Task 2: The Math Teacher Act-Building A Parabolic Light Arch The second act of Talent Night needs a massive light apparatus for the singing math teachers.
The lights must be hung from the ceiling in a parabolic shape. The following information
explains how the lights are hung:
To make this parabolic shape, a metal track light bracket is needed which also serves to
hold the lights.
. The metal track light bracket is held to the ceiling by two chains which also bring
electricity to the lights.
• One chain is hooked to the bracket at a height of 10 m and 5 m to the right of the
centre of the stage.
• The second chain location is symmetrical to the first.
• The height of the highest light must be 18 metres above the stage and 7 meters to the
right of the stage.
• Each light must be 0.6 metres apart horizontally starting from the highest light.
Your task is to find the following information:
1. Find the equation of the metal track bracket in vertex form and standard form.
2. The coordinates where the bracket reaches the stage
3. The number of lights required to fill the bracket
4. The height of each light bulb
Ceiling
Chain
Lights
Note: This image is not
drawn to scale of the task
and NOT an accurate
representation of the act
Centre Stage

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

cretdit to source

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).

answer: i wpould go with c

step-by-step explanation:

it would take 5 hours i think idk i'm not that good at math.can you me with my questions i need asap.