Lizzie came up with a divisibility test for a certain number $m \neq 1$: Break a positive integer $n$ into two-digit chunks, starting from the ones place. (For example, the number $354764$ would break into the two-digit chunks $64, 47, 35.$)

Find the alternating sum of these two-digit numbers, by adding the first number, subtracting the second, adding the third, and so on. (In our example, this alternating sum would be $64-47+35=52.$)

Find $m,$ and show that this is indeed a divisibility test for $m$ (by showing that $n$ is divisible by $m$ if and only if the result of this process is divisible by $m$).

Line segment eg is partitioned by point f in the ratio 1: 1. point e is at e (0, 4), and point f is at (1, 3). what are the coordinates of point g? (−1, 5) (2, 2) (3, 1) (4, 0)

For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius and height 2r minus the volume of two cones, each with a radius and height of r. a cross section of the sphere is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is the volume of the cylinder with radius r and height 2r is and the volume of each cone with radius r and height r is 1/3 pie r^3. so the volume of the cylinder minus the two cones is therefore, the volume of the cylinder is 4/3pie r^3 by cavalieri's principle. (fill in options are: r/2- r- 2r- an annulus- a circle -1/3pier^3- 2/3pier^3- 4/3pier^3- 5/3pier^3- 2pier^3- 4pier^3)

Find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x â’ 1 , y = 0, x = 5; about the x-axis v = sketch the region. sketch the solid, and a typical disk or washer.