stuck on three math questions

Test Preparation SAT Preparation
1

<p>I would be grateful if people can help.</p>

<ol>
<li><p>ok there is a diagram and I will try to explain itwith words. theres a semicircle drawn in the first and second quadrant. point R is on the negative x-axis while the opposite point is on the positive x-axis. the given point S on the semicircle is (1.5, 4) and it is the greatest y-coordinate of the semicircle. the question says to find the x-coordinate of point r. the answer is E but I can't figure out why.
a.-5.5
b. -4
c. -3.5
d.-3
e.-2.5</p></li>
<li><p>the tin can in the figure above is a cylinder that is 8 inches high and has a base of radius 3 inches. of 5 pencils with lengths 6 inches, 8.5 inches, 9 inches, 10.5 inches and 12 inches, how many cannot fit entirely inside the can?answer is 4 but dont know why.</p></li>
<li><p>LM is 7 and MN is 8, which of the following could be hte length of LN. answer is 14. can someone elaborate why?</p></li>
</ol>

<p>thanks</p>

<p>edit-btw all questions are from the collegeboard online course</p>

2

<p>1) I remember this problem, but I can’t really explain without the diagram.</p>

<p>All I can tell you is determine the radius of the circle, and go from there to find another point on the circle.</p>

<p>2) The largest pencil that can fit in the can is the length of the hypotenuse of the triangle formed by the diameter of the base and the height of the cylinder.</p>

<p>3) Don’t restrict yourself to thinking that L,M, and N must be on a straight line. Imagine if they were vertices of a triangle, and apply the Triangle Inequality Theorem.</p>

3

<p>

</p>

<p>Are you sure the answer is 4 pencils cannot fit? Because the hypotenuse formed by the length and the diameter of the cylinder is 10. So, it goes to reason that the 6 in., 8.5 in., 9 in. pencils can fit while the 10.5 in. and 12 in. pencils can’t fit. Which would mean that 2 pencils can’t fit.</p>

4

<p>yea i got 2 as well but the answer sheet says 4. ill double check.</p>

<p>edit-nvm i read the answer sheet wrong.</p>

<p>aight thanks guys but I am still confused on number 1.</p>

5

<p>1) 4 is the point farthest away on the semicircle, so 4 is the radius of the circle.</p>

<p>Point R must also be 4 points away from the “center” of the semicircle, or (1.5, 0) because all points on a semicircle are equidistant from the center. 1.5 - 4 = -2.5</p>

6

<p>wow I don’t know how I missed that. thanks a lot.</p>