Write any two laws of indices in division and multiplication​

If sin θ=24/25 and 0 less than or equal to θ less than or equal to π/2, find the exact value of tan 2θ. answers; a) -527/336 b) -336/527 c)7/24 d) 24/7

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?

Answer asap! show all work! find the number of complex roots, the possible number of real roots and the possible rational roots of the polynomial function. then, solve for all roots. x^3 + 2x^2 + 3x + 6 = 0