Answer:
He showed that f(n) ÷ f(n - 1) was a constant ratio.
Given that Jake has proved that a function f(x) is a geometric sequence.
GEOMETRIC SEQUENCE: A geometric sequence is a sequence of numbers where each term is found by multiplying the preceding term by a constant called the common ratio, r.
So, in Jame's proof, he showed that each term is multiplied by a constant to get the next term.
That is, if 'c' is the constant that was used in the proof, then we must have
This implies that
Therefore, he showed that f(n) ÷ f(n - 1) was a constant ratio.
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


The answer is C. You can make a rectangle by putting the diagonals through the center anywhere, but if you want a square, you have to put the two diagonals perpendicular to each other and join their ends. See the diagram.
Through any two points there is exactly one line
Answer:
3.14
Step-by-step explanation:
The formula for the area of a circle is
, where r is the radius. In this circle, the area would therefore be
. However, since this is only a quarter circle, you need to divide the area by 4, meaning that the area of this shape is 3.14 square units. Hope this helps!