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Leni [432]
3 years ago
11

A chessboard has 64 squares. George places 1 grain of rice on the first square, 2 grains on the second square, 4 grains on the t

hird square, 8 grains on the fourth square, and so on, until he has placed grains of rice on 10 squares.
Once George has put rice on the 10th square, he has placed a total of _____ grains of rice on the chess board.
Mathematics
2 answers:
slega [8]3 years ago
7 0

Answer:

1,2,4,8,16,32,64,128,256,512

(2048 experience)

1023 grains of rice if you add it all up

Step-by-step explanation:

Nonamiya [84]3 years ago
6 0

Hey there! I'm happy to help out!

As you can see, our number keeps on doubling. It's like 2×2×2×2.... so on and so forth. Whenever we multiply a number by itself, we can model it as an exponent, so if we had 2², it is two twos being multiplied, and 2×2=4. If it was 2³, it would be 2×2×2=8.

However, we have a one. This signifies a starting point and exponents have our back. Anything to the 0th power is always equal to one! So, this situation would look something like this:

2^0, 2^1, 2^2, 2^3,2^4,... etc.

So, for the second square, we are going to the first power. For the fourth square it's going to the third power. Therefore, the 10th square will be the 9th power!

2^9= 2×2×2×2×2×2×2×2×2= 512

However, we want to find how much he has done in total! So, let's find how much he did on the other squares!

2^8= 256

2^7=128

2^6=64

2^5=32

2^4=16

2³=8

2²=4

2^1=2

2^0=1

Now, we add these all up to find the total grains of rice!

512+256+64+32+16+8+4+2+1=895

Therefore, George has placed a total of 895 grains of rice on the chess board.

I hope that this helps! Have a wonderful day!

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An object is heated to 100°. It is left to cool in a room that
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Answer:

Step-by-step explanation:

Use Newton's Law of Cooling for this one.  It involves natural logs and being able to solve equations that require natural logs.  The formula is as follows:

T(t)=T_{1}+(T_{0}-T_{1})e^{kt} where

T(t) is the temp at time t

T₁ is the enviornmental temp

T₀ is the initial temp

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t is the time (here, it's in minutes)

If we are looking first for the temp after 20 minutes, we have to solve for the k value.  That's what we will do first, given the info that we have:

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Filling in to solve for k:

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Since you're learning logs, I'm assuming that you know that a natural log and Euler's number, e, "undo" each other (just like taking the square root of something squared).  That gives us:

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Divide both sides by 5 to get that

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Now that we have a value for k, we can sub that in to solve for T(20):

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T(20) = 30 + 18.22157435 so

T(20) = 48.2°

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T(t) = 35

T₁ = 30

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k = -.0672944473

t = ?

35=30+100-30)e^{-.0672944473t} which simplifies to

5=70e^{-.0672944473t}

Now divide both sides by 70 and take the natural log of both sides:

ln(\frac{5}{70})=ln(e^{-.0672944473t}) which simplifies to

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Divide to get

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