Theoretical models of the slowing of pulsars predict that the age of a pulsar is approximately equal to p/2r, where p is the pulsar’s current period and r is the rate at which the period is slowing with time. Observations of the pulsar in the Crab Nebula show that it pulses 30 times a second, so p = 0.0333 second, but the time interval between pulses is growing longer by 4.2 * 10–13 second with each passing second, so r = 4.2 * 10–13 second per second. Using that information, estimate the age of the Crab Nebula pulsar. How does your estimate compare with the true age of the pulsar, which was born in the supernova observed in a. d. 1054?

In exponential growth functions, the base of the exponent must be greater than 1,how would the function change if the base of the exponent were 1? how would the fiction change if the base of the exponent were between 0and 1

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24

Square a has a side length of (2x-7) and square b has a side length of (-4x+18). how much bigger is the perimeter of square b than square a?and show all work! you so