Question

Half of ‘a’ added to the product of 6 and k

Answer 1

Answer:

(12k + a)/2

Step-by-step explanation:

Half of a is a/2.

Product of 6 and k is 6k.

Their sum is 6k + a/2 = (12k+a)/2

Answer 2

Answer:

Let the numbers be x and y and their sum 'a' is constant. <br> `:. X+y = a` …(1) <br> Let the product of number be P. <br> `:. P= x* y` <br> `=x(a-x)` [From (1)] <br> `=ax - x^(2)` <br> `rArr (dP)/(dx) = a - 2x` <br> For maxima/minima <br> `(dP)/(dx) = 0` <br> `rArr a-2x = 0` <br> `rArr x = a//2` <br> and `(d^(2)P)/(dx^(2)) = - 2 lt 0` <br> `rArr" P is maximum at " x= a//2` <br> Now `y=a-x=a-a//2=a//2` <br> Therefore, for the maximum product, each number will be half of their sum.