Determine if the following statements are true or false. (a) if ∫c vector f · d vector r = 0 for one closed path c, then vector f is path-independent. true false (b) if the total change of a function f along a curve c is zero, then c must be a contour of f. true false (c) line integralc vector f · d vector r = vector f(q) - vector f(p) when p and q are the endpoints of c. true false (d) if vector f is continuous and vector f = gradf, then vector f is path-independent. true false (e) if f(x) and g(y) are continuous one-variable functions, then the vector field vector f = f(x)vector i + g(y)vector j is path-independent. true false (f) the vector field vector f( vector r ) = vector r in 3-space is path-independent.

rectangle: 9 1/8 x 4 1/9 = 37 37/72in

parallelogram: b times h= 10.3 x 6.2 = 63.86

trapezoid: a+b/2 times h= 42.5

volume of prism: l times w times h= 36

step-by-step explanation:

i have done this all on a piece of paper but idk how to put it on here cuz it needs to be drawn

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.