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The two sides of a triangle are 17 cm and 28 cm long, and the length of the median drawn to the third side is equal to 19.5 cm. Find the distance from an endpoint of this median to
a doctor sees 3 boys to 5 girls in one week . If he sees 40 boys in one day then how many girls does he see that day
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) A palindrome is a word that reads the similar whether read from right to left or from the left to right, the word ROTOR, for example. Let be the number of words of length n,
Repetition Need Not Be Boring : From an early age on, children engage in and learn from repetitive behaviour, such as dropping and picking up things, opening and closing boxes an
elliptical path of celestial bodies
Let 0 ! V1 ! ! Vk ! 0 be a long exact sequence of vector spaces with linear maps. Show that P (??1)i dim Vi = 0.
Alexis needs to paint the four exterior walls of a large rectangular barn. the length of the barn is 80 feet the width is 50 feet and the height is 30 feet. The pain costs 28 dolla
Let Xn be a sequence of distinct real numbers. Defi ne E = {L : L is a subsequential limit of Xn}. Prove E is closed.
Theorem a → • b → = ||a → || ||b → || cos• Proof Let us give a modified version of the diagram above. The three vectors above make the triangle AOB and note tha
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