A. 2x^2 - 3x + 10 = 2x + 21
2x^2 - 3x - 2x + 10 - 21 = 0
2x^2 - 5x - 11 = 0 (quadratic equation)
2x^2 - 6x - 7 = 2x^2
2x^2 - 2x^2 - 6x - 7 = 0
-6x - 7 = 0 (not a quadratic equation)
5x^2 + 2x - 4 = 2x^2
5x^2 - 2x^2 + 2x - 4 = 0
3x^2 + 2x - 4 (quadratic equation)
5x^3 - 3x + 10 = 2x^2
5x^3 - 2x^2 - 3x + 10 = 0 (not a quadratic equation)
Therefore, options a and c can be solved using the quadratic formula.
Answer:
The curvature is 
The tangential component of acceleration is 
The normal component of acceleration is 
Step-by-step explanation:
To find the curvature of the path we are going to use this formula:

where
is the unit tangent vector.
is the speed of the object
We need to find
, we know that
so

Next , we find the magnitude of derivative of the position vector

The unit tangent vector is defined by


We need to find the derivative of unit tangent vector

And the magnitude of the derivative of unit tangent vector is

The curvature is

The tangential component of acceleration is given by the formula

We know that
and 
so

The normal component of acceleration is given by the formula

We know that
and
so

Answer:
n = 8 or n = −6
Explanation:
First, isolate the absolute value:
5 − |n − 1| = −2
7 − |n − 1| = 0
7 = |n − 1|
Then, split this into two equations, since the result of the absolute value could be positive or negative:
7 = n − 1 7 = −(n − 1)
8 = n 7 = −n + 1
n = −6
Answer:
21 3/4 - 13 1/8 = 8 5/8 ft longer
Step-by-step explanation:
We subtract the blue rope from the green rope
21 3/4 - 13 1/8
We need to get a common denominator of 8
21 3/4*2/2 - 13 1/8
21 6/8 - 13 1/8
8 5/8