Absolute maxima and minima

[95atar]

can someone help me solve question 5 on 10f (essential math methods cas)

A rectangular block is that the sides of its base and length are of xcm and 3xcm. The sum of its lengths and edges are 20cm.
Show that the volume Vcm^3 is given by V=15 x^2-12x^3

[BigAl]

I've seen this question when tutoring my student. This question isn't clear that much to be honest

[bonappler]

Alright, so the base of the block has dimensions of 3x and x. For volume to be calculated the height must be known. We can work this out through simple algebra, let the height be equal to y. Now we know that all sides add up to 20cm so we can create this equation: 12x+4x+4y=20 solve for y in terms of x. y=5-2x now all you have to do is multiply the base, height and length and you will get the answer that is required. 3x*x*(5-4x).

[95atar]

A Piece of string 10 meters long is cut into two pieces to form two squares
a)if one piece of the string has length x meters ,show that the combined area of two squares is given by A=1/8(x^2-10x+50)

[95atar]

I've seen this question when tutoring my student. This question isn't clear that much to be honest

What was ur methods study score and wat do u advise me to do as a tutor?

[BigAl]

Well I think this question is not expressed adequately. I mean it looks confusing. Exam questions will be neat don't worry. Check out last years extended response question

[FlorianK]

A Piece of string 10 meters long is cut into two pieces to form two squares
a)if one piece of the string has length x meters ,show that the combined area of two squares is given by A=1/8(x^2-10x+50)

Ok, so you cut of 1 piece and hence you obviously get 2.

The piece you cut off has the length x, hence the other one has the length 10-x

So the circumference of the squares are C₁=x and C₂=10-x

The length of each of the sides is a quarter of the circumeference, so a₁=x/4 and a₂ = (10-x)/4

To get the area you must square them

so
A=a₁²+a₂²
A=x²/16+(100-20x+x²)/16=1/16(x²+100-20x+x²)=1/8(x²+50-10x) Q.E.D