1. (10 pts) Suppose a circle is given, along with a chord that is NOT a...
7. (10) Find the flaw in the following attempted proof of the parallel postulate by Wolfgang Bolyai (Hungarian, 1775 - 1856) (see Fig. 3). Given any point P not on a line l, construct a line 1' parallel to through P in the usual way: drop a perpendicular PQ to / and construct /" perpendicular to PQ. Let I" be any line through P distinct from l'. To see that /" intersects I, pick a point A on PQ between...
The point (1, 10) is the center of a circle and (2, 3) lies on the circle. Find the equation of the line that coincides with the diameter of this circle. (a) (5 pts) Find the slope-intercept equation of the line passing through the two given points. Show work.
Find the measure 9.BC 34 116 90 32 124 128 Suppose the diameter of a circle is 30 centimeters long and a chord is 24 10 penis centimeters long. Find the distance between the chord and the center of the circle 12 centimeters 9 centimeters 16 centimeters 13 centimeters none of the above Suppose a chord of a circle is 5 inches from the center and 24 inches long. Find the length of the radius. 1 points O 5 inches...
Modern Geometry Suppose P is a point on the line l. Justify the following construction for the line perpen- dicular to l through P. 1 • Pick a point O not on l and draw the circle with center 0 and radius OP. Let Q be the second point of intersection of this circle with l. • Draw the line (QO) and let R be the second point of intersection of this line with the circle. • Draw the line...
Results given on page 300 TABLE 12.2 Moments of inertia of objects with uniform density Object and axis Picture Object and axis Picture Thin rod, about center | Cylinder or disk, about center MR ML2 Thin rod, about end ML Cylindrical hoop. MR2 about center | Solid sphere, about diameter Маг Plane or slab, about center Ma2 MR Plane or slab, about edge Ma2 Spherical shell, about diameter MR2 1. b. A very thin, straight, uniform rod has a length...
Help Consider the circle shown in the figure. 10 0 1 2 345 6789 10 11 x (m) What is the diameter of the circle? Please, notice that the circle passes through a number of grid intersection points. 3.8m Sumi Anawr Incorrect. Tries 7/20 Previous Tries
2. (10 pts) Consider the points (-5, -6) and (-1, 10). (a) State the midpoint of the line segment with the given endpoints. (No work required) (b) If the point you found in (a) is the center of a circle, and the other two points are points on the circle, find the length of the radius of the circle. (That is, find the distance between the center point and a point on the circle.) Find the exact answer and simplify...
(3) The following exercise is based on the half-angle formulas. Use the fact that sin(/6) = 1/2 to prove that tan(+/12) - 2-V3. (4) Find real solutions of 3 cos + 4 sin 0 - 5/2. 6 - 10 (5) Express x2 + 4x + 1 in partial fraction form. (6) Consider a line L given by the equation y = 3. - 4. (a) Find an equation of the line parallel to L that passes through the point (2.10)....
all true or false statement. help! Jwotry aise ariswer roblem is worth 3 points. You will receive 1 point for the correct answer and 2 points for stification If a radius of a circle bisects a chord of a circle, then the radius must be perpendicular to the chord. The mid-point of a line segment having (5, 4) and (3,-2) as endpoints is (1, 1). If the discriminant for a particular equation is negative, the roots of that equation are...
Question 1 1 pts As in the figure, a uniform sphere of mass = 0.66 kg and radius r = 3.8 cm is supported by a string (of negligible mass) attached to a wall (whose friction can also be ignored). The center of the sphere is a vertical distance L = 9 cm below the attachment point of the string. Find the tension in the string. (Note that the direction of the tension (along the string) is along a line...