TyErd's questions

[kenhung123]

hey soul sister, ain't that mister mister on the radio stereo

[naved_s9994]

lol!

[/0]

If you take your ship to be the origin, you can model the position of the boats with vectors. For the first boat, you have





The displacement between the boats is then



And the distance is



By minimizing this you can find the time where distance is minimum.

An open tank is to be constructed with a square base and vertical sides to contain of water. What must be the dimensions of the area of sheet metal used in its construction if this area is to be a minimum.

Let the square base have side length , and let the height of the tank be .

Then you want to minimize subject to the constraint .

Solve the second equation for , plug into the first, and minimize.

[TyErd]

Hmm..I dont think we do vectors in Methods. Any other way to do the problem?

[TyErd]

An open tank is to be constructed with a square base and vertical sides to contain of water. What must be the dimensions of the area of sheet metal used in its construction if this area is to be a minimum.

Let the square base have side length , and let the height of the tank be .

Then you want to minimize subject to the constraint .

Solve the second equation for , plug into the first, and minimize.

I keep getting the wrong answer. Can someone show me how to do it

[the.watchman]

Okay, first define some variables (I'll just use the ones decided on earlier)

Then make an equation for the area:



Make an expression for the volume, equate it to 500, and rearrange for h in terms of l:





Sub this into the area equation:



So (for st. points)



(this is a local minimum, but i cbf proving it )

sub this into volume equation to get corresponding value for h

[Yitzi_K]

An open tank is to be constructed with a square base and vertical sides to contain of water. What must be the dimensions of the area of sheet metal used in its construction if this area is to be a minimum.

Let the square base have side length , and let the height of the tank be .

Then you want to minimize subject to the constraint .

Solve the second equation for , plug into the first, and minimize.

I keep getting the wrong answer. Can someone show me how to do it

Just working on what /0 said, , therefore

Subbing that into , we get , which simplifies to

The derivative of that is

Solving that for zero gives:





So the base of the sheet metal is 10 by 10.

Subbing back into gives . So the sides are 10 by 5.

[TyErd]

Thankyou very much !

[TyErd]

For the function has a minimum value at x equals?

[TyErd]

Find the approximation of

[TyErd]

Given that   find in terms of the approximate value of , given that h is small.

[TyErd]

Find the values of for which increases as increases and hence find the maximum value of .

I dont even know where to start on this one. Help?

[brightsky]

Find the approximation of

Let

So now our job is to approximate .

When you consider the graph, and draw a tangent to the graph at (this won't be a really good approximation as 6203 - 4096 is quite big), but the tangent should be very close to the actual point of 4096 + 2107 = 6203.

By linear approximation, (derived from derivatives by first principles).



So is the approximation (just sub in the values in use a calculator to work out the value).

[brightsky]

Given that   find in terms of the approximate value of , given that h is small.

Linear approximation formula:



Hence (just sub values in again to find answer).

[the.watchman]

Find the values of for which increases as increases and hence find the maximum value of .

I dont even know where to start on this one. Help?

This means basically to find when the expression is increasing (eg. derivative > 0), try finding that, then use the right endpoint (when derivative = 0) as the local maximum