A 6ft tall observer is standing at the top of a cliff. He spots a house in the adjacent valley at an angle of depression of 12 degrees. The cliff is 54 ft tall. How far away is the house from the base of the cliff?

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Find all the angles that satisfy the equation cos(θ)=32

The biologist has a second culture to examine. she knows that the population of the culture doubles every 15 minutes. after 1 hour and 15 minutes, her assistant found that 80,000 bacteria were present. a) what was the size of the initial population? b) predict the size of the culture at t=3 hours. what was the size of the population at 40 minutes? explain and justify your answers. c) create a graph of the population as a function of time. find an equation that can be used to predict the size of the population at any time t. d) examine the rate at which the bacteria culture is growing. how fast is the culture growing after 1 hour? after 1.5 hours? after 2 hours? use a time interval of h = 0.01 hours to estimate these rates. interpret these rates in terms of the context of the problem situation. how do these three rates compare?

Bill and felicia each bake cookies for a party. bill bakes 3 times as many cookies as felicia. felicia bakes 24 fewer cookies than bill. bill bakes b cookies and felicia bakes f cookies. what equation can represent this word problem