<p>Wow...never skip 3 days of calc unless you know what you're doing:</p>
<p>1) The positions of two particles on the s-axis are s1=cos (t) and s2=cos (t+(pi/4)).
a) What is the farthest apart the particles ever get?
b) When do the particles collide</p>
<p>2) A customer has asked you to design an open-top rectangular stainless steel vat. It is to have a square base and a volume of 32 cubed feet, to be welded from quarter-inch plate, and to weigh no more than necessary. What dimensions do you recommend?</p>
<p>3) The sum of 2 nonnegative numbers is 20. Find the numbers
a) if the product of one number and the square root of the other is to be as large as possible
b) if one number plus the square root of the other is to be as large as possible</p>
<p>1) (a) Use the two equations to express the difference between the two, i.e. cos(t) - cos(t + pi/4). Then, differentiate. dy/dx = sin(t+pi/4) - sin(t). Set the derivative equal to zero, then solve. In other words, find the intersection between sin(t + pi/4) and sin(t).
(b) find the intersection between the two original equations.</p>
<ol>
<li>V = 32ft.^3. V= l x w x h. Since here, the bottom is flat, V = w^2 x h. Thus, 32 = w^2 x h. Solving for h in terms of w, 32 = (32/w^2)(w^2). I would continue, but i'm tired. sorry.</li>
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