Translate to an equation, then solve
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Answer:
Total weight of the wheat placed on 45th square will be =
Step-by-step explanation:
King rewarded the inventor of chess by giving grain of wheat on every square of the chess board. He places one grain of wheat on first square, 2 on second, 4 on 3rd, 8 on 4th and so on.
In fact he places grains of wheat in a progression S = 1, 2, 4, 8, 16.........n terms where value of n is 64.
We can rewrite the progression as S = 2°, 2, 2², 2³,.........n terms (n = 64)
In a geometric progression we know the nth term =
where a = first term of the series, r = common ratio, n = number of terms
Now we have to calculate the weight of all wheat placed on 45th square.
So we will put the values in the given formula 45th term =
=
=
Then the weight of wheat will be = =
<u>Answer: </u>
sec squared 55 – tan squared 55 = 1
<u>Explanation:</u>
Given, sec square 55 – tan squared 55
We know that,
And,
where Ө is the angle
Substituting the values
Solving,
According to Pythagoras theorem,
Putting this in the equation;
squared 55 - tan squared 55 =
Therefore, sec squared 55 – tan squared 55 = 1