2 story problems for algebra 2/trig

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Homework Help Overview

The discussion revolves around two algebraic problems: one involving the motion of a ball thrown vertically and the other concerning the dimensions of a rectangular garden based on given perimeter and area. The first problem utilizes a quadratic equation to determine the time the ball remains above a certain height, while the second requires setting up a quadratic equation from the garden's dimensions.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants explore the setup of the quadratic equations for both problems, with some questioning the physical meaning of the solutions obtained for the ball's motion. Others discuss the need for two variables in the garden problem and the correct formulation of the quadratic equation.

Discussion Status

There is an ongoing exploration of the problems, with participants providing guidance on setting up equations and questioning assumptions. Some have identified potential errors in the formulation of the garden problem's equation, while others seek clarification on the implications of the solutions for the ball's motion.

Contextual Notes

Participants note that the first problem does not involve trigonometry, despite the thread title suggesting a connection to algebra 2/trigonometry. There is also mention of a sign error in the quadratic equation for the garden problem, indicating a need for careful attention to detail in the setup.

shemer77
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Homework Statement


1) A ball is thrown straight up with an initial velocity of 80 ft/s. Using the formula h=-16t^2 + 80t, determine the interval of time in which the ball is at least 64 feet above the ground?
2) The perimeter of a rectangular garden is 60ft. The area of the garden is 209 ft^2. Set up and solve a quadratic equation to determine the dimensions of the garden

For number 1 do i just do 64=-16t^2 + 80t?
 
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Those are fun problems. Neither of them rely on Trigonometry (referring to "algebr 2/trig" in your subject name). Your #2 needs two variables, maybe like x and y for the two dimensions of the reactangle. x+x+y+y=60 and x*y=209. DO IT!
 
shemer77 said:

Homework Statement


1) A ball is thrown straight up with an initial velocity of 80 ft/s. Using the formula h=-16t^2 + 80t, determine the interval of time in which the ball is at least 64 feet above the ground?
2) The perimeter of a rectangular garden is 60ft. The area of the garden is 209 ft^2. Set up and solve a quadratic equation to determine the dimensions of the garden

For number 1 do i just do 64=-16t^2 + 80t?
That's the first step. Of course, since that is a quadratic equation you can expect to get 2 solutions- and the problem asks for the "interval of time in which the ball is at least 64 feet above the ground". What do the two solutions to that quadratic equation represent physically?
 
1) I got 4 and 1, how is that possible?
2)I got y^2-30y-209=0 as my quadratic equation is that right?
 
shemer77 said:
1) I got 4 and 1, how is that possible?
2)I got y^2-30y-209=0 as my quadratic equation is that right?

No. You made a sign error. You want for #2, y^2-30y+209=0,
Then you are ready to finish the solution.
 
thanks, what about number 1?
 
Well do you understand what hallsofivy said? From the quadratic you concluded that the solution is x=1 and x=4. Do you know what these numbers actually represent physically for the ball in motion?
 

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