Help with questions (1 Viewer)

[Smile12345]

Hello All...

Could someone please help me with the following?

1. 'A 3m piece of wire is cut into two pieces and bent around to form a square and a circle. Find the size of the two lengths, correct to 2 d.p., that will make the total area of the square and circle a minimum'

AND

2. Two cars a travelling along roads that intersect at right angles to one another. One starts 200km away and travels towards the intersection at 80km/h ^-1, while the other starts at 120km away and travels towards the intersection at 60km/h ^-1. Show that their distance apart after t hours is given by and hence find their minimum distance apart."

Thanks in advance.

 

[HeroicPandas]

1) If the wire is cut into 2 pieces which form 1 square and 1 circle, then this means that the perimeter of the square and perimeter of the circle is equal to 3

Let perimeter of square be P1
Let perimeter of circle be P2

Let the side of the square be 'a'
Let the radius of the circle be 'r'

P1 + P2 = 3

Therefore,

4a + 2(pi)r = 3 ....................................[1]

Your aim is to find the values of 'a' and 'r' so that the area of square and circle is to be min

Let area of square be A1
Let area of circle be A2
Let total arae of square and circle be B

B = A1 + A2

B = a² + (pi)r²

U know the procedure to find minimum of area right? (remember when differentiating, there must be a maximum of 2 variables --> eg. A = 3r + 4r², the 2 variables are 'A' and 'r')

The above equation has a total of 3 variables! D: what do we do??

Your turn to take over captain!

 

[Smile12345]

1) If the wire is cut into 2 pieces which form 1 square and 1 circle, then this means that the perimeter of the square and perimeter of the circle is equal to 3

Let perimeter of square be P1
Let perimeter of circle be P2

Let the side of the square be 'a'
Let the radius of the circle be 'r'

P1 + P2 = 3

Therefore,

4a + 2(pi)r = 3 ....................................[1]

Your aim is to find the values of 'a' and 'r' so that the area of square and circle is to be min

Let area of square be A1
Let area of circle be A2
Let total arae of square and circle be B

B = A1 + A2

B = a² + (pi)r²

U know the procedure to find minimum of area right? (remember when differentiating, there must be a maximum of 2 variables --> eg. A = 3r + 4r², the 2 variables are 'A' and 'r')

The above equation has a total of 3 variables! D: what do we do??

Your turn to take over captain!

Thanks ...