Question

An 8×8 chessboard has a square cell (or box, like square a1) which measures η inches on one side.

Complex numbers
asked 2021-07-06

An \(8\times8\) chessboard has a square cell (or box, like square a1) which measures \(\beta\) inches on one side.

Express the two possible moves of your knight in vector form with units in inches.

What are the distances of each possible move from your original position in inches?

What are their angles from the horizontal (x-axis)?

Answers (1)

2021-07-22

This is applicable for every \(n\times n\) square board.

The total number of squares for \(n\times n\) square board can be calculated as

\(1^{2}+2^{2}+3^{2}+\cdots+n^{2}\)

So for a Chess Board with \(8\times8\) squares total no.of squares

\(= 1^{2}+2^{2}+3^{2}+\cdots+8^{2} = 204\)

Thus there are 204 Squares in a \(8\times8\) Chess Board.

0

expert advice

Need a better answer?

Relevant Questions

asked 2021-04-17
Common salt, NaCl, has a density of 2.165 \(\displaystyle\frac{{g}}{{c}}{m}^{{3}}\). The molecular weight of NaCl is 58.44. Estimate the distance between nearest neighbor Na and Cl ions. (Hint: each ion can be considered to have one cube or cell of side s (our unknown) extending out from it)
asked 2021-07-02
An investor plans to put $50,000 in one of four investments. The return on each investment depends on whether next year’s economy is strong or weak. The following table summarizes the possible payoffs, in dollars, for the four investments.
Certificate of deposit
Office complex
Land speculation
Technical school
amp; Strong amp;6,000 amp;15,000 amp;33,000 amp;5,500
amp; Weak amp;6,000 amp;5,000 amp;−17,000 amp;10,000
Let V, W, X, and Y denote the payoffs for the certificate of deposit, office complex, land speculation, and technical school, respectively. Then V, W, X, and Y are random variables. Assume that next year’s economy has a 40% chance of being strong and a 60% chance of being weak. a. Find the probability distribution of each random variable V, W, X, and Y. b. Determine the expected value of each random variable. c. Which investment has the best expected payoff? the worst? d. Which investment would you select? Explain.
asked 2021-05-20
Assume that a ball of charged particles has a uniformly distributednegative charge density except for a narrow radial tunnel throughits center, from the surface on one side to the surface on the opposite side. Also assume that we can position a proton any where along the tunnel or outside the ball. Let \(\displaystyle{F}_{{R}}\) be the magnitude of the electrostatic force on the proton when it islocated at the ball's surface, at radius R. As a multiple ofR, how far from the surface is there a point where the forcemagnitude is 0.44FR if we move the proton(a) away from the ball and (b) into the tunnel?
asked 2021-06-24
Marilda has a block of modeling clay that is 8 inches by 5 inches by 3 inches. She is experimenting with different shapes that can be made from the clay. Give your answers to the nearest tenth. Suppose Marilda wants to make a square pyramid with a 6 by 6 in. base. How tall would it be?
...