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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.
Given f (x) = - x 2 + 6 x -11 determine each of the following. (a) f ( 2) (b) f ( -10) (c) f (t ) Solution (a) f ( 2) = - ( 2) 2 + 6(2) -11 = -3 (
Round 14.851 to the nearest tenth? The tenths place is the ?rst number to the right of the decimal. Here the number 8 is in the tenths place. To decide whether to round up or
The area of a rectangle gets decreased by 8 m2, if its length is decreased by 5 m and breadth increased by 3 m. If we enhance the length by 3 m and breadth by 2 m, the area is en
A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i
Area between Two Curves We'll start with the formula for finding the area among y = f(x) and y = g(x) on the interval [a,b]. We will also suppose that f(x) ≥ g(x) on [a,b].
Terry earns $680 per week. He is entitled to 4 weeks annual leave and receives an additional holiday loading of 17.5%. Calculate his total pay for this holiday period.
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fig angles of a irregular polygons exterior and interior .
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