Answer:
a) 
b) 
Step-by-step explanation:
Recall that given a function f(x,y,z) then
. To find f, we will assume it exists and then we will find its form by integration.
First assume that F =
. This implies that
if we integrate with respect to x we get that
for some function g(y,z). If we take the derivative of this equation with respect to y, we get
This must be equal to the second component of F. Then

This implies that
, which means that g depends on z only. So 
Taking the derivative with respect to z and making it equal to the third component of F, we get
which implies that
which means that g(z) = K, where K is a constant. So

b) To evaluate
we can evaluate it by using f. We can calculate the value of f at the initial and final point of C and the subtract them as follows.

Recall that
so
Also
so
So 
I swear i just saw this on discord
Answer:
6 inches
Step-by-step explanation:
The perimeter of a triangle is a + b + c
Where, a, b, c are the length of the 3 sides of the triangle ;
Using the ruler ;
a = 1.5
b = 2
c = 2.5
Therefore,
a + b + c
1.5 + 2 + 2.5
= 6 in
Answers:
B = 50
a = 10.9
c = 17.0
================================================
Explanation:
This is a right triangle, so the acute angles are complementary, meaning they add to 90
B+40 = 90
B+40-40 = 90-40
B = 50
Also, because this is a right triangle, we can use trig ratios to compute the missing sides
tan(angle) = opposite/adjacent
tan(40) = a/13
a = 13*tan(40)
a = 10.908
a = 10.9
cos(angle) = adjacent/hypotenuse
cos(40) = 13/c
c*cos(40) = 13
c = 13/cos(40)
c = 17.0
note: make sure your calculator is in degree mode
The equation that represents this hanger is: 4w=25
The weight of one circle is: 6.25