What is a peppered moth?

2 answers:

amm18124 years ago

6 0

The peppered moth is a temperate species of night-flying moth. Peppered moth evolution is an example of population genetics and natural selection.

Natali [406]4 years ago

4 0

The Peppered Moth is widespread in Britain and Ireland and frequently found in ordinary back gardens, yet its amazing story has made it famous all over the world. It is one of the best known examples of evolution by natural selection, Darwin's great discovery, and is often referred to as 'Darwin's moth'.

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A Texas rancher wants to fence off his four-sided plot of flat land. He measures the first three sides, shown as A, B, and C in

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The answer:
the full question is as follow:
A Texas rancher wants to fence off his four-sided plot of flat land. He measures the first three sides, shown as A, B, and C in Figure below , where A = 4.90 km and θC = 15°. He then correctly calculates the length and orientation of the fourth side D. What is the magnitude and direction of vector D?

As shown in the figure,
A + B + C + D = 0, so to find the magnitude and direction of vector D, we should follow the following method:
D = 0 - (A + B + C) ,
let W = - (A + B + C), so the magnitude and direction of vector D is the same of the vector W characteristics

Magnitude
A + B + C = (4.90cos7.5 - 2.48sin16 - 3.02cos15)I
+ (-4.9sin7.5 + 2.48cos16 + 3.02sin15)J
= 1.25I +2.53J
the magnitude of W= abs value of (A + B + C) = sqrt (1.25² + 2.53²)
= 2.82

the direction of D can be found by using Dx and Dy value
we know that tanθo = Dx / Dy = 1.25 / 2.53 =0.49
tanθo =0.49 it implies θo = arctan 0.49 = 26.02°

direction is 26.02°