The angle of elevation to a nearby tree from a point on the ground is measured to be 45^{\circ} ∘ . How tall is the tree if the point on the ground is 79 feet from the tree? Round your answer to the nearest hundredth of a foot if necessary.

You invested $5000 between two accounts paying 4% and 9% annual interest, respectively. if the total interest earned for theyear was $350, how much was invested at each rate? $was invested at 4% andwas invested at 9%.

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?

Three students, javier, sam, and corrine, participated in a fundraiser where people donated a certain amount of money per lap that the student ran. each student also had some initial donations that were collected before the run. the equations that represent each student's total donation, y, based on the number of laps ran, x, is shown below. match each equation with the correct rate of change for that student.