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patriot [66]
3 years ago
12

In the top row of an chessboard, Tom writes the values 1, 2, 4, 8, 16, 32, 64, 128. In the leftmost column, Tom writes the value

s 1, 3, 9, 27, 81, 243, 729, 2187. In every other square that doesn't have a number yet, Tom writes the product of the leftmost number in that square's row and the topmost number in that square's column. What is the sum of all the numbers on the chessboard?
Mathematics
1 answer:
solmaris [256]3 years ago
7 0
sum\ of\ the\ values\ in\ the\ top\ row:\\\\S=1+2+4+8+16+32+64+128= \frac{1-2^8}{1-2} =2^8-1=255\\\\ the\ sum\ of\ all\ the\ numbers\ on\ the\ chessboard:\\\\S\cdot1+S\cdot3+S\cdot9+S\cdot27+S\cdot81+S\cdot243+S\cdot729+S\cdot2187=\\\\=S\cdot(1+3+9+27+81+243+729+2187)=255\cdot \frac{1-3^8}{1-3} =\\\\=255\cdot \frac{-6560}{-2} =255\cdot3280=836,400\\\\Ans.\ the\ sum\ of\ all\ the\ numbers\ on\ the\ chessboard\ is\ 836,400
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To find c, you must isolate it.
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5/7c ÷ 5/7 = c

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To divide fractions, follow these steps:
Step 1- Turn the second fraction, 5/7 in this case, into its reciprocal. This means swapping the places of the numerator and denominator.
5/7 reciprocal = 7/5

Step 2- multiply the original first fraction and reciprocal second fraction.
13/14 • 7/5
13 • 7 = 91
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13/14 ÷ 5/7 = 91/70

Step 3- Simplify if possible.
91/70
Since 70 can go into 90, you can turn this into a mixed number.
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Both can be divided by 7.
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So simplified, 91/70 equals 1 and 3/10.
As a decimal, this is 1.3.

So the answer is c = 1.3, or 1 and 3/10.

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