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Phoenix [80]
3 years ago
8

If I multiply all whole numbers from 1 through 10 what is the largest power of 4 that is a factor of the product?

Mathematics
1 answer:
Oksanka [162]3 years ago
8 0
If we multiply 1 through 10, the mathematical representation of the product would be,
                        P = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10
Getting the factors of each number,
                         P = 1 x 2 x 3 x (2 x 2) x 5 x (3 x 2) x 7 x (2 x 2 x 2) x 9 x (5 x 2)
Then, we take out all the 2's.
                            2 x (2 x 2) x (3 x 2) x (2 x 2 x 2) x (5 x 2)
Combining all the 2's.
                             2^8 x 3 x 5
  2^8 can also be written as (2 x 2)^4. Thus, the answer is 4. 
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1. sin(x+20) = cos(2x+10)<br> 2. sin (2x+14) = cos(x-5)
lakkis [162]

Answer:

x=20°

2.

x=27°

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sin(x+20)=cos (2x+10)

=sin (90-(2x+10))

so x+20=90-(2x+10)

x+20+2x+10=90

3x=90-30

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10+(x÷16)

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Since 10 x 16 / 16 and x/16 have the same denominator, add them by adding their numerators.

10 x 16 + x / 16

Do the multiplications in 10×16+x.

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