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1. How many closed necklaces of length 7 can be made with 3 colors? (notice that 7 is a prime) 2. How many closed necklaces of length 10 can be made with 3 colors (this is di erent
application
Chain Rule : If f(x) and g(x) are both differentiable functions and we describe F(x) = (f. g)(x) so the derivative of F(x) is F′(x) = f ′(g(x)) g′(x). Proof We will s
The sum of two consecutive odd integers is -112. What is the larger integer? Two consecutive odd integers are numbers in order such as 3 and 5 or -31 and -29, that are each 2 n
You''ve decided you want a plant for your room. At the gardening store, there are 444 different kinds of plants (tulip, fern, cactus, and ficus) and 444 different kinds of pots to
With reference to Fig. 1(a) show that the magnification of an object is given by M=SID/SOD. With reference to Fig. 1(b) show that the size of the penumbra (blur) f is given by f
(a) Determine the matrix that first rotates a two-dimensional vector 180° anticlockwise, and then per- forms a horizontal compression of the resulting vector by a factor 1/2 (leavi
450 students. if there are 50 more boys than girls, how many boys and girls are there?
We are until now going to suppose that there will be no external forces acting on the system, along with the exception of damping obviously. Under this case the differential equati
what is 1/3 + 2/9 equal
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