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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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Step-by-step explanation:

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3 years ago
Help please, try to explain it in steps for me if u can't that's fine, ty!
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Answer:

B

Step-by-step explanation:

We are given that Expression One is:

2\cdot 10^x

And Expression Two is:

4\cdot 10^{x+y}

We are given that the value of Expression Two is 20,000 times greater than the value of Expression One. And we want to find the value of <em>y.</em> In other words:

4\cdot 10^{x+y}=20000(2\cdot 10^x)

We can divide both sides by four:

10^{x+y}=10000\cdot 10^x

Recall that:

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Therefore:

10^x\cdot 10^y=10000\cdot 10^x

Divide both sides by 10ˣ:

10^y=10000

Solve for <em>y: </em>

<em />\displaystyle y = \log_{10}10000 = 4<em />

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Artist 52 [7]
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