Suppose f⃗ (x, y)=−yi⃗ +xj⃗ and c is the line segment from point p=(5,0) to q=(0,4).

(a) find a vector parametric equation r⃗ (t) for the line segment c so that points p and q correspond to t=0 and t=1, respectively. r⃗ (t)=
(b) using the parametrization in part (a), the line integral of f⃗ along c is ∫cf⃗ ⋅dr⃗ =∫baf⃗ (r⃗ (t))⋅r⃗ ′(t)dt=∫ba dt with limits of integration a= and b=
(c) evaluate the line integral in part (b).
(d) what is the line integral of f⃗ around the clockwise-oriented triangle with corners at the origin, p, and q?
hint: sketch the vector field and the triangle.

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18

answer: y=4000x+14000

step-by-step explanation:

answer: ⇒ d. (7.3)(8.52)=62.19

step-by-step explanation:

product it's going to be multiply by the numbers, fractions, factors, and multiples.

1. (29.5)(1.7)=50.15

2. (13.2)(4.5)= 59.4

3. (4.67)(9.8)= 45.76

4. (7.3)(8.52)= 62.19

hope this !

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