Directions: For a spinning amusement park ride, the velocity v in meters per second of a car moving around a curve with a radius r meters is given by the formula v= √ar, where a is the car’s acceleration in m/s2. 1. For safety reasons, a ride has a minimum acceleration of 39.2 m/s2. If the cars on the ride have a velocity of 14 m/s what is the smallest radius that any curve on the ride may have?

2. What is the acceleration of a car moving at 8m/s around a curve with a radius of 2.5m?

Need ! give step by step solutions on how to solve number one [tex]\frac{9-2\sqrt{3} }{12+\sqrt{3} }[/tex] number two [tex]x+4=\sqrt{13x-20}[/tex] number three (domain and range) [tex]f(x)=2\sqrt[3]{x} +1[/tex]

Questions 9-10. use the table of educational expenditures to answer the questions. k-12 education expenditures population indiana $9.97 billion 6.6 million illinois $28.54 billion 12.9 million kentucky $6.58 billion 4.4 million michigan $16.85 billion 9.9 million ohio $20.23 billion 11.6million 9. if the amount of k-12 education expenses in indiana were proportional to those in ohio, what would have been the expected value of k-12 expenditures in indiana? (give the answer in billions rounded to the nearest hundredth) 10. use the value of k-12 education expenditures in michigan as a proportion of the population in michigan to estimate what the value of k-12 education expenses would be in illinois. a) find the expected value of k-12 expenditures in illinois if illinois were proportional to michigan. (give the answer in billions rounded to the nearest hundredth) b) how does this compare to the actual value for k-12 expenditures in illinois? (lower, higher, same? )

Given the expression (7 ? 4i) ? (2 + 6i), perform the indicated operation and write the answer in the form a + bi.