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4 years ago

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Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = x2z2i + y2z2j + xyzk, S is the part of the paraboloid z = x2 + y2 th

at lies inside the cylinder x2 + y2 = 16, oriented upward.

1 answer:

worty [1.4K]4 years ago

7 0

Answer:

0

Step-by-step explanation:

CHECK ATTACHMENT

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Find the hypotenuse of each isosceles right triangle when the legs are of the given measure. 6 sqrt 2

Gemiola [76]

Isosceles right triangles have two equal sides (a and b) that are not the hypotenuse (c). And when two sides are equal, so are their opposite angles. There are only 180° degrees in any triangles, thus the right angle = 90°, so 90 left for the two equal, means that 2x=90,
x = 45°.

There are several ways to go about solving a triangle like this. The best and easiest is simply to memorize that the hypotenuse is exactly root2 times the other sides. Or, each isosceles side is the hypotenuse (c) ÷ root2
$a = b = c \div \sqrt{2} \\ c = a\sqrt{2} \\ c = 6 \sqrt{2} \times \sqrt{2} = 6 \times 2 = 12$
Another way to do it is the longer proof of Pythagorean Theorem:
${c}^{2} = {a}^{2} + {b}^{2}... \: \: c = \sqrt{({a}^{2} + {b}^{2})} \\$
$c= \sqrt{({6 \sqrt{2}) }^{2} + ({6 \sqrt{2})}^{2}} \\ = \sqrt{(2 \times{(6 \sqrt{2} )}^{2} )} = \sqrt{2(36 \times 2)} \\ c = \sqrt{144} = 12$

7 0

3 years ago

Our math team had m students last year, but this year it has already n students! By what percent did the number of students grow

AlekseyPX

For this case we are going to assume the following:
m: whole number greater than zero.
n: integer greater than zero.
Where,
n> m
According to these assumptions, the percentage of growth is given by the following formula:
$(n / m) * 100 - 100$
Answer:
the number of students did grow by:
$(n / m) * 100 - 100$

4 0

4 years ago

Read 2 more answers

I NEED REAL HELP IF NOT REAL GET BANNED

kari74 [83]

Answer:

Every minute, the hour hand moves 1/2 of a degree, and the minute hand moves 6 degrees. So in 48 minutes, the hour hand moves 24 degrees and the minute hand moves 288 degrees. 288-180-24=84. So, 84 degrees.

6 0

3 years ago

PLEASE HELP GUYS/GIRLS

den301095 [7]

Answer:

3

Step-by-step explanation:

7 0

3 years ago

In the cordinate plane what is the length of the line segment that connects points at (0, -1) and (-7, -2) ? Enter your answer i

allsm [11]

Answer:

≈ 7.07

Step-by-step explanation:

Calculate the length using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (- 7, - 2)

d = $\sqrt{(-7-0)^2+(-2+1)^2}$

= $\sqrt{(-7)^2+(-1)^2}$

= $\sqrt{49+1}$ = $\sqrt{50}$ ≈ 7.07

4 0

4 years ago