Vincent wants to build a rectangular vegetable garden with an area of 600 square feet. He has 100 feet of fence and wants to use all the fence to completely enclose the garden. He correctly uses the equation x(50−x)=600 to model the scenario, where x represents the length, in feet, of one side of the garden. To find the value of x, he correctly rewrites the equation in standard form as x2−50x+600=0. Which of the following statements best describes how to calculate the dimensions of the garden?   Answer A: The equation is equivalent to open parenthesis, x plus 20, close parenthesis, times, open parenthesis, x plus 30, close parenthesis, equals 0 , and it has two positive solutions, x equals 20 and x equals 30 , so the garden has dimensions of 20 feet by 30 feet.     Answer B: The equation is equivalent to open parenthesis, x minus 20, close parenthesis, times, open parenthesis, x minus 30, close parenthesis, equals 0 , and it has two positive solutions, x equals 20 and x equals 30 , so the garden has dimensions of 20 feet by 30 feet.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.