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Direction Cosines This application of the dot product needs that we be in three dimensional (3D) space not like all the other applications we have looked at to this point.
We will firstly notice the undamped case. The differential equation under this case is, mu'' + ku = F(t) It is just a non-homogeneous differential equation and we identify h
A librarian is returning library books to the shelf. She uses the call numbers to denote while the books belong. She requires placing a book about perennials along with a call numb
The radius of the in circle of a triangle is 4cm and the segments into which one side is divided by the point of contact are 6cm and 8cm. Determine the other two sides of the tria
1. Suppose n ≡ 7 (mod 8). Show that n ≠ x 2 + y 2 + z 2 for any x, y, z ε Z. 2. Prove ∀n ε Z, that n is divisible by 9 if and only if the sum of its digits is divisible by 9.
A circle touches the side BC of a triangle ABC at P and touches AB and AC when produced at Q and R. Show that AQ= 1/2 (perimeter of triangle ABC) Ans: Since the length o
In figure, XP and XQ are tangents from X to the circle with centre O. R is a point on the circle. Prove that XA+AR=XB+BR Ans: Since the length of tangents from externa
The football boosters club had 80 T-shirts made to sell at football games. Through mid-October, they had only 12 left. What percent of the shirts had been sold? Denote the numb
construct the green''s function that satisfies dG''''-(2x+1)G''+(x+1)G=delta(x-s), G(0,s)=G(1,s)=0
The distribution of sample means is not always a normal distribution. Under what circumstances is the distribution of sample means not normal?
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