AP Calc help

Test Preparation AP Test Preparation
1

<p>I have no idea how to approach this. </p>

<p>You are planning to close off a corner of the first quadrant with a line segment 20 units long running from (a,0) to (0,b). Show that the area of the triangle enclosed by the segment is largest when a=b.</p>

<p>It's asking to find a max right?</p>

<p>And this one is the same. I'm having tons of trouble with this problem as well.</p>

<p>A 1125-ft^3 open-top rectangular tank with a square base x ft on a side and y ft deep is to be built with its top flush with the ground to catch runoff water. The costs associated with the tank involve not only the material from which the tank is made but also an excavation charge proportional to the product xy.</p>

<p>If the total cost is c=5(x^2+4xy) +10xy, what values of x and y will minimize it?</p>

<p>Does anyone have tips for me on how to approach these? Thanks in advance</p>

2

<p>The answer to the second one is x=15 and y=5. Let me work out the first one..</p>

3

<p>I'm actually attempting, and failing at, those exact problems. i assume we have the same book.</p>

<p>i'm not sure about these answers but I have a few others from that section if you need</p>

4

<p>Oh you have the same textbook? Which one do you have?</p>

5

<p>For the first question, you know that a represents the distance along the x-axis, that b represents the distance along the y-axis, and according to the Pythagorean Theorem, that a^2 + b^2 = 20^2.</p>

<p>The area of the triangle is given by A = 1/2ab. Solve the above equation for a or b, and then replace that variable in the Area equation. Take the derivative of that equation (you'll need the product rule and the chain rule (to navigate the square root)), and go from there.</p>