Check the picture.
let the length of a side of each of the squares removed be x.
The box formed will have dimensions: 80-2x, 50-2x, x(the height)
So the volume can be expressed as a function of x as follows:
f(x)=(80-2x)(50-2x)x=
so
the solutions of f'(x)=0 gives the inflection points, so the candidates for maxima points,
solving the quadratic equation, either by a calculator, graphing software, or by other algebraic methods as the discriminant formula, we find the solutions
x=10 and x=33.333
plug in f(x) these values to see which greater:
cm cubed
which is negative because (50-66.666)<0
Answer: 18000 cm cubed
(8x^2-9y^2-4x)+(x^2-3y^2-7x)
First, get rid of the parentheses and combine like terms
(8x^2+x^2)(-9y^2-3y^2)(-4x-7x)
9x^2-12y^2-11x is your answer
For rhombus A:
base = 7 in
area = 35 in²
Area of rhombus = b * h
⇒ 35 = 7 * h
⇒ h = 35/7
⇒ h = 5 in
Rhombus B:
height = 3*5 = 15 in
base = 7*3 = 21 in
Area = 15 * 21 = 315 in²
Area
of rhombus B is 9 times area of rhombus A. When the dimensions are
increased to 3 times the initial dimension, area became 9 times.