We know that
see the picture to better understand the problem
in the right triangle ABC
Applying the Pythagoras Theorem
AB²=BC²+AC²-------> BC²=AB²-AC²
AB=8 ft
AC=4 ft
BC²=8²-4²-----> BC²=48--------> BC=√48-------> BC=6.93 ft
the answer is6.93 ft
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
Since each pound casts $0.58 and the total spent is $2.03, you divide 2.03 by .58 to find the total amount of pounds.
2.03/.58=203/58=3.5
Therefore, Percy bought 3.5 pounds of tomatoes.
It's 14 because when you divide you get 13 with a remainder of 58 which is over half of 99 which means that you round up to 14
