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bazaltina [42]
2 years ago
12

Replace the ? with one of the following symbols (<, >, =, or ≠) for 4 + 3 + 7 ? 7 + 0 +7 A. > B. ≠ C. = D. <

Mathematics
1 answer:
ExtremeBDS [4]2 years ago
6 0
What do you mean as that
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Find the surface area of x^2+y^2+z^2=9 that lies above the cone z= sqrt(x^@+y^2)
Mashcka [7]
The cone equation gives

z=\sqrt{x^2+y^2}\implies z^2=x^2+y^2

which means that the intersection of the cone and sphere occurs at

x^2+y^2+(x^2+y^2)=9\implies x^2+y^2=\dfrac92

i.e. along the vertical cylinder of radius \dfrac3{\sqrt2} when z=\dfrac3{\sqrt2}.

We can parameterize the spherical cap in spherical coordinates by

\mathbf r(\theta,\varphi)=\langle3\cos\theta\sin\varphi,3\sin\theta\sin\varphi,3\cos\varphi\right\rangle

where 0\le\theta\le2\pi and 0\le\varphi\le\dfrac\pi4, which follows from the fact that the radius of the sphere is 3 and the height at which the sphere and cone intersect is \dfrac3{\sqrt2}. So the angle between the vertical line through the origin and any line through the origin normal to the sphere along the cone's surface is

\varphi=\cos^{-1}\left(\dfrac{\frac3{\sqrt2}}3\right)=\cos^{-1}\left(\dfrac1{\sqrt2}\right)=\dfrac\pi4

Now the surface area of the cap is given by the surface integral,

\displaystyle\iint_{\text{cap}}\mathrm dS=\int_{\theta=0}^{\theta=2\pi}\int_{\varphi=0}^{\varphi=\pi/4}\|\mathbf r_u\times\mathbf r_v\|\,\mathrm dv\,\mathrm du
=\displaystyle\int_{u=0}^{u=2\pi}\int_{\varphi=0}^{\varphi=\pi/4}9\sin v\,\mathrm dv\,\mathrm du
=-18\pi\cos v\bigg|_{v=0}^{v=\pi/4}
=18\pi\left(1-\dfrac1{\sqrt2}\right)
=9(2-\sqrt2)\pi
3 0
2 years ago
I WILL MARK BRAINLIEST!!!! An underground mine elevator descends 12% of the total depth every minute. The total depth of the ele
Dahasolnce [82]

Answer:

after 1 Min it's -9

after 2 mins it's -1.08

Step-by-step explanation:

12% X 75 = 9

12% X 9 = 1.08

3 0
3 years ago
Read 2 more answers
Write 4x + y = 1 as a slope intercept form
Rainbow [258]
Y=4x−1
Explanation:
The equation of a line in
slope-intercept form
is.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
∣
∣
∣
2
2
y
=
m
x
+
b
2
2
∣
∣
∣
−−−−−−−−−−−−−−−

where m represents the slope and b, the y-intercept.
Rearrange
4
x
−
y
=
1
into this form
subtract 4x from both sides.
4
x
−
4
x
−
y
=
−
4
x
+
1
⇒
−
y
=
−
4
x
+
1
multiply through by -1
⇒
y
=
4
x
−
1
←
in slope-intercept form
3 0
3 years ago
A rectangular prism has a volume of 60 cubic centimeters. The height of the prism is 3 centimeters. What is the area of the base
victus00 [196]

Answer: The area of the base would be 20 sq cm

Step-by-step explanation:

Hope this helps :)

8 0
3 years ago
What is the first operation you start with when solving
Alex17521 [72]
The correct answer is B addition
You will add 4 to both sides then the equation will be 2x=5
5 0
3 years ago
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