Answer:
2.29 ft of side length and 1.14 height
Step-by-step explanation:
a) Volume V = x2h, where x is side of square base and h is hite.
Then surface area S = x2 + 4xh because box is open.
b) From V = x2h = 6 we have h = 6/x2.
Substitude in formula for surface area: S = x2 + 4x·6/x2, S = x2 + 24/x.
We get S as function of one variable x. To get minimum we have to find derivative S' = 2x - 24/x2 = 0, from here 2x3 - 24 = 0, x3 = 12, x = (12)1/3 ≅ 2.29 ft.
Then h = 6/(12)2/3 = (12)1/3/2 ≅ 1.14 ft.
To prove that we have minimum let get second derivative: S'' = 2 + 48/x3, S''(121/3) = 2 + 48/12 = 6 > 0.
And because by second derivative test we have minimum: Smin = (12)2/3 + 4(12)1/3(12)1/3/2 = 3(12)2/3 ≅ 15.72 ft2
Answer:
410
Step-by-step explanation:
You can use the equation f(n)= 14+(n-1)6 and you substitute in 67 for n.
Least 0.5, 1/4, 0.8, 0.9 greatest
Answer: See explanation
Step-by-step explanation:
Your question isn't really clear. Let me help you rephrase it and solve.
Let's say Cesar is creating a schedule to practice his instrument for band. He needs to practice for a total of 10 hours in a week. On Monday he practice for 1 1/2 hours, on Tuesday he practiced for 2 1/4 hours, and on Wednesday he practiced for 1 1/2 hours.
The total hours that Cesar has used in practicing will be:
= 1 1/2 + 2 1/4 + 1 1/2
= 5 1/4
To get the number of hours that Cesar need to practice during the rest of the week in order to have his 10 total hours, we subtract 5 1/4 hours from 10 hours. This will be:
= 10 - 5 1/4
= 4 3/4 hours.
Cesar needs to practice for 4 3/4 hours more.
Answer: angle p = 124°
Step-by-step explanation: Angle W and angle P are opposite interior angles so they have the same measure.
