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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 cos?+sin? = √2 cos?, prove that cos? - sin? = √2 sin ?. Ans: Cos? + Sin? = √2 Cos? ⇒ ( Cos? + Sin?) 2 = 2Cos 2 ? ⇒ Cos 2 ? + Sin 2 ?+2Cos? Sin? = 2Cos 2 ? ⇒
What is Matrices?
The sum of three times a greater integer and 5 times a lesser integer is 9. Three less than the greater equivalent the lesser. What is the value of the lesser integer? Let x =
find inverse of [1 2 3 2 4 5 3 5 6]
1 Data is to be transmitted over Public Switched Telephone Network (PSTN) using 8 levels per signaling elements. If the bandwidth is 3000 Hz, deduce the theoretical maximum transfe
reduction
The temperature at 6 P.M. was 31°F. Through midnight, it had dropped 40°F. What was the temperature at midnight? Visualize a number line. The drop from 31° to 0° is 31°. There
Reduce the following rational expression to lowest terms. x 2 - 2 x - 8/ x 2 - 9 x + 20 Solution When reducing a rational expressio
Jessica has a picture in a frame with a total area of 288 in2. The dimension of the picture without the frame is 12 in through 14 in. What is the larger dimension, in inches, of th
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