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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 10 by 10, by cutting equal squares of side x from the corners and folding up the sides, first draw the box...
The box is 10-2x by 10-2x by x. Try again to draw it...
The volume of the box is (10-2x)(10-2x)x. Can you see the solution?
Simplify the volume. It is 4x3 - 40x2 + 100x. Can you see the solution?
Differentiate. This is a simple polynomial. Can you see the solution?
The deriviative is dy/dx = 12x2 - 80x + 100. Can you see the solution?
The maximum volume occurs when the deriviative is zero. Can you see the solution?
Solve for 12x2 - 80x + 100 = 0. How about the quadratic equation? Last chance to solve it yourself...
There are two roots of x: 5, and 5/3. 5, however, is not valid because you can not cut a square of 5 by 5 four times out of a square 10 by 10 and leave any volume at all, so the answer is 5/3.
What else can I help you with?
If 1200cmof material is avaiable to make a box with a square base and an open top find the largest possible volume of the box?
== ==1250347 because my calculus book tells me so
If 1900 square centimeters of material is available to make a box with a square base and an open top find the largest possible volume of the box.?
To maximize the volume of a box with a square base and an open top, we can use the formula for surface area ( S = x^2 + 4xh ) (where ( x ) is the side length of the base and ( h ) is the height). Given that ( S = 1900 ) cm², we can express ( h ) in terms of ( x ): ( h = \frac{1900 - x^2}{4x} ). The volume ( V = x^2h ) can then be maximized by substituting ( h ) into the volume formula and using calculus to find the critical points, resulting in a maximum volume of approximately 12,250 cm³ when ( x \approx 25 ) cm.
What are the square inches to a box?
To get the square inches in the box you need to multiply the length times width so a 2 inch by 4 inch box is 2x4= 8 square inches
How many box in a squre box?
4-8 boxes in a square box!
What is the correct name for square and squiggly brackets?
* round brackets, open brackets or parentheses: ( ) * square brackets, closed brackets or box brackets: [ ] * curly brackets, squiggly brackets, swirly brackets, braces, or chicken lips: { }
If 1200cmof material is avaiable to make a box with a square base and an open top find the largest possible volume of the box?
== ==1250347 because my calculus book tells me so
What piece of metric equipment would be used to measure a square box?
A ruler.
Piece Box?
Piece Box
How do you get a hammer to open a challenge box?
you just select the hammer, press A, go to the square you want to open and press A again
What does PS in a square like box on the bottom of a ceramic piece mean you know it is a signature mark but who?
Peter Schnarr
Where is the fuse box located on a 1998 Chevy Lumina Sedan?
Believe there are three fuse boxes. 1) Open Passanger side door. Look at access panel on side of dash. 2) Open Hood. 5" square box on right side rear of wind washer. 3) Open Hood. 4" square box on left side
I have to open btd file?
btd files are created with a cool piece of software called Business-in-a-box. However, you can't open these files with anything else.
Where is the fuse box for 2002 suzuki aerio?
On the left side of the dashboard lower you will find a rectangle with a small square box opening , pull this and the door will open exposing the fuse box.
Where is the fuse box Suzuki Aerio 2002?
On the left side of the dashboard lower you will find a rectangle with a small square box opening , pull this and the door will open exposing the fuse box.
What is the diameter of the largest circle that will fit inside 14 inch box?
Assuming that the 14 inch box is square, you could fit a circle inside with a 14 inch diameter.
Where Is Horn Located On A 1990 Buick Century?
If you look under the passenger side back seat there should be a box, open the box there should be a flap on the inside lid, open the flap and remove the piece of paper that will reveal that you are a complete idot.
Why do ford keys have a red bit on the top?
The red square (sometimes a dot) on your key means that it is a master key. It will open every lock on your car. If the key has no red square or a black square then it is a secondary key that will open the doors, the boot and the ignition but will not open the storage compartments such as the glove box.
