Answer:
8.69 × 10^4
For a clearer answer look at the image.
Step-by-step explanation:
10² + 10² = 10^4
5.84 + 2.85 = 8.69
8.69 × 10^4
The next larger thousandth is 36.994 .
The next smaller thousandth is 36.992 .
Neither of those is any nearer to 36.993
than 36.993 already is.
The last '3' at the end of 36.993 is in the thousandths' place.
There is no more piece of another thousandth after it.
So 36.993 is already on a complete thousandth, and
there's no rounding required.
Answer:
132.233 ft2
Step-by-step explanation:
Let's call the width of the rectangle 'w' and the length 'x'. So the area of the semicircle is:



And the area of the rectangle is:

If the perimeter of the window is 41 feet, we have:



Now, the equation for the total area of the window is:



To find the maximum area, we can find the x-coordinate of the vertex of the quadratic equation:

So the width that gives us the maximum area of the window is 6.45 feet, and the area will be:

This is a polygon with vertices on the lattice. Let's use Pick's Theorem,
A = (1/2) B + I - 1
where A is the area, B is the number of lattice points on the boundary and I is the number of lattice points in the interior.
In addition to the 3 vertices there are 3 more boundary points on UV and 6 more on WV, none on UV, B=3+3+6=12. In the interior I count I=9 lattice points.
A = (1/2) 12 + 9 - 1 = 14
Answer: 14
Obviously they just want us to say this is a right triangle, so the legs are altitude and base,
A = (1/2) b h (1/2) |UW| |WV| = (1/2) (4) (7) = 14
That checks.