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If the lengths of all sides of a box are doubled, how much is the volume increased?
a. 2 times
b. 4 times
c. 6 times
d. 8 times
d. The volume of a box is taken by multiplying length × length × length or l × l × l = l3. If the length is doubled, the new volume is (2l ) × (2l ) × (2l ) or 8(l 3). When we differnciate the two expressions, we will see that the difference is a factor of 8. Thus, the volume has been increased by a factor of 8.
Solve by factorization X 2 +(a/a+b + a+b/a)x+1 = 0 X 2 +(a/a+b + a+b/a)x+1 => X 2 +(a/a+b x a+b/ax + a/a+b .a+b/a) => X[x+a/a+b] +a+b/a[a+a*a+b]= 0 => X= -a
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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.
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