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1. Show that there do not exist integers x and y for which 110x + 315y = 12.
2. If a and b are odd integers, prove that a2 +b2 is divisible by 2 but is NOT divisible by 4. Hint:
Any odd number can be written 2k + 1 for some integer k.
3. Prove that for any prime number p, √ p is irrational. Hint: Follow the same method that was used to prove √ 2 is irrational, by first supposing √ p can be expressed as a=b.
The figure shows the sketch graphs of the functions
What decimal is represented by point A on the number line? The hash marks indicate units of 0.01 between 0.75 and 0.80. Point A is 0.77. See the ?gure below.
Find out the general formula for the tangent vector and unit tangent vector to the curve specified by r → (t) = t 2 i → + 2 sin t j → + 2 cos t k → . Solution First,
Explain the Graphical Technique of Linear Equations.
In an election contested between A and B, A obtained votes equal to twice the no. of persons on the electoral roll who did not cast their votes & this later number was equal to twi
Find the normalized differential equation which has {x, xex} as its fundamental set
a data set has a mean of 3, a median of 4, and a mode of 5.which number must be in the data set-3,4,5?
HOW DO CHILDREN LEARN? : Have you ever tried teaching a young child what "ball" means? Did you do it by a lot of verbal description" Or did you let the child actually handle a b
If 7 cosec?-3cot? = 7, prove that 7cot? - 3cosec? = 3. Ans: 7 Cosec?-2Cot?=7 P.T 7Cot? - 3 Cosec?=3 7 Cosec?-3Cot?=7 ⇒7Cosec?-7=3Cot? ⇒7(Cosec?-1)=3Cot? ⇒7(C
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