. Use strong induction to show that every positive integer can be written as a sum of distinct powers of two, that is, as a sum of a subset of the integers 20 =1, 21 =2, 22 =4, and so on. [Hint: For the inductive step, separately consider the case where k+1 is even and where it is odd. When it is even, note that (k+1)∕2 is an integer.]

Its due ! write an equation in which the quadratic expression 2x^2-2x 12 equals 0. show the expression in factored form and explain what your solutions mean for the equation. show your work.

You are saving to buy a bicycle; so far you save 55.00. the bicycle costs 199.00. you earn 9.00 per hour at your job. which inequality represents the possible number of h hours you need to work to buy the bicycle?

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?