Consider f and c below. f(x, y) = x2 i + y2 j c is the arc of the parabola y = 2x2 from (−1, 2) to (1, 2) (a) find a function f such that f = ∇f. f(x, y) = x3 3+ y3 3 correct: your answer is correct. (b) use part (a) to evaluate c ∇f · dr along the given curve c.

In this exercise we have to perform the parameterization of the given function and we will have:

In there is some scalar function such that:

Then we want to find such that:

So the vector filed is conservative, which means the fundamental theorem applies; the line integral of along any path parameterized by some vector-valued function over is given by:

In the case:

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H0 : μ1 - μ2 = 0

H0 : μ1 - μ2 > 0

Test statistic = 3.96

Critical value = 1.67

Reject H0

We can conclude that there is significant evidence to support the claim that geese do travel more Than pelicans

Step-by-step explanation:

M= xbar1 = 191 ; M = xbar2 = 190 miles

n1 = 61 n2 = 61

s = 1.429 ; s2 = 1.355

Hypothesis :

H0 : μ1 - μ2 = 0

H0 : μ1 - μ2 > 0

Test statistic :

(x1 - x2) ÷ √[(s1²/n1) + (s2²/n2)]

(191 - 190) ÷ √[(1.429²/61) + (1.355²/61)]

1 ÷ √[(0.0334760) + (0.0300987)]

1 ÷ √0.0635747

1 ÷ 0.2521402

= 3.966

Degree of freedom :

df = n - 1

df = 61 - 1 = 60

Critical value :

Tcritical at 0.05%, df = 60

Tcritical = 1.67

Decision region:

Reject H0 if Tstatistic > Tcritical

Since ;

3.96 > 1.67 ; We reject H0

We can conclude that there is significant evidence to support the claim that geese do travel more Than pelicans