<p>Math question, #18 grid-in: Given a square with sides of 3, a smaller square with sides of sqrt 2 inside the larger square, and a common center for the two squares. If a circle were to be drawn inside the large square but outside the small square (touching neither), what is a possible value of the radius of the circle?</p>
<p>At first I thought that the radius could be anything greater than 1/2 the diagonal of the small square (which would be 1), and less than 1/2 the diagonal of the large square (which would be 1.5 x (sqrt 2). But then I thought that, no, the upper limit would actually be equal to 1/2 of the SIDE of the larger square (which would be 1.5). So I ended up answering 1.4</p>
<p>Anyone else remember this one? Did I get it wrong? Tricky problem.</p>
<p>i answered 1.45, because i got that half the diagonal of the inner square was 1.4, and half the side of the outer square was 1.5. i think you guys probably did it right, though, and we could answer anything between 1 and 1.5. did you guys anser "308" for that one asking for the product of P an R? i think it was 11 times 28. the math this time around seemed, overall, harder than the last 2 times i took the SAT I.</p>
<p>Math question, #18 grid-in: Given a square with sides of 3, a smaller square with sides of sqrt 2 inside the larger square, and a common center for the two squares. If a circle were to be drawn inside the large square but outside the small square (touching neither), what is a possible value of the radius of the circle?</p>
<p>are you sure about the 1 and 1.5 inclusive? cuz i'd be ecstatic if it were...but wouldn't it touch the tip of the square (that is the diagonal?)</p>
<p>and what about the parabola translation question? was it f(x) - 3 or f(x - 3)</p>
<p>So you have an outer square with an area of 9 and an inner square with sides of length sqrt (2). The radius of the circle has to be larger than half of the diagonal of the square with sides of sqrt (2) and smaller than 3/2. Using the pythagorean theorem, half of the diagonal of the inner square is 1, so 1 < x < 1.5 exclusive.</p>
<p>for f(x) - 3, i spent a bit of time on it, plugging in values... pretty much just plug in 0... f(0) = 2, and on the graph of g(x) the y intercept was -1, so the equation for g(x) was f(x) - 3, and so g(0) = 2 - 3 = -1</p>