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3 years ago

44 tens is the same as

Mathematics

1 answer:

Lilit [14]3 years ago

8 0

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What is <br>1.63 x 0.98 =

yarga [219]

Answer:

1.5974

Step-by-step explanation:

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3 years ago

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When does it stop being partly cloudy and start being partly sunny?

evablogger [386]

Answer:

50/50

Step-by-step explanation:

50/50

At what point does it stop being partly cloudy and start being partly sunny outside? 50/50, as you'd expect. Partly cloudy - In a forecast, this means that less than half of the day will be cloudy. For a current condition, this means that less than half of the sky is covered by clouds.

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3 years ago

This? .......................................................

adelina 88 [10]

Answer:

109.6

Step-by-step explanation:

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3 years ago

Get brainiest if right?

aev [14]

Answer:

30 mph

Step-by-step explanation:

train stopped after 520 miles

780 miles to go

stopped at 20 hours

stopped for 4 hours

34 hours used up...

26 hours left

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780 miles/26 hrs = 30 m/hr

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3 years ago

Evaluate 1^3 + 2^3 +3^3 +.......+ n^3

Molodets [167]

Notice that

$(n+1)^4-n^4=4n^3+6n^2+4n+1$

so that

$\displaystyle\sum_{i=1}^n((n+1)^4-n^4)=\sum_{i=1}^n(4i^3+6i^2+4i+1)$

We have

$\displaystyle\sum_{i=1}^n((i+1)^4-i^4)=(2^4-1^4)+(3^4-2^4)+(4^4-3^4)+\cdots+((n+1)^4-n^4)$

$\implies\displaystyle\sum_{i=1}^n((i+1)^4-i^4)=(n+1)^4-1$

so that

$\displaystyle(n+1)^4-1=\sum_{i=1}^n(4i^3+6i^2+4i+1)$

You might already know that

$\displaystyle\sum_{i=1}^n1=n$

$\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2$

$\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6$

so from these formulas we get

$\displaystyle(n+1)^4-1=4\sum_{i=1}^ni^3+n(n+1)(2n+1)+2n(n+1)+n$

$\implies\displaystyle\sum_{i=1}^ni^3=\frac{(n+1)^4-1-n(n+1)(2n+1)-2n(n+1)-n}4$

$\implies\boxed{\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4}$

If you don't know the formulas mentioned above:

The first one should be obvious; if you add $n$ copies of 1 together, you end up with $n$ .
The second one is easily derived: If $S=1+2+3+\cdots+n$ , then $S=n+(n-1)+(n-2)+\cdots+1$ , so that $2S=n(n+1)$ or $S=\dfrac{n(n+1)}2$ .
The third can be derived using a similar strategy to the one used here. Consider the expression $(n+1)^3-n^3=3n^2+3n+1$ , and so on.

7 0

4 years ago