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aksik [14]
3 years ago
5

Simplify the expression. Write the answer using scientific notation. (4 × 108)2 16 × 1016 1.6 × 1016 8 × 1017 1.6 × 1017

Mathematics
1 answer:
sammy [17]3 years ago
6 0

Answer:

\large\boxed{\bigg(4\times10^8\bigg)^2=1.6\times10^{17}}

Step-by-step explanation:

\text{The sicientific notation:}\ a\times10^k,\ \text{where}\ 1\leq a10\\\\=1.6\times10\times10^{16}\qquad\text{use}\ a^n\times a^m=a^{n+m}\\\\=1.6\times10^{17}

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Let d represent the distance of the destination from the starting point.

After 45 min, Henry has already driven d-68 miles.  After 71 min., he has already driven d-51.5 miles.

So we have 2 points on a straight line:

(45,d-68) and (71,d-51.5).  Let's find the slope of the line thru these 2 points:

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The distance to his destination would be d - (0.635 miles/min)(79 min), or 

d - 50.135 miles.  We don't know how far his destination is from his starting point, so represent that by "d."

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After 71 minutes, he has        d - 51.5 miles to go; and

After 79 minutes, he has         d -  x miles to go.  We need to find x.

Actually, much of this is unnecessary.  Assuming that Henry's speed is 0.635 miles/ min, and knowing that there are 8 minutes between 71 and 79 minutes, we can figure that the distance traveled during those 8 minutes is

(0.635 miles/min)(8 min) = 5.08 miles.  Subtracting thix from 51.5 miles, we conclude that after 79 minutes, Henry has (51.5-5.08), or 46.42, miles left before he reaches his destination.




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