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Let a, b, c 2 Z+.
(a) Prove that if a|b, then ac|bc for all c.
(b) If a|bc, can you conclude that either a|b or a|c? Justify your answer with a proof or a counter example.
(c) Prove that gcd(a, a + b) = gcd(a, b).
the base b of a triangle increases at the rate of 2cm per second, and height h decreases at the rate of 1/2 cm per second. Find rate of change of its area when the base and height
The HCF & LCM of two expressions are respectively (x+3) and (x cube-7x+6). If one is x square+2x-3 , other is? Solution) (x+3) * (x^3-7x+6) = (x^2+2x-3) * y ( ) (HCF*LCM=
Left-handed limit We say provided we can make f(x) as close to L as we desire for all x sufficiently close to a and x Note that the change in notation is extremely m
Example Write down the equation of a circle alongwith radius 8 & center ( -4, 7 ) . Solution Okay, in this case we have r =8 , h = -4 and k = 7 thus all we have to do i
Solve the subsequent differential equation. 2xy - 9 x 2 + (2y + x 2 + 1) dy/dt = 0 Solution Let's start off via supposing that wherever out there in the world is a fun
Any 15 foot ladder is resting against the wall. The bottom is at first 10 feet away from the wall & is being pushed in the direction of the wall at a rate of 1 ft/sec. How rapid is
Two planes leave the airport at the similar time. Minutes later, plane A is 70 miles due north of the airport and plane B is 168 miles due east of the airport. Determine the distan
Divides a given line segment internally in the ratio of 1:3 Construction : i )Draw a ray AX making an acute angle with AB. ii) Mark 4 points at equal distance. on AX Let
to plot (5,-4), start at (0,0) and move 5 units left and 4 units down
dans chaque cas recris l expression sous la forme d un rappot reduit 5kg/600g
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