Aball is thrown across a playing field from a height of h = 6 ft above the ground at an angle of 45° to the horizontal at the speed of 20 ft/s. it can be deduced from physical principles that the path of the ball is modeled by the functiony = −32/((20)^2)x^2 + x + 6 where x is the distance in feet that the ball has traveled horizontally find the maximum height attained by the ball. (round your answer to three decimal places.)

(b) find the horizontal distance the ball has traveled when it hits the ground. (round your answer to one decimal place.

Browning labs is testing a new growth inhibitor for a certain type of bacteria. the bacteria naturally grows exponentially each hour at a rate of 6.2%. the researchers know that the inhibitor will make the growth rate of the bacteria less than or equal to its natural growth rate. the sample currently contains 100 bacteria. the container holding the sample can hold only 300 bacteria, after which the sample will no longer grow. however, the researchers are increasing the size of the container at a constant rate allowing the container to hold 100 more bacteria each hour. they would like to determine the possible number of bacteria in the container over time. create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.

The perimeter of a stage is 116 feet. it is 17 feet wide. how long is it?

Aclothing designer is selecting models to walk the runway for her fashion show. the clothes she designed require each model’s height to be no more than y inches from 5 feet 10 inches, or 70 inches. which graph could be used to determine the possible variance levels that would result in an acceptable height, x?