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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.
If a+b+c = 3a , then cotB/2 cotC/2 is equal to
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Sales increased through only 1/2% last month. If the sales from the previous month were $152,850, what were last month's sales? Multiply through the decimal equivalent of 1/2 %
The temperature in Hillsville was 20° Celsius. What is the equivalent of this temperature in degrees Fahrenheit? This problem translates to the expression 3 {[2 - (-7 + 6)] + 4
(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
find the integral dx/1-x
Determine the value of the unknown side of a right triangle: The two legs of a right triangle are 5 ft and 12 ft. How long is the hypotenuse? Now Let the hypotenuse be c ft.
Let a = 5200 and b = 1320. (a) If a is the dividend and b is the divisor, determine the quotient q and remainder r. (b) Use the Euclidean Algorithm to find gcd(a; b). (c)
Cartesian Graph of Density of Water - Temperature: Example: The density of water was measured over a range of temperatures. Plot the subsequent recorded data on
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