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:
Point D is invariant
Step-by-step explanation:
A geometry tool such as GeoGebra can help with this effort.
Using the geometry tool, I found it easier to move points P and Q, rather than trying to move lines m1, m2, and n. That has the same effect.
The problem setup has points A, B, and C remaining where they started. I was a little surprised to see that point D also remains in the same location. (I could not see any obvious reason why. Perhaps proportions are involved.)
Attached are two different sets of m1, m2, and n for the same A, B, C. You can see that point D remained in the same place. "Quadrangle" PQRS is colored in both figures.
Slope equation: y2-y1/x2-x1
-5-3/2-(-6)
-8/8
-1 is the slope
Answer:
80
Step-by-step explanation:
The three angles of a triangle add to 180 degrees. One angle is 10, the second is a right angle( which is 90 degrees). Let the third angle be x
10 +90 +x = 180
Combine like terms
100 +x =180
Subtract 100 from each side
100-100 +x= 180-100
x = 80
Answer:
#11: last option is answer
#12: first option is answer
Step-by-step explanation:
#11) 5x + 6 ≤ 11
5x ≤ 5
x ≤ 1 to graph this you need a solid dot on 1 and shading to the left
#12) 5p+ 4 > 14
5p > 10
p > 2 to graph this you need an open dot on 2 and shading to the right