Abox with a square base and open top must have a volume of 13,500 cm3. find the dimensions of the box that minimize the amount of material used. sides of base cm height cm

base: 30 cm

height: 15cm

Step-by-step explanation:

Let 'b' be the length of the side of the base, and 'h' the height of the box. The volume is given by:

The total area of material used is:

Using both equations to solve for 'b':

The value of 'b' for which the derivate of the area function (A) equals zero, is the value that yields the minimum area.

If b=30, the height 'h' is:

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation: