<span>The answer is x = 2
Hope this helps. </span>
If the length, breadth and height of the box is denoted by a, b and h respectively, then V=a×b×h =32, and so h=32/ab. Now we have to maximize the surface area (lateral and the bottom) A = (2ah+2bh)+ab =2h(a+b)+ab = [64(a+b)/ab]+ab =64[(1/b)+(1/a)]+ab.
We treat A as a function of the variables and b and equating its partial derivatives with respect to a and b to 0. This gives {-64/(a^2)}+b=0, which means b=64/a^2. Since A(a,b) is symmetric in a and b, partial differentiation with respect to b gives a=64/b^2, ==>a=64[(a^2)/64}^2 =(a^4)/64. From this we get a=0 or a^3=64, which has the only real solution a=4. From the above relations or by symmetry, we get b=0 or b=4. For a=0 or b=0, the value of V is 0 and so are inadmissible. For a=4=b, we get h=32/ab =32/16 = 2.
Therefore the box has length and breadth as 4 ft each and a height of 2 ft.
You want to find the unit rate...
1350 divided by 8 = 168.75 if its asking for an estimate it will be 169
When two straight lines cut each other vertical angles are formed. There are two pair of vertical angles .Vertical opposite angles are always equal .
In the figure Substituting the values of the angles given.
x+40=3x.
Subtracting x both sides.
40=3x-x
40=2x. Dividing both sides by 2.
X=20.
First you want to find the length and width of the rectangle using the distance formula:
d=√(x2-x1)²+(y2-y1)²
AB=√(6-3)²+ (-2 - -2)²
AB=√3² + 0
AB=√9
AB=3
BC=<span>√(6-6)²+ (5 - -2)²
BC=</span>√0 + 7²
BC=√49
BC=7
We can find the area by multiplying these two distances together:
A=(3)(7)
A=21 units²
