Find the area of the following shape. you must show all work to receive credit.
1 answer:
Answer:
<h2>A = 57</h2>Step-by-step explanation:
Use the Pick's theorem
Let P be a polygon in the plane whose vertices have integer coordinates. Then the area of P can be determined just by counting the lattice points on the interior and boundary of the polygon!
In fact, the area is given by
where <em>i</em> is the number interior lattice points, and<em> b</em> is the number of boundary lattice points.
Look at the picture.
Substitute:
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9514 1404 393
Answer:
- after 7 minutes
- 19,600 feet
Step-by-step explanation:
Here's the "pencil and paper" solution:
The two altitude equations are ...
- y = 41300 -3100x
- y = 2800x
They can be solved by setting the expressions for y equal to each other.
2800x = 41300 -3100x
5900x = 41300
x = 41300/5900 = 7
y = 2800·7 = 19600
The planes will both be at 19,600 feet after 7 minutes.
_____
Attached are solutions from a graphing calculator, and from a calculator app that is able to solve systems of equations.
I find the graphing calculator the easiest to use. I can enter equations using a keyboard, and the solution is displayed in a form that can be copied and pasted.
The calculator app on my phone requires equation entry using a small on-screen keyboard, with multiple key hits required to access some functions. (y is obtained by hitting the x key twice, for example.)
The "pencil and paper" solution is not so difficult, but requires a certain amount of writing (or good short-term memory). The solutions for x and y require separate calculations, whereas the other methods give both x and y at the same time.
