Suppose an airline policy states that all baggage must be box shaped with a sum of length, width, and height not exceeding 96 in. What are the dimensions and volume of a square-based box with the greatest volume under these conditions?

Step-by-step explanation:

As the base is a square so the length is a, width is a and the height is h.

According to the question,

a + a + h = 96

h = 96 - 2a     .... (1)

Volume of the box, V = length x width x height

V = a x a x h

V = a² (96 - 2a)    from equation (1)

V = 96a² - 2a³

Differentiate both sides

Now put it equal to zero.

192 a - 6a² = 0

a = 32 in

h = 96 - 2 x 32

h = 32 in

Thus, the length and the width os teh base is 32 in and the height is 32 in.

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500

8.3 and the 3 is repeating

hope this .