The mean diameters of X and Y, two planets in the same solar system, are 6.4 × 103 km and 1.8 x 104 km, respectively. The mass of X is 0.20 times the mass of Y. The value of g on Y is 8.4 m/s². (a) What is the ratio of the mean density of X to that of Y (px/py)? (b) What is the value of g on X? m/s² (c) The mass of Y is 1.020 x 1025 kg. What is the escape speed on X? m/s

Calculate the result for each of the following cases using the correct number of significant figures. a. 3.07670 10.988 b. 1.0093 105 9.98 104 c. 5.44231064.008103

A rod extending between x = 0 and x = 14.0 cm has uniform cross-sectional area A = 9.00 cm2. Its density increases steadily between its ends from 2.70 g/cm3 to 19.3 g/cm3. (a) Identify the constants B and C required in the expression = B + Cx to describe the variable density. (b) The mass of the rod is given by m=allmaterialdV=allxAdx=014.0cm(B+Cx)(9.00cm2)dx Carry out the integration to find the mass of the rod.

The average life expectancy in Japan is 81 years. What is this time in SI units?

Show that 3, by calculating the change in volume V of a cube with sides of length L.

A pirate has buried his treasure on an island with five trees located at the points (30.0 m, 20.0 m), (60.0 m, 80.0 m), (10.0 m, 10.0 m), (40.0 m, 30.0 m), and (70.0 m, 60.0 m), all measured relative to some origin, as shown in Figure P1.69. His ships log instructs you to start at tree A and move toward tree B, but to cover only one-half the distance between A and B. Then move toward tree C, covering one-third the distance between your current location and C. Next move toward tree D, covering one-fourth the distance between where you are and D. Finally move toward tree E, covering one-fifth the distance between you and E, stop, and dig. (a) Assume you have correctly determined the order in which the pirate labeled the trees as A, B, C, D, and E as shown in the figure. What are the coordinates of the point where his treasure is buried? (b) What If? What if you do not really know the way the pirate labeled the trees? What would happen to the answer if you rearranged the order of the trees, for instance, to B (30 m, 20 m), A (60 m, 80 m), E (10 m, 10 m), C (40 m, 30 m), and D (70 m, 60 m)? State reasoning to show that the answer does not depend on the order in which the trees are labeled. Figure 1.69

One student uses a meterstick to measure the thickness of a textbook and obtains 4.3 cm 0.1 cm. Other students measure the thickness with vernier calipers and obtain four different measurements: (a) 4.32 cm 0.01 cm. (b) 4.31 cm 0.01 cm, (c) 4.24 cm 0.01 cm, and (d) 4.43 cm 0.01 cm. Which of these four measurements, if any, agree with that obtained by the first student?

(a) Suppose that a person has an average heart rate of 72.0 beats/mm. How many beats does he or she have in 2.0 years? (b) In 2.00 years? (c) In 2.000 years?

In Jules Vernes novel, Twenty Thousand Leagues Under the Sea, Captain Nemo and his passengers undergo many adventures as they travel the Earths oceans, a. If 1.00 league equals 3.500 km, find the depth in meters to which the crew traveled if they actually went 2.000 104 leagues below the ocean surface. b. Find the difference between your answer to part (a) and the radius of the Earth, 6.38 106 m. (Incidentally, author Jules Verne meant that the total distance traveled, and not the depth, was 20,000 leagues.)

State how many significant figures are proper in the results of the following calculations: (a) (106.7)(98.2)/(46.210)(1.01) (b) (18.7)2 (c) (1.601019)(3712)