Mikey is reading a 604-page book. He read 148 pages last week. If he reads for x hours at 19 pages per hour, which equation repr
2 answers:
You might be interested in
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 = =
To prove that the diagonals are congruent, you need to formula to compute the distance between two points:
Using that formula, you may prove that , which means that the two diagonals have the same length.
To prove that they are perpendicular, you need the formula to compute the slope of a segment. The slope, knowing the enpoints, is given by
You can use this formula to prove that
In fact, if one slope is the opposite of the reciprocal of the other, the two segments are perpendicular.
Finally, to prove that they bisect each other, you first need to find the point where they meet. First of all, you need to find the line the segments lie on: the formula is
where is one of the points belonging to the line, and you already know how to find the slope. Then, you find the point of intersection, say A, by solving the system involving the two lines:
And use again the formula for the distance between two points to prove that