the radii of earth n pluto are 6,371 kilometers and 1,161 kilometers, respectively. approximately how many spheres the size of p
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Answer: 31.25%
Step-by-step explanation: To answer the question <em>what percent of 80 is 25</em>, we translate the question into an equation.
So we have "what percent" that's x, "of 80" means times 80, "is 25" = 25.
Now to solve for <em>x</em>, since <em>x</em> is being multiplied by 80, we need to divide by 80 on both sides of the equation. On the left side of the equation the 80's cancel and we have <em>x</em> and on the right side of the equation, we have 25 ÷ 80 which gives us 0<em>.</em>3125. Now, remember that we want to right our answer as a percent so to write 0.3125 as a percent, we move the decimal point 2 places to the right and we get 31.25%.
Therefore, 31.25% of 80 is 25.
One way to do it is with calculus. The distance between any point 
on the line to the origin is given by
Now, both
and 
attain their respective extrema at the same critical points, so we can work with the latter and apply the derivative test to that.
Solving for
, you find a critical point of 
.
Next, check the concavity of the squared distance to verify that a minimum occurs at this value. If the second derivative is positive, then the critical point is the site of a minimum.
You have
so indeed, a minimum occurs at.
The minimum distance is then
Now, both
Solving for
Next, check the concavity of the squared distance to verify that a minimum occurs at this value. If the second derivative is positive, then the critical point is the site of a minimum.
You have
so indeed, a minimum occurs at
The minimum distance is then