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The sum of three consecutive even integers is 102. What is the value of the largest consecutive integer?
Three consecutive even integers are numbers in order such as 4, 6, and 8 or -30, -28 and -26 that are each 2 numbers apart. Let x = the ?rst and smallest consecutive even integer. Let x + 2 = the second consecutive even integer. Let x + 4 = the third and largest consecutive even integer. Sum is a key word for further so the equation becomes (x)+ (x + 2) + (x + 4) = 102. Combine such as terms on the left side of the equation: 3x + 6 = 102. Subtract 6 from both sides of the equation: 3x + 6 - 6 = 102 - 6; simplify: 3x = 96. Divide each side of the equation by 3: 3x/3 = 96/3. The variable is now alone: x = 32; thus the further larger integer is: x + 2 = 34. The largest even integer would be: x + 4 = 36.
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Solve : 4x2+2x+3=0 Ans) x^2 + (1/2)x = -(3/4) (x+1/4)^2 = 1/16 - 3/4 = -11/16 implies x = (-1+i(11)^(1/2))/4 and its conjugate.
QR is the tangent to the circle whose centre is P. If QA || RP and AB is the diameter, prove that RB is a tangent to the circle.
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.
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Differentiate following. f ( x ) = sin (3x 2 + x ) Solution It looks as the outside function is the sine & the inside function is 3x 2 +x. The derivative is then.
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