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aev [14]
3 years ago
8

The perfect square game is played as follows: player 1 says a positive integer, then

Mathematics
1 answer:
avanturin [10]3 years ago
6 0

Answer: the number can be 9

Step-by-step explanation:

we want that

n + n - 1 + n-2 + .... + 2 + 1 = X

X must be a perfect square.

And the last number, 1, must be said by player 1, so n must be an odd number.

n + (n - 1) + (n -2) + ... + (n - n + 1) = n*n - (1 + 2 + 3 + .... + n)

and we know that:

(1 + 2 + 3 + 4 + ... + n) = n*(n + 1)/2

So we have:

x = n*n - n*(n + 1)/2 = n*n - n*n/2 - n/2 = n*n/2 - n/2 = n*(n + 1)/2

Now we want to find X such that is a perfect square and n must be an odd integer.

You can start giving different values for n until you reach a value of X that is a perfect square, for example, if you take n = 9, we have X = 36.

and 36 = 6*6

So if player 9, he will win always.

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Write the following equation in logarithmic form <br> a^(4b-6)=3c+d
Tomtit [17]

Hello from MrBillDoesMath!

Answer:  (4b-6) log(a) = log (3c + d)

Discussion:

Take the log of both sides of the equation:


log ( a ^(4b-6))  = log (3c + d)  


As the log functions causes exponents to become multiplexers, this equation is the same as


(4b-6) log(a) = log (3c + d)


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3 0
3 years ago
Joy needs to mix a 20% acid solution with a 60% acid solution to create 100 millileters of a 28% solution. How many millileters
dalvyx [7]

Answer:

Joy must use 80 milliliters of solution at 20% and 20 milliliters of solution at 60%

Step-by-step explanation:

Let

x -----> milliliters of solution at 20%

y -----> milliliters of solution at 60%

we know that

x+y=100 ----> equation A

20\%=20/100=0.20

60\%=60/100=0.60

28\%=28/100=0.28

so

0.20x+0.60y=0.28(x+y)

0.20x+0.60y=0.28(100)

0.20x+0.60y=28 ----> equation B

Solve the system of equations by graphing

Remember that the solution of the system is the intersection point both graphs

The solution is the point (80,20)

see the attached figure

therefore

Joy must use 80 milliliters of solution at 20% and 20 milliliters of solution at 60%

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3 years ago
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