Determine two positive numbers whose product is 360, and the sum of one of the numbers and 10 times the other number is a minimum.

Step-by-step explanation:

Let be one number and be the other number.

The product of the two numbers is 360.

Sum of one of the numbers and 10 times the other number be z

Differentiating with respect to we get

Equating with zero

Double derivative of z

at

So is minimum at

So, one number is 60 and the other number is 6.

answer: answer

step-by-step explanation:

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x