Sale price = original price - discount
discount = 44% of original price = 44% of $37 = 0.44 x 37 = $16.28
Sale price = $37 - $16.28 = $20.72
All others did not satisfy the inequality simultaneously except #4 and #6
For #4:
2 < 5(1) + 2 i.e. 2 < 7 (true)
2 >= 1/2(1) + 1 i.e. 2 >= 3/2 (true)
For #6
2 < 5(2) + 2 i.e. 2 < 12 (true)
2 >= 1/2(2) + 1 i.e. 2 >= 2
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
It is
If you have a slope (which is before the x) then it’s a linear equation
