Answer:
m = -75/4
Step-by-step explanation:
1. Subtract 95/4 from both sides
m + 95/4 = 5
x + 95/4 - 95/4 = 5 - 95/4
2. Simplify, which will get you -75/4
The answer is true it goes up by 5 every time
Y = 1/3x - 4 because y = mx + b the slope (m) is 1/3 and the y-intercept (b) is -4
Let
denote the rocket's position, velocity, and acceleration vectors at time
.
We're given its initial position

and velocity

Immediately after launch, the rocket is subject to gravity, so its acceleration is

where
.
a. We can obtain the velocity and position vectors by respectively integrating the acceleration and velocity functions. By the fundamental theorem of calculus,


(the integral of 0 is a constant, but it ultimately doesn't matter in this case)

and



b. The rocket stays in the air for as long as it takes until
, where
is the
-component of the position vector.

The range of the rocket is the distance between the rocket's final position and the origin (0, 0, 0):

c. The rocket reaches its maximum height when its vertical velocity (the
-component) is 0, at which point we have

