Tutor profile: Glenn C.
find the inverse of the function f(n)= -2n^3+1
reversing each step in reverse order, f^-1(n) = ((n-1)/-2))^(1/3)
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?
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.
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?
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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