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arsen [322]
3 years ago
7

Can somebody please help me with the highlighted question?

Mathematics
1 answer:
Brrunno [24]3 years ago
7 0
What does it say? half is cut off
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Find the area of the part of the sphere x2 + y2 + z2 = 100z that lies inside the paraboloid z = x2 + y2.
vekshin1
x^2+y^2+z^2=100z\iff x^2+y^2+(z-50)^2=50^2

The surface of interest can be parameterized by

\mathbf r(u,v)=\begin{cases}x(u,v)=50\cos u\sin v\\y(u,v)=50\sin u\sin v\\z(u,v)=50(\cos v+1)\end{cases}

with 0\le u\le2\pi and 0\le v\le\arccos\dfrac{49}{50}.

The area of the surface S is given by the surface integral

\displaystyle\iint_S\mathrm dA=\iint_T\left\|\mathbf r_u\times\mathbf r_v\right\|\,\mathrm du\,\mathrm dv

We have

\|\mathbf r_u\times\mathbf r_v\|=50^2\sin v

so the area is given by the double integral

\displaystyle50^2\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\arccos(49/50)}\sin v\,\mathrm dv\,\mathrm du=100\pi
6 0
3 years ago
PLEASE HELP!!! ill give you brainlest:)) TPWK!!!
docker41 [41]

Answer:

82m²

Step-by-step explanation:

split it into a rectangle and square

3x6=18

8x8=64

total area = 82

4 0
2 years ago
Read 2 more answers
A: 1/2
S_A_V [24]

A= -2

B= Y-1= -1/2 (X-3)

7 0
3 years ago
Read 2 more answers
What is the correct order of steps for bisecting angle ABC?
Marizza181 [45]

The correct order for bisecting angle ABC is F D E B C A. Option D

<h3>Steps in bisecting angles</h3>

The steps involved in bisecting angles are;

  • Place compass point on the vertex of the angle (point B).
  • Stretch the compass to any length that will stay OF the angle
  • Swing an arc so the pencil crosses both sides (rays) of the given angle. You should now have two intersection points with the sides (rays) of the angle
  • Place the compass point on one of these new intersection points on the sides of the angle. Stretch the compass to a sufficient length to place your pencil well into the interior of the angle, this should be within the rays of the angle
  • Place an arc in this interior
  • Without changing the span on the compass, place the point of the compass on the other intersection point on the side of the angle and make a similar arc. The two small arcs in the interior of the angle should be intersecting
  • Connect the vertex of the angle (point B) to this intersection of the two small arcs

From the listed steps, the correct order for bisecting angle ABC is F D E B C A. Option D

Learn more about bisectors here:

brainly.com/question/11006922

#SPJ1

8 0
1 year ago
how do you write y - 2 = -(x - 3) in slope-intercept form? A) y = x + 3 B) y = x - 1 C) y = -x + 5 D) y = -3x - 1
SashulF [63]
C) y= -x+5
explain:
y-2=-x+3
y= -x+3+2
so y= -x+5
5 0
2 years ago
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