1. Briana is shopping for a new cell phone provider. In her city 3 providers: Company A, Company B and Company C. Cell phone radio towers broadcast a cell phone signal in a circular pattern. The table below shows the locations of the cell phone towers for the three companies as well as the coverage radius.
TowerLocationCoverage Rasius
Company Adowntown 4 miles
Company B
Coast (2 miles west and 4 miles north of Downtown)
5 miles
Company CPark (4 miles east and 4 miles north of downtown)3 miles
Using Downtown as the origin (0, 0), write the equations of the coverage radius for each tower.
Briana's house is located 2 miles east and 5 miles north of Downtown. Her job is located 3 miles to the south of her house. Which service provider should she choose in order to ensure she is covered at both locations? Explain your answer.
2.A carpenter wants to build a elliptical table top from a 4 foot by 6 foot sheet of plywood. She traces out the ellipse using a string attached to thumbtacks located at the foci of the ellipse. How far apart are the thumbtacks if the carpenter wants to cut out the largest possible ellipse from the plywood? Give your answer in exact radical form.
3.The paths of two comets are represented by the hyperbola with the equation 9x^2-5y^2-54x-10y+31=0.Each branch represents the path of one comet.What are the points along each path at which the comets' paths are closest? Give your answers in exact radical form.
4.A kicker kicks a football toward the opponent's goal line during a game. The ball begins its flight with an initial velocity of 70 ft/s when it is kicked at a height of 2 ft by the kicker. To the nearest foot, what maximum height will the ball reach? The height of the football, h,after t seconds is given by the function h(t)= 1/2 gt^2+v0t+h0. Where v0 is the initial vertical velocity, h0 is the initial height, and g=-32 ft/s^2 is the downward acceleration due to gravity.
p.s. i need help setting these word problems up, i not asking for yall to just hand me the answer. if you cant help without rudeness keep it scrolling pls & thank you.
