Question

Keep calm and carry on wants to design a bag for a new airline. This new airline has a policy that the sum of the dimensions of the bag must be less than 100 centimeters. The width of the bag must be 7 centimeters greater than the depth. The bag should have a volume of approximately 25,000 cubic centimeters.

The team has come up with the function V(d)=2d^3-79d^2-651d+25000, which represents the volume of the bag given it’s depth. The graph of this function is shown. What are the possible heights of the bag?
A) -17.868 centimeters, 17.584 centimeters, 39.784 centimeters
B) 17.584 centimeters, 39.784 centimeters
C) 128.736 centimeters, 57.832 centimeters, 13.432 centimeters
D) 57.832 centimeters, 13.432 centimeters

Answer 1

B) 17.584 centimeters, 39.784 centimeters

Answer 2

B. 17.584 centimeters, 39.784 centimeters.

Explanation:

We have been given a function
`V(d)=2d^3-79d^2-651d+25,000`, represents the volume of the bag given it’s depth. We are asked to find the possible heights of the bag.

The height of the bag will be equal to depth of bag. To find depth of bag, we need to find x-intercepts of our function.

Upon looking at our graph, we can see that our function crosses x-axis at
`d=-17.868`,
`d=17.584` and
`d=39.784`.

Since height cannot be negative, therefore, possible heights of bag will be 17.584 centimeters and 39.784 centimeters and option B is the correct choice.