fast or slow

Charlie should not look at that clock and the seconds will affect the 25 minutes, whether it be less or more

Charlie should not use an hourglass as he might flip it over too soon or quick and it's not very accurate

therefore using the stopwatch allows him to accurately and fairly keep track of the exact time

4 0
3 years ago
Describe and correct the error in writing the phrase as an expression?
lesantik [10]

Answer:

12 < x

Step-by-step explanation:

In writing 12 less than a number x, the expression, 12 - x is wrong because "less than" is not the same thing as "minus" (-). Rather, the sign, "<" should have been used as follows:

12 < x.

4 0
2 years ago
A student leaving school walks 2.8 km north and then walks 1.2 km south. What is
vova2212 [387]

Answer: 1.6km

Step-by-step explanation: 2.8km - 1.2km

The student is still north from school.

I hope this answer helped! :)

4 0
3 years ago
Read 2 more answers
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