(Solved): pleaae help solve this worksheet 1. Some examples of consecutive positive odd integers are: 3 and 5, ...

1. Some examples of consecutive positive odd integers are: 3 and 5, 19 and 21, etc. Thus, if $$n$$ is the first positive odd integer, then $$\mathrm{n}+2$$ is the next consecutive positive integer. Show that the difference between the reciprocals of two consecutive positive odd integers is: $$\frac{2}{n(n+2{)}^{\text{. }}}$$ [2T, 2A, 1C] 2. Newton's Law of gravitation states that any two objects exert a gravitational force on each other due to their masses: $$F_g=\frac{G{m}_1{m}_2}{r^2}$$ where $$F_g$$ is the gravitational force $$G$$ is a constant (the universal gravitational constant) $$m_1$$ and $$m_2$$ are the masses of the two objects, and $$r$$ is the separation distance between the two objects' centres. Consider you as one mass and a planet as another mass. In one situation, you are standing on the surface of Earth ( $$6371\mathrm{km}$$ in radius). In another situation, you are standing on the surface of Mars (3389.5 $$\mathrm{km}$$ in radius). Earth is $$9.35$$ times more massive than Mars. How many times greater is the gravitational force between you and Earth than between you and Mars? [2T, 2A, 1C] 3. The Ottawa Senators is deciding on ticket prices for a game against the Toronto Manle Leafs foc the 2021-22 season lif it hannens. 3. The Ottawa Senators is deciding on ticket prices for a game against the Toronto Maple Leafs for the 2021-22 season (if it happens, with covid-19). They expect 13,000 people to attend at an average price of $$\$180$$ per ticket (this probably actually is the average price of a ticket for a Leafs vs. Senators game, believe it or not!). For every $$\$5$$ decrease in average ticket price, they expect to have 400 more people attend. a) Create a quadratic equation to model this situation. [1T, 1C] b) What will the maximum revenue be? $$[3\mathrm{A},1\mathrm{C}]$$ c) What should the average ticket price be to maximize revenue? How many tickets will they sell at this price? [2T] d) The maximum capacity of the Canadian Tire Centre (where the Senators play) is 17,000. What are the domain and range of this function? [2T, 1C] e) Graph this relationship. Indicate the values of the points at both ends and at the vertex. [1T, 1A, 1C] 4. a) Determine the value(s) of $$k$$ such that $$g(x)=2x^2+kx+26$$ intersects the function $$f(x)=?2x^2+7x+17$$ at only 1 point. (Hint: There are two possible values for $$k$$, and thus two different parabolas that intersect $$f(x)$$ at only 1 point). [6T, 1C] b) Graph $$f(x)$$ and $$g(x)$$ using technology (Desmos.com suggested) and clearly indicate the point of intersection between $$f(x)$$ and each of the two possible $$g(x)$$ functions. Print this off and include it in your assignment. [2K, 1T]