The table to below gives the orbital periods T (in years) of the planets known to Newton as a function of their mean distance R from the sun in AUs (where 1 AU = the earth’s mean orbital radius). Plot plot a log-log graph of the period versus the distance on the graph paper provided as Figure 5.6 on the next page.

What is the location of point g, which partitions the directed line segment from d to f into a 5: 4 ratio? –1 0 2 3

Which of the statements about the graph of the function y = 2x are true? check all of the boxes that apply. the domain is all real numbers x because the exponent of 2 can be any real number when the x-values increases by 1 unit, the y-value multiplies by 2. the y-intercept is (0, 1). the graph never goes below the x-axis because powers of 2 are never negative. the range is all real numbers.

Consider a cube that has sides of length l. now consider putting the largest sphere you can inside this cube without any point on the sphere lying outside of the cube. the volume ratio -volume of the sphere/ volume of the cube is 1. 5.2 × 10−1 2. 3.8 × 10−1 3. 1.9 4. 2.5 × 10−1 5. 3.8