In the diagram of circle O, tangent PB is drawn as is secant PAC. We wish to prove the Secant/Tangent Length Theorem, i. e. PA x PC = PB^2. (a) Explain why PAB is similar to ΔPBC (i. e. explain which two angles pairs must be congruent and why).
(b) Set up a proportion involving PA, PB, PC, and based on the similar triangles and rewrite it in product form. Draw the two similar triangle separately and in the same orientation to help.

Since opening night, attendance at play a has increased steadily, while attendance at play b first rose and then fell. equations modeling the daily attendance y at each play are shown below, where x is the number of days since opening night. on what day(s) was the attendance the same at both plays? what was the attendance? play a: y = 8x + 191 play b: y = -x^2 + 26x + 126

In the following diagram it is given that dec, ab || dc, ad || eb, and ad is congruent to bc. a)why isn't abc a parallelogram even though it has a pair of parallel sides and a pair of congruent sides b)explain why be must be congruent to bc. further explain what type of triangle this makes triangle abc and what it tells you about angle 1 and angle 2c) finally why must angle 3 be congruent to angle 1? further, explain why we know that angle 3 is congruent to angle 2

Find the volume of the solid obtained by rotating the region enclosed by the curves y=1x and y=7^-x about the x-axis. (use symbolic notation and fractions where needed.) volume =