2. a farmer is planning to create a temporary ‘pen’ for livestock, by cutting a large section of plastic netting into strips, joining the strips together and then fixing the combined length to posts. he decides the fence must be 2 m high, and must form a shape that is nearly square: either a precise square or a rectangle whose length and width do not differ by more than 5 m.
if the length and width are both whole numbers of metres, what is the greatest area than can be created from 156 m2 of netting?

The greatest area is 380m², using two strips 19 meters long and two strips 20 meters long, which is nearly a square.

Explanation:

The area of the plastic netting is 156 m² and its height is told to be 2 m, so solving the equation of the area for the length, you can calcualte how many linear meters of plastic netting the farmer will use:

Area = length × height 156 m² = length × 2 m ⇒ length = 156 m² / 2m = 78 m

So, you have to create the greatest possible area with 78 linear meters of plastic netting.

The greatest possible area enclosed by a fixed amount perimeter is a square.

If the figure were a precise square each side would be 1/4 of 78m, i.e. 78 m / 4 = 19.5 m.

But you need to use whole numbers that do not differ by more than 5 meters.

Suppose two sides measure 19 m and the other two sides measure 20 m. You can check that makes the perimeter equal to 78 m:

19 m + 19m + 20 m + 20m = 78 m.

That figure is a rectangle whose area is 19 m × 20 m = 380 m²

Since, that is the figure most similar to a square using wholde numbers you know that is the greatest area.

You can prove that using other numbers:

18m + 18m  + 21m + 21m = 78m18m × 21m = 378m²

As you see, the are for a rectanle 18 × 21 is smaller than the area for a rectangle 19 × 20. And the area will decrease as you move further away from the square shape.

Thus, the greatest area is 380m², using two strips 19 meters long and two strips 20 meters long, which is nearly a square.

Timbre  (/ˈtæmbər/  tam-bər, also known as  tone color  or  tone quality  from  psychoacoustics) is the perceived sound quality of a  musical note, sound or tone. timbre distinguishes different types of sound production, such as  choir voices  and  musical instruments, such as  string instruments,  wind instruments, and  percussion  instruments. it also enables listeners to distinguish different instruments in the same category (e.g. an  oboe  and a  clarinet).the physical characteristics of sound that determine the perception of timbre include  spectrum  and  envelope. singers and instrumental musicians can change the timbre of the music they are singing/playing by using different singing or playing techniques. for example, a violinist can use different bowing styles or play on different parts of the string to obtain different timbres (e.g., playing  sul tasto  produces a light, airy timbre, whereas playing  sul ponticelloproduces a harsh, even and aggressive tone). on  electric guitar  and  electric piano, performers can change the timbre using  effects units  and  graphic equalizers.in simple terms, timbre is what makes a particular musical sound have a different sound from another, even when they have the same  pitch  and  loudness. for instance, it is the difference in sound between a guitar and a piano playing the same note at the same volume. both instruments can sound equally tuned in relation to each other as they play the same note, and while playing at the same amplitude level each instrument will still sound distinctively with its own unique tone color. experienced  musicians  are able to distinguish between different instruments of the same type based on their varied timbres, even if those instruments are playing notes at the same  pitch  and  loudness.

  the tendency to view one's own culture  and  group as superior  is called. cultural relativism.