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SashulF [63]
2 years ago
15

Round 1627187 to the nearest ten?

Mathematics
2 answers:
Eduardwww [97]2 years ago
7 0

Answer:

1627190

Step-by-step explanation:

(see attached for reference)

Given the number 1627187, we can see that the number in the tens place is the number 8.  

How we round this depends on the number immediately to the right of this number. (i.e the digit in the ones place)

Case 1: If the digit in the ones place is less less than 5, then the number in the tens place remains the same and replace all the digits to its right with zeros

Case 2: If the digit in the ones places is 5 or greater, then we increase the digit in the tens place and replace all the digits to its right with zeros.

In our case, the digit in the ones places is 7, this greater than 5, hence according to Case 2 above, we increase the digit in the tens place by one (from 8 to 9) and replace all the digits to its right by zeros giving us:

1627190

n200080 [17]2 years ago
4 0

Answer:

1627190 is your answer. Have a nice day!

Step-by-step explanation:

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Answer:

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Part B: From 2 to 4 seconds, the height of the water balloon stays the same at 75 feet, therefore the water balloon's height is the same during the interval [2,4] From 10 to 12 seconds, the height of the water balloon stays the same at 0 feet, therefore the water balloon's height is the same during the interval [10,12] From 12 to 14 seconds, the height of the water balloon stays the same at 0 feet, therefore the water balloon's height is the same during the interval [12,14] 

Part C: The interval, [4,6] of the domain is when the water ballon's height decreases the fastest. The interval [4,6] decreases by 35 feet. The two other intervals that decrease are [6,8] and [8,10] which both have the same slope. They decrease by 20 feet. Therefore, this helps us conclude that the interval [4,6] decreases the fastest because 35 feet is a more significant decrease than 20 feet. 

Part D: I predict that the height of the water balloon at 16 seconds is 0 feet. This is because at 10-14 seconds, the water balloon's height is 0 feet. In read-world situations, if the water balloon is on the ground which is 0 feet, it stays on the ground due to gravity. 

Step-by-step explanation:

I hope this helps! I also do not know if it is all correct but I did research and everything so hopefully it is correct! Good luck!

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So we expect a general solution of the form

h_n=c_1(-1)^n+(c_2+c_3n+c_4n^2)2^n

With h_0=0,h_1=1,h_2=1,h_3=2, we get four equations in four unknowns:

\begin{cases}c_1+c_2=0\\-c_1+2c_2+2c_3+2c_4=1\\c_1+4c_2+8c_3+16c_4=1\\-c_1+8c_2+24c_3+72c_4=2\end{cases}\implies c_1=-\dfrac8{27},c_2=\dfrac8{27},c_3=\dfrac7{72},c_4=-\dfrac1{24}

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h_n=-\dfrac8{27}(-1)^n+\left(\dfrac8{27}+\dfrac{7n}{72}-\dfrac{n^2}{24}\right)2^n

(b) Let G(x)=\displaystyle\sum_{n\ge0}h_nx^n be the generating function for h_n. Multiply both sides of the recurrence by x^n and sum over all n\ge4.

\displaystyle\sum_{n\ge4}h_nx^n=5\sum_{n\ge4}h_{n-1}x^n-6\sum_{n\ge4}h_{n-2}x^n-4\sum_{n\ge4}h_{n-3}x^n+8\sum_{n\ge4}h_{n-4}x^n
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From here you would write each term as a power series (easy enough, since they're all geometric or derived from a geometric series), combine the series into one, and the solution to the recurrence will be the coefficient of x^n, ideally matching the solution found in part (a).
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