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Word-Problems Questions
Let n be an integer. Use Definition 1.6 to explain why 2n + 7 is an odd integer.
Give three reasons why the following graph is not continuous on the interval (0, 10).
What is the range of the function given by the following graph?
The graph of y = x2 is stretched vertically by a factor of 3, stretched horizontally by a factor of 5, and translated horizontally to the left by 12. Determine the equation that results from these transformations.
A mass suspended on a spring will exhibit sinusoidal motion when it moves. If the mass on a spring is 85 cm off the ground at its highest position and 41 cm off the ground at its lowest position and takes 3.0 s to go from the top to the bottom and back ag
At Canada's Wonderland, a thrill seeker can ride the Xtreme Skyflyer. This is essentially a large pendulum of which the rider is the bob. However, in this case there is a vertical net for safety. The riders horizontal distance to the safety net is given f
The largest Ferris Wheel in the world is the London Eye in England. The height (in meters) of a rider on the London Eye after t minutes can be described by the function
Tides are cyclical phenomena caused by the gravitational pull of the sun and the moon. On a particular retaining wall, the ocean generally reaches the 3 m mark at high tide. At low tide, the water reaches the 1 m mark. Assume that high tide occurs at 12:0
The city of Windsor, Ontario, receives its maximum amount of sunlight of 15.28 hrs on June 21, and its least amount of sunlight of 9.08 hrs on December 21. (8 marks) Due to the earth's revolution about the sun, the hours of daylight function is periodic.
The average monthly temperatures in New Orleans, Louisiana, are given in the following tables
A sine function that has an amplitude of 16 units, a period of 5 units, a vertical displacement of 3 units up and a phase shift of 2.5 units left. Graph this function and show each step.
For each, determine the amplitude, the axis of the curve, the range, the period, the phase shift, and the zero(s) within one period. Keep your solutions neat and organized.
For the following sinusoidal functions, graph one period of every transformation from its base form and describe each transformation. Be precise.
A cosine function has been vertically stretched by a dilation factor of 45, reflected by the x-axis, horizontally stretched by a dilation factor of 10 and translated up by 33 units. Determine the values of the parameters a, k, d, and c.
Determine the period of each of the following periodic relations, and whether the relation is a function or not.
Solve the following quadratic trigonometric equations algebraically (without graphing technology) for all solutions in the domain 0 ≤ θ ≤ 360°. Use exact solutions whenever possible.
Solve the following linear trigonometric equations algebraically (without graphing technology) for all solutions in the domain 0 ≤ x ≤ 360°. Use exact solutions whenever possible.
Given that for How many solutions are possible for θ? In which quadrants would you find the solution(s)? Determine the reference angle for this equation to the nearest degree. Determine all the solutions to the equation to the nearest degree
Verify the following algebraically
Verify the following for
Prove the following identities. Show all of your steps.
Consider triangle ABC: (20 marks) a = 132, b = 224, and ∠C = 28° Sketch the triangle(s). Solve for c using Cosine law. Solve for the missing angles using Sine law only and then separately using Cosine law only. Investigate the discrepancy (ie. one has two
Two hunters leave the same camp site in the morning, each on their fourwheeler. One heads 30° north of east for 50 km, and the other goes for 64 km heading 80° west of south, and stop for a break. Calculate the distance that separates the two hunters (Exp
Determine the following ratios within their given context. Make sure that you sketch each triangle appropriately. (9 marks) Determine the exact value of given that x is in quadrant III and . Determine the exact value of given that y is in quadrant IV an
In ΔABC, a = 7.2 cm, b = 9.3 cm, ∠A = 35° (6 marks) Determine the number of possible solutions. Determine the measure(s) of ∠B if it exists.
Determine and sketch the principle angle for the reference angle 35° in quadrant II.
Determine whether -105° and -465° are co-terminal angles. Justify your answer fully.
Vanna has just financed the purchase of a home for $200 000. She agreed to repay the loan by making equal monthly blended payments of $3000 each at 4%/a, compounded monthly. (14 marks) Create an amortization table using a Microsoft Excel spreadsheet. In y
$100 is deposited at the end of every week for five years in an account that pays 14%/a, compounded weekly. (8 marks) What type of annuity is this? Find the future value of the annuity using the formula. Find the future value of the annuity using a spread
Following one side of a new street in a neighbourhood, the house numbers increase by six. The house number of the first house on the street is 319. Express this sequence recursively and explicitly.
A high performance all-terrain vehicle (ATV) is bought at a price of $20,000. It loses 10% of its value very year. Express this scenario as a sequence recursively and explicitly (provide its general term).
Compare each the arithmetic and geometric sequences to a function that we covered in a previous unit. Use an example in your explanation.
Consider the Fibonacci sequence.
Determine the constant term of each binomial expansion.
Express the following expansions as a binomial in the form . Leave clear evidence of your reasoning
Determine the values of the following tables. Show all of your work. Be mindful of possible multiple solutions.
Compare and contrast the following in details
The initial dryweight of Botryococcus braunii, a green microalgea, is 50 mg/L. Under the right conditions of light, temperature, salinity and pH, the algea triples every three hours for the first 15 hours of growth.
A bacteria culture population of 50 bacteria doubles in size every 20 minutes. (8 marks) Establish the function rule that models this situation and graph it. How long will it take for the bacterial culture grow to a population of 250 000?
The plutonium isotope Pu-239 is a radioactive material. The half-life of plutonium isotope Pu-239 is 24,360 years. Ten grams of plutonium is released in a nuclear accident. (8 marks) Determine the rule, domain and range of the function model. How long wil
Determine the rule of an exponential function that has the given properties. Validate your answer using a graph. (12 marks) Has a base of 6, an asymptote at , has parameter k = ±1, and passes through the coordinate points (3, -4) and (4, 11). Has an initi
Determine the exact value of x.
You have learned about quadratic and linear function in earlier grades. Explain in a variety of ways how you can distinguish the exponential function from the quadratic function and linear function . (Hint: compare the rate of change using finite diffe
State the domain, range, x-intercept(s), y-intercept(s) and asymptote(s) of the given function.
Transform the graph of into . Show a table of values and a graph (neatly sketched by hand) for each step of the transformation starting from
Solve:
Prove that f and g are equivalent using both the graphical and algebraic approach. If they are not, provide a counter-example that shows how they are not equivalent.
Tom and Kim are arguing about the following functions
To protect the endangered species, some leatherback sea turtles are introduced into a protected ecosystem. The following function models the population of leatherback sea turtles, P as a function of the time, t in years, since they are introduced in the p
The following function gives the height h meters, of a batted baseball as a function of the time, t seconds, since the ball was hit.
Bob and Jack enter a 1000 km go-kart race. Bob drives 4 km/h faster than Jack, but his go-kart gets a flat tire, which takes 30 minutes to repair. If both of them finish the race in a tie, then how fast were each boy going during the race?
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