The height of an arrow is shot upward at an initial velocity of 40 meters per second can be modeled by h=40t-5t^2 where h is the
1 answer:
We are given the equation for the height of the arrow. If you graph it, you see that it's a parabola and that the arrow kinda peaks and then falls back down. Another way of thinking about this problem is that you're looking for the time when the height is 0. You can see on the graph that there are two times that h=0. The first is obviously at t=0, when the arrow hasn't left the ground yet. The second is what we're looking for, when the arrow reaches the ground.
To solve this, let's set h=0. So 0=40t-5t^2. If you factor this, you get 5t(8-t) = 0. Continuing that leads to 5t=0 where t=0 which we already knew, and 8-t=0 where t=8. So that second time is when the arrow is back on the ground. Therefore your answer is 8 sec.
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We have been given that Sterre charges $35 to file tax returns, but files for free if she only needs the easiest form. Also, she donates $2 to clean water projects per tax return she files.
Further we know that Sterre charged $7,245 and made a donation of $1,242 this year for the tax returns she filed.
Let x be the number of free income tax returns and y be the number of $35 income tax returns.
Therefore, we can set up:
Since she donates $2 for each return that she files, therefore, we can set up:
Therefore,
Sterre filed 414 tax returns for free and filed 207 tax returns for $35.