A farmer estimates that he has 9,000 bees producing honey on his farm. The farmer becomes concerned when he realizes the populat
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Answer:
Step-by-step explanation:
<em><u>The correct question is </u></em>
If ABCD is a square and AB = 10, what is the measure of AC? (rounded to the nearest hundredth)
see the attached figure to better understand the problem
we know that
All four sides of the square are congruent and all four interior angles are equal to 90°.
so
AB=BC=CD=AD
In the right triangle ACD
Applying the Pythagorean Theorem
we have that
substitute the given value
First check for the critical points of <em>f</em> by checking where the first-order derivatives vanish.
Notice how the point (1, 2) lies on the line <em>y</em> = 2<em>x</em> ; at this point, we get a value of <em>f</em>(1, 2) = -5 (MIN).
Next, check the points where the boundary lines intersect, which occurs at the points (0, 0), (0, 2), and (1, 2). We already checked the last one. We find <em>f</em>(0, 0) = 1 (MAX) and <em>f</em>(0, 2) = -3.
Now check on the boundary lines themselves. If <em>x</em> = 0, then
which has a maximum value of -3 when <em>y</em> = 2 (so we get the same critical point as before).
If <em>y</em> = 2, then
with a maximum of -5 when <em>x</em> = 1.
If <em>y</em> = 2<em>x</em>, then
with the same maximum of -5 when <em>x</em> = 1.