Linear Algebra

If the company made a total of $301.50, how many children attended? Explain how you found your answer. 301.5-69-3.5S = 2.50

According to Heron's formula, the area, A, of a triangle is given by A=[s(s-a)(s-b)(s-c)], where a, b, and c are the side lengths of the triangle and s is one-half the perimeter of the triangle, s-a+b+c. Calculate the 2 area of a triangle with side lengths 6.7 cm, 6.2 cm, and 7.1 cm. Round your answer to the nearest tenth of a square centimetre. [6 MARKS]

14. The number of users of a new webmail service doubles every 5 months. About how many months will it take for the number of users to increase from 54 000 to 536 000? [3 marks] a 11 months b 20 months c 17 months d 13 months

15. The formula D=0.099M¹ gives the drinking rate, D litres per day, of a mammal with body mass M kilograms. Determine the body mass of a mammal with a drinking rate of 25 L/day. [4 mark]

2. A person's body mass index, B, is B=2, where m kilograms is the mass and h metres is the height. Determine the body mass index of a person 181 cm tall with mass 66 kg. [4 MARKS]

4. Kleiber's Law states that the energy required per day, P kilocalories, for an animal with mass M kilograms, is given by the formula P-70M* a) Determine the energy required per day by a 1400 kg elephant. [3 MARKS] b) Determine the energy required per day by a 0.043 kg mouse. [3 MARKS] c) The energy required by a human is 2500 kcal per day. Determine its body mass. Explain your strategy. [5 MARKS]

5) In a recent session of Parliament a total of 150 Conservative members, 30 Liberal members and 8 members of the NDP showed up to vote for a private members bill in the House of Commons. Exactly 94 votes for the bill and 94 votes against were tabulated. There were three times as many conservatives who voted for the bill as there were Liberals who voted against the bill. Additionally, there were fifteen times as many conservatives voting against the bill as there were non-conservatives voting for the bill. How many Conservatives, how many Liberals and how many NDP members voted for the bill? Solve using a system of equations.

2. In each case, find the critical numbers of f(r). Then use the second derivative test to decide whether the critical numbers lead to relative extrema. If f"(c) = 0 or f"(c) does not exist for a critical number c; then the second derivative test gives no information. In this case, use an alternative method instead (for example the first derivative test). (a) f(x) = x³ - 6x² +7 (b) f(x) = x^7/3 + x^4/3

1- The graph of the function f is given. 2 - The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower and upper estimates for the distance (in ft) that she traveled during these three seconds. 3 - Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed, and values of the rate at two-hour time intervals are shown in the table. 4 - Use this graph and a midpoint Riemann sum with six equal subintervals to estimate the distance traveled (in feet) by the car while the brakes are applied. 5- Use this definition with right endpoints to find an expression for the area under the graph of f as a limit. Do not evaluate the limit. 6- Use this definition with right endpoints to find an expression for the area under the graph of f as a limit. Do not evaluate the limit. 7- Use this definition with right endpoints to find an expression for the area under the graph of f as a limit. Do not evaluate the limit. 8- Use this definition with right endpoints to find an expression for the area under the graph of f as a limit. Do not evaluate the limit. 9- Determine a region whose area is equal to the given limit. Do not evaluate the limit. 10 - Determine a region whose area is equal to the given limit. Do not evaluate the limit. 11- Let A be the area under the graph of an increasing continuous function f from a to b, and let L,, and R, be the approximations to A with n subintervals using left and right endpoints, respectively. (a) How are A. L., and R. related? 12- Exercise (a) Estimate the area under the graph of f(x) = 3 cos(x) from x = 0 to x = x/2 using four approximating rectangles and right endpoints. Is your estimate an underestimate or an overestimate? Exercise (b) Estimate the area under the graph of f(x) = 3 cos(x) from x = 0 to x = x/2 using four approximating rectangles and left endpoints. Is your estimate an underestimate or an overestimate?

6) Consider the following equation where d is a scalar (i.e a simple single real number) and A, B, C are each invertible matrices. d(BA+C) = C-A Solve for the matrix B.