The figure shows red point P at rest on the x-axis. If it has a constant angular acceleration a= 1.28 rad/s2 and the circle's radius is 1.24 m, calculate the time Tit takes to complete one revolution. Y T=_ S x Record your numerical answer below, assuming three significant figures. Remember to include a "_" as necessary.
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- econds squared, Ol 72. n divide out and T = VT². The factor 2T has no units so a in the analysis. 10. The period of rotation of the Sun is 2.125 x 10° seconds. This is equivalent to 2.125 (3) Ms (1) us (2) ms (4) Ts 11. Human hair grows at the rate of 3 nanometers per second. This rate is equivalent to (1) 3 x 10-3 m/s (2) 3 x 10-6 m/s (3) 3 x 10-9 m/s (4) 3 x 10-12 m/s 12. The wavelength of red light is 7 x 10-7 meter. Express this value in nanometers. 13. If m represents mass in kg, v represents speed in m/s, and r represents radius in m, show that the force F in the formula F = in the unit kg m/s?. mv? can be expressed 14. If PE, represents the potential energy stored in a spring in kg m2/s², and x represents the change in spring length from its equilibrium position in m, what is the unit for the spring constant k in the formula PE, = }kx?A quarter-circle plate has radius R. A triangular section is removed from the circle leaving the shaded shape shown below. The area of the figure can be expressed as some numerical factor times R². Determine the numerical factor with 3 digits. Exception: if the first digit of the numerical factor is 1, include 4 digits on your answer. R RThe wheel of an odometer has a radius of 30.00 cm. It was used to measure the distance between two stations A and B. If the odometer counter reads 226. How far is the distance from A to B? Express your answer in meters.
- The height of a certain hill (in feet) is given by h(x, y) = 10 (2xy - 3 x^2 - 4y^2 -18x +28y + 12), where y isthe distance in miles (north), x the distance east of South Hadley, Massachusetts.a.) Where is the top of the hill located? b.) How high is the hill? c.)How steep is the slope (in feet per mile) at a point 1 mile north and one mile east of South Hadley? Inwhat direction is the slope steepest, at that point? d.) Make a contour map and a 3D plot of the area surrounding South Hadley, from 8 miles west to 4 mileseast, and 2 miles south to 8 miles north. Plot only positive heights on the 3D graph; use If to help yououtSolve the ff. problems by providing a solution. Round-off your answer to the nearest hundredths (with 2 decimal places).Calculate the value of the error with one decimal place for: z = x/y where x = 8.9 +/- 0.5 and Please enter the answer without +/- sign. y = 4 +/- 0.2
- Supply all missing information with the correct numerical values. Do not include the units. Round off all answers to two decimal places. Do not forget the negative sign (-) if needed. Borsalino wants to buy some ice cream in the nearest convenience store. He has to walk 5.3 meters, 12 degrees in the north of east direction to reach the doorstep of the convenience store. He then enters the store and walks straight to cashier, two meters due northwest. Let A be the displacement vector with a magnitude of 5.3 meters directed 12 degrees in the north of east direction, and let B be the displacement vector with a magnitude of two meters due northwest. Express vectors A and B in unit vector component form. A = B = î+ R = î. The net displacement is given by the vector sum: R=A+B. By Pythagorean theorem, the magnitude of the displacement is: IRI= meters. The direction of the resultant displacement is 4= north of east. 7Supply all missing information with the correct numerical values. Do not include the units. Round off all answers to two decimal places. Do not forget the negative sign (-) if needed. Borsalino wants to buy some ice cream in the nearest convenience store. He has to walk 5.3 meters, 12 degrees in the north of east direction to reach the doorstep of the convenience store. He then enters the store and walks straight to cashier, two meters due northwest. Let A be the displacement vector with a magnitude of 5.3 meters directed 12 degrees in the north of east direction, and let B be the displacement vector with a magnitude of two meters due northwest. Express vectors A and B in unit vector component form. À = B = The net displacement is given by the vector sum: R = À +B. Ř= By Pythagorean theorem,the magnitude of the displacement is: meters. %3D The direction of the resultant displacement is: north of east.Supply all missing information with the correct numerical values. Do not include the units. Round off all answers to two decimal places. Do not forget the negative sign (-) if needed. Borsalino wants to buy some ice cream in the nearest convenience store. He has to walk 5.3 meters, 12 degrees in the north of east direction to reach the doorstep of the convenience store. He then enters the store and walks straight to cashier, two meters due northwest. Let Å be the displacement vector with a magnitude of 5.3 meters directed 12 degrees in the north of east direction, and let B be the displacement vector with a magnitude of two meters due northwest. Express vectors A and B in unit vector component form. A = B = + The net displacement is given by the vector sum: Ř =Á + B. + By Pythagorean theorem, the magnitude of the displacement is: |Ř = meters. The direction of the resultant displacement is: $ = north of east
- Supply all missing information with the correct numerical values. Do not include the units. Round off all answers to two decimal places. Do not forget the negative sign (-) if needed. Borsalino wants to buy some ice cream in the nearest convenience store. He has to walk 5.3 meters, 12 degrees in the north of east direction to reach the doorstep of the convenience store. He then enters the store and walks straight to cashier, two meters due northwest. Let A be the displacement vector with a magnitude of 5.3 meters directed 12 degrees in the north of east direction, and let B be the displacement vector with a magnitude of two meters due northwest. Express vectors A and in unit vector component form. À= ぐー B = 7+ The net displacement is given by the vector sum: Ř =Á +B. Ř= 7+ By Pythagorean theorem,the magnitude of the displacement is: |Ř = meters. The direction of the resultant displacement is: 3D north of east.Supply all missing information with the correct numerical values. Do not include the units. Round off all answers to two decimal places. Do not forget the negative sign (-) if needed. Borsalino wants to buy some ice cream in the nearest convenience store. He has to walk 5.3 meters, 12 degrees in the north of east direction to reach the doorstep of the convenience store. He then enters the store and walks straight to cashier, two meters due northwest. Let À be the displacement vector with a magnitude of 5.3 meters directed 12 degrees in the north of east direction, and let B be the displacement vector with a magnitude of two meters due northwest. Express vectors and in unit vector component form. %3! + B = + Ř=À +B. The net displacement is given by the vector sum: Ř= By Pythagorean theorem,the magnitude of the displacement is: IŘ = meters. !3! The direction of the resultant displacement is: north of east.Supply all missing information with the correct numerical values. Do not include the units. Round off all answers to two decimal places. Do not forget the negative sign (-) if needed. Borsalino wants to buy some ice cream in the nearest convenience store. He has to walk 5.3 meters, 12 degrees in the north of east direction to reach the doorstep of the convenience store. He then enters the store and walks straight to cashier, two meters due northwest. Let A be the displacement vector with a magnitude of 5.3 meters directed 12 degrees in the north of east direction, and let B be the displacement vector with a magnitude of two meters due northwest. Express vectors A and B in unit vector component form. À = B - Î + The net displacement is given by the vector sum: R = Á + B. Ř = By Pythagorean theorem,the magnitude of the displacement is: |Ř| = meters. The direction of the resultant displacement is: north of east.