If you project S onto the (x,y)-plane, it casts a "shadow" corresponding to the trapezoidal region
T = {(x,y) : 0 ≤ x ≤ 10 - y and -4 ≤ y ≤ 4}
Let z = f(x, y) = √(16 - y²) and z = g(x, y) = -√(16 - y²), each referring to one half of the cylinder to either side of the plane z = 0.
The surface element for the "positive" half is
dS = √(1 + (∂f/∂x)² + (∂f/dy)²) dx dy
dS = √(1 + 0 + 4y²/(16 - y²)) dx dy
dS = √((16 + 3y²)/(16 - y²)) dx dy
The the surface integral along this half is
You'll find that the integral over the "negative" half has the same value, but multiplied by -1. Then the overall surface integral is 0.
Answer:
x3 − 4x2 − 3 divided by x + 1 = x4−4x3+x−3 over x
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Step-by-step explanation:
Actually, DIEDERICK drove faster than BROOK. What you can do to find out the answer, is divide. Brook drove 180 miles in 3 hours, so divide 180 by 3, and you get 60. If you divide 160 by 4, you get 40. So, that means that Diederick drove faster than Brook.
Answer: 20
explanation: simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers
It is linear because it is a straight line when graphed. It is not proportional because there is not always a constant ratio between them.
