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An open box is to be made from a flat piece of material 8 inches long and 3 inches wide by cutting equal squares of length xfrom the corners and folding up the sides?
You really should consider trying this yourself before reading the answer, and you should understand the answer, otherwise you will not learn the lesson. Read each step, and do not proceed unless you understand it.
To maximize the volume of an open box made from a sheet of material 8 x 3, by cutting equal squares of side x from the corners and folding up the sides, first draw the box...
The box is 8-2x by 3-2x by x. Try again to draw it...
The volume of the box is (8-2x)(3-2x)x. Can you see the solution?
Simplify the volume. It is 4x3 - 22x2 + 24x. Can you see the solution?
Differentiate. This is a simple polynomial. Can you see the solution?
The deriviative is dy/dx = 12x2 - 44x + 24. Can you see the solution?
The maximum volume occurs when the deriviative is zero. Can you see the solution?
Solve for 12x2 - 44x + 24 = 0. How about the quadratic equation? Last chance to solve it yourself.
There are two roots of x: 3, and 2/3. 3, however, is not valid because you can not cut a square larger than 1.5 out of the original side of 3, so the answer is 2/3.
What else can I help you with?
Are squares straight?
No they are not, they have corners.
What two states of the four corners are perfect squares?
Colorado and wyoming
What has 4 corners and 4 sides?
quadrilaterals like squares and rectangles and parallelograms and a rhombus
How can 2 identical squares be cut and to form a bigger squares?
They can't, unless you're cutting them all into different sizes.
How do you find diagonals of squares and rectangles?
They are the lines joining the opposite corners. To find them you will need to look for them!
An open box is to be made from a flat piece of material 20 inches long and 6 inches wide by cutting equal squares of length x from the corners and folding up the sides Write the volume of the box?
It is 4x^3 - 13x^2 + 30x cubic inches.
An open box is to be made from a flat piece of material 16 inches long and 5 inches wide by cutting equal squares of length x from the corners and folding up the sides. Write the volume of the box?
the volume of the box would be 4x^3-42x^2+80x since a volume wasn't given to find 'x' or a set 'x' wasn't given, that is the equation you would use
Are squares straight?
No they are not, they have corners.
How many corners do rectangles have?
Rectangles and squares both have 4 corners.
Do all squares have corners?
Yes squares ALWAYS have corners but they can be a sharp point or a very slightly rounded edge. Hope this helps!!
How many corners do 5 squares and 3 triangles have?
Each square has four corners, and each triangle has three corners. 5 squares X 4 corners/square = 20 corners 3 triangles X 3 corners/triangle = 9 corners 20 + 9 = 29 corners total.
What is a productogon?
it is a triangle with circles at the corners, and squares in the middle of the corners. The squares have numbers in them, and you have to put numbers in the circles. However, the numbers in the circles have to add up to the number of the square between them. Simple, right?
What two states of the four corners are perfect squares?
Colorado and wyoming
A shape with four right angle corners?
Any rectangle (including squares).
An open box is to be made from a flat piece of material 20 inches long and 6 inches wide by cutting equal squares of length x from the corners and folding up the sides Write the volume Vof the box?
If you take a square, side x, from each corner then the base of your box becomes (20-2x) by (6-2x). The height is then x. Draw a picture if it will help you visualize. Also, please feel free to do your own homework. We know school is back in session, but please do not use Wikianswers to cheat on assignments. kthxbai
What has 4 corners and 4 sides?
quadrilaterals like squares and rectangles and parallelograms and a rhombus
How many corners does 3 squares have?
well that's a dumb question figure it out! but, its 12
