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Tutor profile: Glenn C.

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Glenn C.
teach at a community college
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Questions

Subject: Pre-Calculus

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Question:

find the inverse of the function f(n)= -2n^3+1

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Glenn C.
Answer:

reversing each step in reverse order, f^-1(n) = ((n-1)/-2))^(1/3)

Subject: Trigonometry

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Question:

You're on a sailboat cruising parallel to the shore. You want to triangulate your position so you take a reading and find that the course to the lighthouse is 27 deg to the left of the course you're on . 3.5 miles further down, the reading is 45 degrees. Where are you relative to the lighthouse?

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Glenn C.
Answer:

Draw the picture. It's a triangle with two interior angles of 180-45, 180-27, and included side of 3.5. Solve for the side opposite the 135 degrees. This is the distance to the lighthouse.

Subject: Calculus

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Question:

You want to create a window with maximum area that has two semicircular ends attached to a rectangle. You're limited to 50 linear feet of framing to build it. What're the dimensions of the window?

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Glenn C.
Answer:

Draw the window and label the width and length. The width is equal to the diameter of the circular ends. The formula for the area is l times w plus pi (radius ) squared = l x w +pi x (diameter/2) squared. You need to maximize that area subject to the constraint that 2(l+w) + 2 x pi x d/2) = 50. You need to use the constraint equation to solve for d, substitute into the area formula so that there is only one variable. Then differentiate with respect to w (d), set equal to zero, and solve for w. This is the critical number. It's also the width that maximizes the area.

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