Find the sum of a finite geometric sequence from n = 1 to n = 8, using the expression −2(3)^n − 1.

Graph the system: f(x)= 3/x-2; f(x)= 1/2x + 2

Find the solution(s) to the system of equations. select all that apply y=x^2-1 y=2x-2

Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?