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The common difference in the arithmetic sequence 9, 7, 5, 3, . . . is

The common difference in the arithmetic sequence , , , , , . . . is

Which of the given formulas for the general term of the sequence –5, –15, –25, –35, –45, . . . is correct?

In the formula for the general term of a geometric sequence , the common ratio is

The eighth term in the sequence 458 752, 114 688, 28 672, 7168, … is

The 6th term in the sequence , 1, , , . . . is

How many terms are in the sequence 6, 54, 486, 4374, 39366, …, 3 188 646?

The 7th term of the geometric series 256 + 32 + 4 + is

Determine the sum of the infinite geometric series with t₁ = –12 and r = .

The sum of an infinite geometric series is and its common ratio is . What is the first term of the series?

What are the three other angles in standard position that have a reference angle of 55°?

The point (48, –90) is on the terminal arm of ÐA. Which is the set of exact primary trigonometric ratios for the angle?

The coordinates of a point P on the terminal arm of an angle are shown. What are the exact trigonometric ratios for , , and ?

Marco is 950 m due east of the centre of the park. His friend Ray is 950 m due south of the centre of the park. Which is the correct expression for the exact distance between the two boys?

Determine the length of x, to the nearest tenth of a centimetre.

Determine, to the nearest tenth of a centimetre, the two possible lengths of a.

Which of the following triangles cannot be solved using the sine law?

Diagrams not drawn to scale.

Which strategy would be best to solve for x in the triangle shown?

Determine the measure of x, to the nearest tenth of a degree.

If °, r = 21 cm, and p = 24 cm, what is the length of q, to the nearest centimetre?

A company purchases a new computer system valued at $42 000. For income tax purposes, an accountant determines that the annual depreciation rate (rate of decrease in value) for the equipment is 11%.
a) Make a table of values to show the value of the system over the first 5 years.
b) Determine an explicit formula in function notation to model the value of the system in year n.
c) What is the value of the system at the end of year 20?
d) How realistic is the answer to part c)? Explain.

In a lottery, the first ticket drawn wins a prize of $25. Each ticket after that receives a prize that is twice the value of the preceding prize.
a) Write a function to model the total amount of prize money given away.
b) How many prizes are given out if the total amount of prize money is approximately $2 million?

Two wires are connected to a tower at the same point on the tower. Wire 1 makes an angle of 45° with the ground and wire 2 makes an angle of 60° with the ground.
a) Represent this situation with a diagram.
b) Which wire is longer? Explain.
c) If the point where the two wires connect to the tower is 35 m above the ground, determine exact expressions for the lengths of the two wires.
d) Determine the length of each wire, to the nearest tenth of a metre.
e) How do your answers to parts b) and d) compare?

An airplane is flying over the town of Colonsay, between two tracking stations. The angle of elevation from Station 1 is 36° and from Station 2 is 48°. If the stations are 1675 m apart, what is the altitude of the plane, to the nearest tenth of a metre?

Two ranger stations, A and B, are located in a pine forest and are 10 km apart. A forest fire breaks out at point F and is spotted by both rangers. The angle formed at station A by the line of sight to the fire and the line to station B is 63.2°. The angle at station B formed by the line of sight to the fire and the line between the ranger stations is 57.9°.
a) How far is station A from the fire, to the nearest tenth of a kilometre?
b) How far is station B from the fire, to the nearest tenth of a kilometre?
c) Which ranger is closer to the fire, and by how much?