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natali 33 [55]
3 years ago
7

Find the volume of a smaller wedge cut from a sphere of radius 66 by two planes that intersect along a diameter at an angle of π

/6
Mathematics
1 answer:
djverab [1.8K]3 years ago
4 0

Answer:

The answer is "\frac{\pi a^3}{9}".

Step-by-step explanation:

please find the complete question in the attached file.

Let the sphere center be (0,0,0) and then let the intersection diameter lie all along the z-axis.  

So one of the collision plans is the xz-plane the other is the path via an xz-plane angle.

\theta = \frac{\pi}{6}

All appropriate region could then be indicated in spherical coordinates

E= {(\rho, \theta, \phi) : 0 \geq \rho \geq a, 0 \geq \theta \geq \frac{\pi}{6}, 0 \geq \phi \geq \pi }

Calculating the volume:

\to v(E)=\int \int_{E} \int dV\\

            =\int_{0}^{\frac{\pi}{6}} \int_{0}^{\pi} \int_{0}^{a} \rho^2 \sin \phi d \rho d \phi d \theta\\\\ =\int_{0}^{\frac{\pi}{6}} d \theta \int_{0}^{\pi} \sin \phi d \int_{0}^{a} \rho^2 d \rho\\\\= [\theta]^{\frac{\pi}{6}}_{0} [-\cos \phi]^{\pi}_{0} [\frac{\rho^3}{3}]^{a}_{0}\\\\= \frac{\pi}{6} [1+1] \frac{a^3}{3}\\\\=\frac{\pi a^3}{9}

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What is the x intercept of 2x + 4y = 20
zhuklara [117]

Answer:

10

Step-by-step explanation:

x- intercept is where the equation intersect the x-axis. So, at x-axis y = 0

2x + 4*0 = 20

           2x = 20

Divide both sides by 2

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x = 10

4 0
3 years ago
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20% of the girls in class have blonde hair. 16 girls do not have blonde hair. How many total students
yawa3891 [41]
The problem is to find how many students have either blond hair or glasses and then divide that by the total number of students; that will find the probability.
Since 7 have blonde hair and 9 have glasses, that would be a total of 16 persons if there were no overlap; that is, no blonde wears glasses and nobody who wears glasses is a blonde.
But there are 4 persons who have both blond hair and wears glasses. That means, of the 7 who are blondes, 3 of them do not wear glasses. And, of the 9 who wear glasses, 5 of them are not blondes.
So we have 3 who are blondes without glasses, 5 who wear glasses who are not blondes, and 4 blonds with glasses, for a total of 12 persons.
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3 years ago
PLEASE HELP!!!!!!!!!!!!!
solniwko [45]

Answer:

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Step-by-step explanation:

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6 0
3 years ago
Un cuerpo de 180 kg se debe lanzar hacia una distancia de 25 m. ¿Qué valor tiene el trabajo que se realiza al lanzarlo?
dsp73

Answer:

45, 000 J o 45 KJ

Step-by-step explanation:

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2 years ago
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Note how the left side has a square bracket and the right side has a curved parenthesis. This isn't a typo. The square bracket tells the reader "include the endpoint -8 as part of the solution set". The parenthesis tells the reader "do NOT include the endpoint infinity as part of the solution set". 

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