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:
1. Yes; 2. Yes ; 3. No; 4. Yes
Step-by-step explanation:
The proportion will have to be read the same way. For example top Δ bottom to the lower Δ bottom (locate in the same place)
14/21 = 6 /9 Yes because the top Δ bottom to lower Δ bottom = top side to
lower same side
13.5/21 = 9/ 14 Yes because the same two sides to the same two sides in
the lower Δ
9/13.5 = 6 21 No because top Δ side to lower Δ same location but the
second one top Δ side to the lower bottom
14 /6 = 21/6 Yes because top Δ bottom to top side = lower Δ bottom to
lower side (in the same place)
Answer:
x = 47°
Step-by-step explanation:
m∠DPB + ∠BPC = 180° (Definition of a straight line)
Plug in the corresponding numbers and variables to the corresponding places:
x + 133 = 180
Isolate the variable, x. Subtract 133 from both sides:
x + 133 (-133) = 180 (-133)
x = 180 - 133
x = 47
47° is your answer.
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Answer: The mean of the data is 278.
Step-by-step explanation:
To the the mean of the data, we’ll have to add all the numbers up and divide it by the amount of data.
275+279+279+276+278+277+280+282+284+270=2780
2780/10=278
Answer:
measure of a angle 1 = x
measure of angle 2= 3x
3x+1x=180 ( linear pair)
4x=180
x= 180÷4
x= 45
angle one = x= 45
angle two = 3x = 3×45= 135
the 2 angles are
45 and 135
