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:
(a)
,
,
,
,
,
,
.
(b)
,
,
,
,
,
,
,
.
Step-by-step explanation:
In this exercise we only need to recall the formula for C(n,k):

where the symbol
is the factorial and means
.
By convention 0!=1. The most important property of the factorial is
, for example 3!=1*2*3=6.
(a) The explanations to the solutions is just the calculations.
.
(b) The explanations to the solutions is just the calculations.
For all the calculations just recall that 4! =24 and 5!=120.
Answer:
the difference is 25
Step-by-step explanation:
to get from 10 to 0 is 10 units and from 0 to -15 is 15
10+15 = 25
3 + 2 = 4 + 1 is true
1 +2 = 3 + 3 and 0 + 3 = 3+1 is not true
Emma's estimate is not reasonable because a serving of soup is typically about 1-2 cups and 2 quarts = 8 cups.
would you eat 8 cups of soup? no.