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3 years ago

7

Divide each of the following by 10, 100, and 1000: 67.8, 456.8, 531.20.

1 answer:

Inessa05 [86]3 years ago

6 0

67.8: 6.78, 0.678, 0.0677
456.8: 45.68, 4.568, 0.4568
531.20: 53.12, 5.312, 0.5312
The pattern here is that the number of 0s there are in the digit of whatever you are dividing by, that is how many places you move the decimal place to the right. For example, by dividing 67.8 by 100, the decimal place has been moved 2 places to the right, resulting in the number 0.678

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If a,b,c are all non-zero numbers and a+b+c=0, prove that

Butoxors [25]

<em>Given - a+b+c = 0</em>

<em>To prove that- </em>

<em>a²/bc + b²/ac + c²/ab = 3</em>

<em>Now we know that</em>

<em>when x+y+z = 0,</em>

<em>then x³+y³+z³ = 3xyz</em>

<em>that means</em>

<em> (x³+y³+z³)/xyz = 3 ---- eq 1)</em>

<em>Lets solve for LHS</em>

<em>LHS = a²/bc + b²/ac + c²/ab</em>

<em>we can write it as LHS = a³/abc + b³/abc + c</em><em>³</em><em>/abc</em>

<em>by multiplying missing denominators,</em>

<em>now take common abc from denominator and you'll get,</em>

<em>LHS = (a³+b³+c³)/abc --- eq (2)</em>

<em>Comparing one and two we can say that</em>

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vazorg [7]

Answer:

Tap A will take 2 hours and tap B will take 6 hours to fill the tank when turned on alone.

Step-by-step explanation:

Let tap B fills the pool alone in the time = x hours

So in one hour part of pool will be filled = $\frac{1}{x}$

Another tap A when turned on, it takes time to fill the pool = x-5 hours

So in one hour part of the same pool filled = $\frac{1}{x-5}$

Now both the taps A and B are turned on then time taken to fill the pool = 3 hours.

Part of the pool filled in one hour by both the taps = $\frac{1}{3}$

Now we form an equation

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$\frac{x-5+1}{x(x-5)}=\frac{1}{3}$

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Time taken by tap A = 6 - 4 = 2 hours.

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