Answer:
x=4 Inch
Step-by-step explanation:
Length of the Square = 24 Inches
If a Square of Length x cm is cut out from each corner
Length of the Box = 24-x-x=(24-2x) Inches
Width of the Box =24-x-x=(24-2x) Inches
Height of the box = x inches
Volume of a Cuboid = Length X Width X Height
V(x)= x(24-2x)(24-2x)
Simplifying
V(x)=4x(12-x)(12-x)
To determine the value of x at which V is largest, we take the derivative of V(x) and solve for the critical points.
V(x)=4x(12-x)(12-x)
Set the derivative equal to zero to obtain the critical points
x cannot be equal to 12 as it divides the length of the square cardboard into exactly two equal parts.
When x=4
V(4)=4*4(12-4)(12-4)=16*8*8=1024 Cubic Inches
When x=4 Inch, the volume, V of the open box is largest.
Answer:
yes they are not equal because (x + a) = 2x + 2a
Answer:
length = 115 cm
width = 108 cm
Step-by-step explanation:
The perimeter of a rectangular swimming pool is 446 centimeters
LEt L be the length of the pool
The width of the pool is 7 centimeters less than the length of the pool.
width = length - 7
W= L-7
Given perimeter = 446
Perimeter of rectangle = 2(length)+2(width)
446 = 2(L) + 2(W) we know W = L-7
446 = 2(L) + 2(L-7)
446 = 2L + 2L - 14
Add 14 on both sides
460 = 4L
divide by 4 on both sides
L= 115
Length L= 115
Width W = L - 7 = 115 - 7= 108
Answer: 14 years
Step-by-step explanation:
Let the cat's age when it died = x.
Therefore, the child's age is 2 + x because he/she got the cat when he/she was 2 years old.
We can set up an equation.
x + (2+x) = 30
2x + 2 = 30
2x = 28
Therefore, x = 14
