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=
![[4000-160x-100x+4 x^{2} ]x=(4 x^{2}-260x+4000)x](https://tex.z-dn.net/?f=%5B4000-160x-100x%2B4%20x%5E%7B2%7D%20%5Dx%3D%284%20x%5E%7B2%7D-260x%2B4000%29x)
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
<u>Answer with step-by-step explanation:</u>
We know that the formula for area of a circle is given by:
<em>Area of a circle =
</em>
So to find the area of circle, we basically need to know the radius of the circle.
If we know the circumference of the circle, we can calculate the area of the circle too.
Formula for the circumference of the circle is given by:

So if we know the circle's circumference, we can find the value of radius and then find the area of circle with it.
They made profit of
by selling 190 kg of taffy in 400 g bags at rate of
each.
<u>Solution:
</u>
Given that
To raise money, the Boy Scouts bought 190 kg of taffy for
.
They sold the tafty in 400 g bags for
Need to calculate the profit the made.
Cost price of 190 kg of taffy = 
As 1 kg = 1000 gram,
So 190 kg of taffy = 
So cost price of 190000 gram of taffy = 
Now let us calculate number of 400 grams bags which can be made from 190000 grams of taffy
Number of 400 grams bags = 
Amount generated from 1 bag of 400 gram taffy = 3.28
So amount generated from 475 bags of taffy = 
Selling price of 190000 grams of taffy = amount generated from 475 bags of taffy = 

Hence they made profit of
by selling 190 kg of taffy in 400 g bags at rate of 
Factor: (M-2n)(M^2+2Mn+4n^2)
Answer:
width = 2.5 feet
Step-by-step explanation:
Suzanne has a rectangular garden which is 18 feet long and 11 feet wide.
Area of the garden = length times width = 18 times 11= 198 square foot
Let 'w' be the width of the border
Length of the garden with border = 18+2w
Width of the garden with border = 11+2w
Area of the garden with border = 
Area of the border = 
She has 168 square foot of paving stones,

Solve for w
apply quadratic formula
a= 4, b= 58 and c=-168



we get two values for w

