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Answer:
f x y z 4y cos (< x >) y x sin z z xy k s is the hemisphere x2 y2 z2 25 z ≥ 0 oriented upward
use stokes theorem to evaluate f dr
s is the hemisphere x 2 y 2 z 2 16
consists of the top and the four sides but not the bottom of the cube with vertices oriented outward
stokes theorem triangle with vertices
f xyz x y 2 i y z 2 j z x 2 k where k is the triangle with vertices
∫ f ∙ dr c when f x y z 2xi 3zj xk and c is the triangle with vertices 0 0 0 1 1 1 and 0 0 2
s is the part of the paraboloid z 1 − x2 − y2 that lies above the xy plane oriented upward
Answer:
Step-by-step explanation:
The triangle is a right angle triangle. This is because one of its angles is 90 degrees.
Let us determine x
Taking 47 degrees as the reference angle,
x = adjacent side
11 = hypotenuse
Applying trigonometric ratio,
Cos # = adjacent side / hypotenuse
# = 47 degrees
Cos 47 = x/11
x = 11cos47
x = 11 × 0.6820
x = 7.502
Let us determine y
Taking 47 degrees as the reference angle,
y = opposite side
11 = hypotenuse
Applying trigonometric ratio,
Sin # = opposite side / hypotenuse
# = 47 degrees
Sin 47 = y/11
x = 11Sin47
x = 11 × 0.7314
x = 8.0454
Answer:
88 hours on dump truck
24 hours on fire engine
Minimum cost is $3480
Step-by-step explanation:
D > 0; f >0
Plant A : 10d+5f >100
Plant B: 5d +15f >800
Cost:
C(x,y)+30D+35F
197 days....200-3 days = 197
