The height of a rocket, launched from the ground, is given by the function y=30t-5t^2, where y is in meters and t is in seconds. An observer is sitting at ground level a distance d from the launch point. If r is the distance between the observer and where the rocket is, show that dr/dt= (30t-5t^2)(30-10t)/sqrt(30t-5t^2)^2 + d^2. Show all your work.

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?

Change negative exponents to positive. then solve. round to four decimal places

Which of the following is a cost homeowners insurance does not protect? a. the cost of repair or replacement of a home lost in a natural disaster. b. additional living expenses required while your home is repaired after a disaster. c. replacement costs for all contents in your home, including high cost electronics. d. the cost of medical expenses incurred by somebody getting injured on your property. select the best answer from the choices provided