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When we estimate distances from velocity data, it is sometimes necessary to use times
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Calculus, Early Transcendentals
- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forward#4 4.3 Please show workarrow_forwardAstronomer Edwin Hubble postulated a relationship between the distance between Earth and the velocity at which a galaxy appears to be traveling away from Earth. The following table shows observations of seven galaxies. Distance is measured in megaparsecs (1 Mpc is approximately 3,260 light-years), and velocity is measured in kilometers per second. Distance (Mpc) Velocity (km/s) 51.8 4,590 12.2 1,234 271 17,695 46.2 3,752 58.2 5,118 46.2 3,752 29.1 1,734 (a) Find the equation of linear regression line for the data where distance is the independent variable, x, and velocity is the dependent variable. (Round your numerical answers to two decimal places.) ŷ = (b) Using the equation from part (a), estimate the velocity (in kilometers per second) at which a galaxy 110 Mpc from Earth is traveling. (Round your answer to the nearest whole number.) km/sarrow_forward
- (b) Use a calculator to verify that Ex = 152.8, Ex² = 3428.98, Ey = 244, Ey2 = 9570 and Exy = 5475.4. %3D %3D %3D Compute r. (Round your answer to four decimal places.) dons the yalue of r imply that y should tend to increase or decrease? Explain your answer.arrow_forwardA body moves on a coordinate line such that it has a position s = f(t) =t - 5t + 4 on the interval 0 sts7, with s in meters and t in seconds. a. Find the body's displacement and average velocity for the given time interval. b. Find the body's speed and acceleration at the endpoints of the interval. c. When, if ever, during the interval does the body change direction? ..... The body's displacement for the given time interval is m. (Type an integer or a simplified fraction.)arrow_forwardWhen we estimate distances from velocity data, it is sometimes necessary to use times to, t₁, t2, t3, ... that are not equally spaced. We can still estimate distances using the time periods At; = t; t₁1. For example, a space shuttle was launched on a mission, the purpose of which was to install a new motor in a satellite. The table provided gives the velocity data for the shuttle between liftoff and the jettisoning of the solid rocket boosters. Use these data to estimate the height, h, above Earth's surface of the space shuttle, 62 seconds after liftoff. (Give the upper approximation available from the data.) h = ft Event Time (s) Velocity (ft/s) Launch 0 Begin roll maneuver 10 End roll maneuver 15 Throttle to 89% 20 Throttle to 67% 32 Throttle to 104% 59 Maximum dynamic pressure 62 Solid rocket booster separation 125 0 180 319 442 742 1100 1453 4151arrow_forward
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