Applications of Maximisation and Minimisation.. (1 Viewer)

[GaDaMIt]

I need help with the last few questions in an exercise im doing..



1) The point A lies on the positive half of the x-axis, and the point B lies on the positive half of the y-axis, and the interval AB passes through the point P(5,3). Find the coordinates of A and B so that triangle AOB has minimum area.

2)A man in a rowing boat is presently 6km from the nearest point A on the shore. He wants to reach as soon as possible a point B that is a further 20km down the shore from A. If he can row at 8km/hr and run at 10km/hr, how far from A should he land?

3)a) An open rectangular box is to be formed by cutting squares of side length x cm from the corners of a rectangular sheet of metal that has length 40cm and width 15cm. Find the value of x in order to maximise the volume of the box

3)b) An open rectangular box is to be formed by cutting equal squares from a sheet of tin which has dimensions a metres by b metres. FInd the area of the squares to be removed if the box is to have maximum volume. Check your answer to part ( a).

 

[ianc]

Hi there!!



Here's the answer to Question 1:

[i have let A be (x,0) and B be (0,y)]

Hence A is (10,0) and B is (6,0)

I haven't done maths since the hsc, so im a little rusty. I hope it's right!

I'll try and do some more for you now.

 

[bos1234]

how did u insert the symbols on here?

 

[GaDaMIt]

[i have let A be (x,0) and B be (0,y)]

Lol.. i cant believe i didnt see that.. thanks

 

[ianc]

I used equation editor in Microsoft Word, did a "print screen", pasted it into a gif and uploaded to imageshack.


Question 2 is all about getting the diagram.

 

[ianc]

With question 3a you need to visualise the 3d box.

Question 3b is doing exactly the same thing but instead of 40cm and 15cm, you have a and b; so you follow the same steps but with fiddly algebra. Feel free to ask if you need me to do it for you as well.


Good luck with Year 12!!!!!!!!

 

[GaDaMIt]

With question 3a you need to visualise the 3d box.

Question 3b is doing exactly the same thing but instead of 40cm and 15cm, you have a and b; so you follow the same steps but with fiddly algebra. Feel free to ask if you need me to do it for you as well.


Good luck with Year 12!!!!!!!!

Answer for a is 10/3.

Your reasoning for x must be positive is incorrect, 55 - 35 is still positive. 15 is incorrect cause the width of the rectangle is 15, thus you couldnt get 2 15cm edges from that width, as required. Other than that, thanks a lot

 

[ianc]

whoops i stuffed up the quadratic bit

sorry about that!! I fixed it up here:

Have a good one!