Answer:
a.

b.


Step-by-step explanation:
Remember that for any curve
The tangent vector is given by

And the normal vector is given by

a.
For this case, using the chain rule

And also remember that

Therefore

Similarly, using the quotient rule and the chain rule

And also

Therefore

Notice that
1. 
2. 
b.
Simlarly

and

Therefore

Then

and also

And since

Answer:
6
Step-by-step explanation:
Given mixed operations there is a particular order that must be followed.
Using the order set out in the acronym PEMDAS
P - Parenthesis ( brackets ), E- Exponents ( powers ), M - Multiplication, D - Division, A- Addition, S - Subtraction
8 + 24 ÷ (2 × 6) - 4
= 8 + 24 ÷ 12 - 4 ← parenthesis
= 8 + 2 - 4 ← division
= 10 - 4 ← addition
= 6 ← subtraction
Step-by-step explanation:
With each draw, the probability of selecting a green marble is 2/3 and the probability of selecting a yellow marble is 1/3.
To pick two of the the same color, they can either pick green twice or yellow twice.
P = (2/3)(2/3) + (1/3)(1/3)
P = 5/9
To pick two different colors, they can either pick green first then yellow, or yellow first then green.
P = (2/3)(1/3) + (1/3)(2/3)
P = 4/9
Expected value for Derek is:
D = (5/9)(-1) + (4/9)(1)
D = -1/9
The expected value for Mia is:
M = (5/9)(1) + (4/9)(-1)
M = 1/9