3 ft 10 ft Perimeter: Area:
1 answer:
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Let . Then differentiating, we get
We approximate at
with the tangent line,
The -intercept for this approximation will be our next approximation for the root,
Repeat this process. Approximate at
.
Then
Once more. Approximate at
.
Then
Compare this to the actual root of , which is approximately <u>1.76929</u>2354, matching up to the first 5 digits after the decimal place.
Move the decimal to the right (you go to the right since the exponent is positive, if the exponent was negative then you would move left) seven times, giving you 9,300,000 miles (for Earth). You then do the same with the next equation, giving you 140,000,000 miles (for Mars).
Finally, to find the official number of miles, you simply work the equation 140,000,000 - 9,300,000 .. giving you 130,700,000 miles.
If your teacher wants you to put it back into exponential form, then you first make the number into a decimal that is greater than one and less than ten.
1.30700000
Then, what you want to do is count all of the zeros as a single exponent, giving you 5, but we're not done yet. To get the correct answer, you have to also count the numbers until you reach the decimal. Remember to take out the zeros, because they're not really necessary anymore!
1.307×