Now that you know more about the Golden Ratio, do you believe its common presence shows evidence of a grand design within the universe or is it simply a coincidence? Explain why you feel that way.

Kayla wants to find the width, ab, of a river. she walks along the edge of the river 65 ft and marks point c. then she walks 25 ft further and marks point d. she turns 90° and walks until her location, point a, and point c are collinear. she marks point e at this location, as shown. (a) can kayla conclude that δ and δ are similar? why or why not? (b) suppose de = 15 ft. what can kayla conclude about the width of the river?

Non-euclidean geometry was discovered when, in seeking cleaner alternatives to the fifth postulate, it was found that the negation could also be true a. true b.false

The moats separating people from the animals are 5 m wide for lions and 4 m wide for the elephants. if the lion’s moat is 4 m deep, how deep should the elephants’ moat be?