color%7Bred%7D%20Question%7D%7D%7D%7D" id="TexFormula1" title=" \huge{\green}\fcolorbox{blue}{cyan}{\bf{\underline{\red{\color{red} Question}}}}" alt=" \huge{\green}\fcolorbox{blue}{cyan}{\bf{\underline{\red{\color{red} Question}}}}" align="absmiddle" class="latex-formula">
1 answer:
You might be interested in
Answer:
in
Step-by-step explanation:
Let x be the side of square.
Length of box=8-2x
Width of box=15-2x
Height of box=x
Volume of box=
Substitute the values then we get
Volume of box=V(x)=
Differentiate w.r.t x
Again differentiate w.r.t x
Substitute x=6
Substitute x=5/3
Hence, the volume is maximum at x=
Therefore, the side of the square , in cutout that gives the box the largest possible volume.
Answer:
<h3>B. 4units</h3>Step-by-step explanation:
Find the diagram attached. The diagram is a similar triangle.
From the diagram, XZ/XY = CA/AB
Given XZ = 2x-2+2x-2 = 4x-4
XY =5x-7
CA = 2x-2
AB= x+1
On substituting this parameters into the formula to get x first
4x-4/5x-7 = 2x-2/x+1
cross multiply
(4x-4)(x+1) = 5x-7(2x-2)
open the parenthesis
4x²+4x-4x-4 = 10x²-10x-14x+14
4x²-4 = 10x²-24x+14
10x²-4x²-24x+14+4 = 0
6x²-24x+18 = 0
x²-4x+3 = 0
x²-3x-x+3 = 0
x(x-3)-1(x-3) =0
(x-3)(x-1) = 0
x = 3 and 1
Next is to get length AX.
Given AX = 2x-2
Substitute x = 3 into the expression
AX = 2(3)-2
AX = 6-2
AX = 4 units
Hence the measure of length AX is 4 units
