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Answers by Emma D.

 Hi Phillipp,    The first step to optimization problems is setting up equations that characterize the constraints under which you are working.  In this problem, the total weight of the nuts and bolts must add up to 100kg.   (weight of nuts) + (weight of...

Hi Alanna,    Let's call the original length of the wire LW (for length warm) and the shorter length of the cooler wire LC (for length cold).     In cooling from 21C to 0C, the wire shortens by a*(21C - 0C)*LW, where a is the coefficient of thermal expansion...

Hi James,    First determine the maximum torque (T_max) that the shaft will be subjected to.  The maximum torque is power (3MW) divided by angular frequency (200rpm converted to rad/s).   Next calculate the polar moment of inertia in terms of the external radius,...

Hello Stevie,    Let's assume that the original wood beam is simply-supported and capable of holding 2690lb evenly distributed along its length.  This 2690lb includes the weight of the wood.  The shear and tensile strength of the wood can be estimated using the following...

Hello Thorgerdur,    You can begin both problems by replacing 314 with its modular 7 representation: 314^163 = 6^163 mod 7   (a)  Note how powers of 6 repeat cyclically in the modular 7 number system: 6^1 = 6 mod 7 6^2 = 1 mod 7 6^3 = 6 mod...

Hi Ana,  To visualize how the graph moves, rewrite y = (x - 3)^2 + 4 so that it is easier to compare with y = x^2.  old: y = x^2 new: (y' - 4) = (x' - 3)^2 Now you can see that the transformation changed y to (y' - 4) and x to (x' - 3).   y = y' - 4 ---->...

Here is a graphical way to think of it.   Suppose you wanted to divide the number 1 by 0.  In other words, you want to find y = 1/x when x = 0.  Well, try graphing the function y = 1/x.  You will notice that to the left of x = 0, the value of y approaches negative infinity...

Hi Maria,  One way to solve this problem is to use the Law of Sines: sin(A)/a = sin(B)/b = sin(C)/c.  Here a, b, c are the lengths of the sides, and A, B, C are the angles across from (not touching) the sides a, b, c respectively.   Since you are given b, c, and B, you could...

Here is a way to remember that the angles of a triangle sum to 180 degrees. Imagine a squat triangle, with two very acute angles and one very obtuse angle.  If this triangle is very stout, then the acute angles are ~0 and the obtuse angle is ~180 degrees.