Answer:
For maximum volume the dimension should be;
w= 1.5ft , b=3ft and h= 2ft
Step-by-step explanation:
The surface area of the rectangular box
S = 2wb + 2wh + 2bh = 27ft^2 ......1
Given that b = 2w
Substituting into eqn 1
2w(2w) + 2wh + 2h(2w) = 27
4w^2 + 2wh + 4hw = 27
h(6w) = 27 - 4w^2
h = (27 - 4w^2)/6w .......2
The volume of a rectangular box is given as
V=w×b×h
V= w×2w×h = 2hw^2 ....3
Substituting eqn2 into eqn3
V=2w^2(27-4w^2)/6w
V = w(27-4w^2)/3 = (27w-4w^3)/3
To find the maximum point, we need to differentiate the eqn above.
At maximum dV/dw = 0
dV/dw = (27 - 12w^2)/3 = 0
12w^2 = 27
w^2 = 9/4
w = 3/2ft = 1.5ft
b = 2w = 6/2 = 3ft
h = (27 - 4w^2)/6w
h = (27 - 4(3/2)^2)/6(3/2)
h = ( 27 - 9)/6 = 18/9
h = 2ft
Answer: If you are solving for x, the answer would be...
2x-f(x)=9
Step-by-step explanation: Solve for x by simplifying both sides of the equation, then isolating the variable.
Hope this helps you out! ☺
Supplementary angles are angles whose sum is equal to 180°.
Let one angle be x
The other angle is said to be 26°more than the other so it is x + 26
x + (x+26) = 180
x + x + 26 = 180
2x = 180 - 26
2x = 154
x = 154/2
x = 77
1st angle, x, is equal to 77°
2nd angle, x + 26°, is 77° + 26° = 103°
77° + 103° = 180°
180° = 180°
Answer:
<u>True Statements:</u>
"Kaylee's necklace can have 25 pieces of rotelle"
"Kaylee's necklace can have 10 macaroni noodles and 15 pieces of rotelle"
"Kaylee's necklace can have 1 macaroni noodle"
Step-by-step explanation:
First condition:
max pieces is 25
Checking the choices, we eliminate anyone having more than 25 pieces.
choice 1 - 26 piece NO
choice 2 - 25 piece OK
choice 3 - 25 piece OK
choice 4 - 25 piece OK
choice 5 - 1 piece OK
choice 6 - 25 piece OK
So we eliminate first choice. Now, 2nd condition is 15 macaroni or 50 rotelle, so that's 50/15 = 3.33 rotelle = 1 macaroni
We check each choice and convert macaroni to rotelle and make sure they are under 50
choice 2 - 25 rotelle, so OK
choice 3 - 10*3.33 + 15 = 48.3, under 50, so OK
choice 4 - 14*3.33 + 11 = 57.62, NOT OK
choice 5 - 1*3.33 = 3.33 rotelle OK
choice 6 - 16*3.33 + 9 = 62.28 rotelle , NOT OK
So finally, the statements that are TRUE are:
Choice 2, Choice 3, Choice 5
Answer:
A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven
Step-by-step explanation:
Like the midpoint theorem search that up and angle addition postulate