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]2 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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2d +9= 19<br> The solution is d =

Novosadov [1.4K]

${\huge{\boxed{\mathbb{QUESTION}}}$

2d +9= 19

The solution is d =

${\huge{\boxed{\mathbb{ANSWER\:WITH\:EXPLANATION}}}$

Hello there, first we can place our equation, which you have stated

$2d+9=19$ , this algebra, in algebra we want to find the exact value of the variable, or have the variable on one side of the equation.

First we can subtract $9$ with both sides of the equation giving us the result of $2d=10$ , this can also be represented as $2\cdot d=10$ , now just divide both sides of the equation by $2$ , our answer is $d=5$ .