the exact value of sin θ, if the terminal arm of the angle in standard position passes through the points (-3,4) is

the solution to the rational equation 11/r =7/5-10/r is

 The use of a ladder is considered safe if the angle between the ground and the ladder is less than 75°. Charlie’s 5 ft long ladder is 1 ft from the base of a wall.a.) Is the ladder being used safely? b.)How far away from the wall is the minimum distance Charlie’s other ladder should be if it is 10 ft long? 

triangle abc has the following dimensions: a=17°, a = 37in, b = 91 in. the number of triangles possible with these dimensions is (are) 

The temperature at which water freezes is 0°C or 32°F. The temperature at which water boils is

100°C or 212°F. The relationship between degrees Celsius and degrees Fahrenheit is shown

through the graph below.

a.) Given, that 1°C is 33.8°F (or t1=33.8 ) and d = 1.8, write out the general formula, tn, that

represents the relationship between degrees Fahrenheit and degrees Celsius. Be sure to define

the variables.

b.) Given two points on the graph, the freezing point of water at 0°C or 32°F and the boiling

point of water at 100°C or 212°F, calculate the slope of the line. Explain how this value

relates to the general formula found in part a.

c.) What is the y-intercept of the graph? Explain how this value relates to the general formula found in part a.

A special event organizer wants to get the word out to 100,000 teens in the area about a concert coming up in three months. By posting the event on the musicians' website, 100 teens in the area will find out about the event in the first week. Research suggests that each of those teams will tell for new teens about the event, in those friends each hotel for more teens about it.

a.) how many times does this pattern need to continue until 100,000 teens know about the event?

b.) what assumption is made in order to answer part a?

During the first year of production, 8 000 000 tonnes of copper were extracted from a Peruvian mine. Production has declined by 8% each year since then.a.) What was the total mass of the copper mined during the first four years of production?b.) How many years will it take for production to fall below 100 000 per year? c.) If the production trend continues, how much copper will be extracted from the mine over its lifetime? 

Gary is a fitness trainer who makes 30 and 45 minute appointments

with clients. Gary’s contract allows him to make up to 30 hours of

appointments in a week. State the inequality that represents all the

possible combinations of appointments that Gary can make in a

week. Graph the inequality.

During a soccer match, Tony, at point A, passes the ball to Eoin, at point C, to avoid the defender at point B. Eoin then kicks the ball towards the 7.32 m wide net in an attempt to score. The path of the ball is modeled by the absolute value function . Suppose a Cartesian plane is superimposed over the opponent’s half of the pitch such that the opposite corners of the field of play have the coordinates (0, 60) and (90, 0), as shown. 

a.At what point does Eoin receive the ball?

b. If player B does not intercept the ball, verify whether or not the ball makes it into the goal.

c.If Tony passes the ball from point (5,36), state the domain and range of the absolute value function, within the context of this situation.