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miv72 [106K]
3 years ago
15

What is the best value 6 in 567,000

Mathematics
1 answer:
Alja [10]3 years ago
3 0

Answer:

60,000

Step-by-step explanation:

because it is 500,00 + 60,000 = 7,000 + 000 + 00 + 0 = 567,000

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Determine formula of the nth term 2, 6, 12 20 30,42​
nalin [4]

Check the forward differences of the sequence.

If \{a_n\} = \{2,6,12,20,30,42,\ldots\}, then let \{b_n\} be the sequence of first-order differences of \{a_n\}. That is, for n ≥ 1,

b_n = a_{n+1} - a_n

so that \{b_n\} = \{4, 6, 8, 10, 12, \ldots\}.

Let \{c_n\} be the sequence of differences of \{b_n\},

c_n = b_{n+1} - b_n

and we see that this is a constant sequence, \{c_n\} = \{2, 2, 2, 2, \ldots\}. In other words, \{b_n\} is an arithmetic sequence with common difference between terms of 2. That is,

2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2

and we can solve for b_n in terms of b_1=4:

b_{n+1} = b_n + 2

b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2

b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2

and so on down to

b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)

We solve for a_n in the same way.

2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)

Then

a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)

a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))

a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))

and so on down to

a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2

\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}

6 0
2 years ago
Easy question:
Delvig [45]

Answer:

3 hours and 45 minutes

Step-by-step explanation:

let's assume the tank has a volume of x liters.

let's assume the speed of filling it is x/6 liters per hour for A and x/10 liters per hour for B.

the formula to calculate the time is:

time = volume / speed

If the pumps work together, the total speed is x/6 + x/10, which is 16/60 x

So the time this takes is:

time = x / (16/60 x) = 60/16 hours = 3.75 hours = 3 hours and 45 minutes.

8 0
2 years ago
if I have a question on my work that says solve the equation how could I solve this one, (7,-6): m = -4 ..... im not really sure
Nimfa-mama [501]

Answer:

y= -4x+22

Step-by-step explanation:

slope= -4

-6=-4(7)+b

-4x7=-28

-6=-28+b

28-6=22

so the equation would be y= -4x+22

b=y-intercept

mx=slope multiplied by x

6 0
3 years ago
What is the value of x in the figure?<br><br> Enter your answer in the box.<br><br> x =
raketka [301]

Answer:

x=90-22

x=68

as the ray divide the right angle into 2

5 0
3 years ago
can someone help me understand this? The length of the rectangle is two more then its width. the perimeter of the rectangle is 7
Tema [17]

Answer:

length = 24 meters

Step-by-step explanation:

1. l = 2w

2. P = 2l + 2w

P=72

3. 72 = 2l + 2w

4. Substitute w=l/2 to solve for l

72 = 2l + 2(l/2) ---> 72 = 3L - Divide by 3 on both sides

L= 24 meters

4 0
3 years ago
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