Tutorial 1: Review of Basic Concepts
Let[pic]. List the elements of A that belong to the given set.
Let set M =[pic]. List the elements of M that belong to the given set. i.
Multiply out the brackets:
a) 7(x + 2y) – 2(3y – 5x)
(b) 2x2 + y – z2 – 2(3x2 + 2y – z)
(c) (2x – 5)(5 + 2x)
(d) (9y - 8)(3y - 3)
Evaluate the following without using a calculator.
(e) 4[pic] =
Find expressions for the following algebraic functions, simplify the answers as far as possible. a) [pic] =
b) [pic] =
(d) [pic] =
Factor completely: x2 + 3xy – 154y2 =
Factor out the greatest common factor: 36x9y9 – 27x7y7 + 90x4y3
Simplify the complex function.
A manufacturer's cost is given by C = 400 [pic] + 200, where C is the cost and n is the number of parts produced. Find the cost when 512 parts are produced.
Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 9 mi, the distance between the cars was 3 mi more than the distance traveled by the car heading east. How far had the eastbound car traveled?
Tutorial 2: Equations and Inequalities
Solve the following inequalities:
a) [pic] > [pic]
One solution is 30% acid and another is 10% acid. How many cubic centimetres of each should be mixed to obtain 100cc of a solution that is 18% acid?
Kelly fisher has a total of $30,000 invested in two municipal bonds that have yields of 8% and 10% interest per year, respectively. If the interest Kelly receives from the bonds in a year is $2640, how much does she have invested in each bond?
Kafka Inc. imports hard drives and sells them on the internet. The profit is given by the equation P = 137n - 7250, where n is the number of hard drives sold. How many hard drives must be sold for the company to break even? Round your answer to the units place, in other words, to the nearest number of hard drives.
Solve the equation for the indicated variable: E = mc2 for c
Solve the equation: 3(2z - 4) = 5(z + 3)
Find approximate solutions of the equation: 3x2- 4.7x + 0.4=0
Find expressions for the Revenue, Cost, and Profit from selling x thousand items.
Suppose the sales of a particular brand of appliance satisfy the relationship
S(x) = 240x + 4200,
where S(x) represents the number of sales in year x, with x = 0 corresponding to 1982. Find the number of sales in 1988.
b). p2 + 2p -15 > 0
The profit made when t units are sold, t > 0, is given by P = t2 - 36t + 323. Determine the number of units to be sold in order for P = 0 (the break- even point).
John has a total of $50,000 invested in two municipal bonds that have yields of 8% and 12% interest per year, respectively. If the interest John receives from the bonds in a year is $4640, how much does she have invested in each bond?
If a rocket is propelled upward from ground level, its height in meters after t seconds is given by h = -9.8t2 + 107.8t. During what interval of time will the rocket be higher than 274.4 m?
John owns a cafe. A mathematical model connecting p, the profit per day from selling coffee (in dollars) and x, the price per cup of coffee (in dimes) is
P(x) = -2x2 + 32x - 20
Find the profit per day if the price per cup of coffee is $2.10 (x =2.10)
Suppose that the number of frequent flier miles (in billions) earned by customers of various airlines, but not yet redeemed in year x, could be approximated by the polynomial function:
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