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bogdanovich [222]
3 years ago
15

A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess

board. On the second square the king would place to grasowe
on the third square four grains of wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining squares how many of
should be placed on square 13? Also find the total number of grains of wheat on the board at this time and the total weight in pounds. Assume that each grant what we 7000 pound)
How many grains of wheat should be placed on square 13?
grains​
Mathematics
1 answer:
Ivahew [28]3 years ago
8 0

Answer:

1. 65536

2. 458752000

Step-by-step explanation:

2 to the power of 16 is 65536

458752000=65536*7000

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Find the number b such that the line y = b divides the region bounded by the curves y = 25x2 and y = 1 into two regions with equ
Dennis_Churaev [7]

Answer:

y=1/∛4 divides the area in half

Step-by-step explanation:

since the minimum value of x² is 0 (for x=0 ) and for y=1

1 = 25*x² → x= ±√(1/25) = ±1/5

then the total area between y=1  and y = 25*x²  is bounded to  x=±1/5 and y=0 . Since there is a direct relationship between x and y , we can find the value of x=a that divides the region in 2 of the same area. thus

Area below x=C = Area above x=C

Area below x=C = Total area -  Area below x=C

2*Area below x=C = Total area

Area below x=C = Total area /2

∫ 25*x² dx from x=c to x=-c =  1/2 ∫ 25*x² dx from x=1/5  to x=-1/5

25*[c³/3 - (-c)³/3] = 25/2 * [(1/5)³/3 - (-1/5)³/3]

2*c³/3 = (1/5)³/3

c = 1/(5*∛2)

thus

y=25* x²  = 25*[1/(5*∛2)]² = 1/∛4

thus the line y=1/∛4 divides the area in half

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