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Brums [2.3K]
2 years ago
9

Which of the following is a prime number? 61 39 27 76

Mathematics
2 answers:
Zolol [24]2 years ago
7 0
61 is the prime number.

39 is divisible by 3 and 13.
27 is divisible by 9 and 3.
76 is divisible by several numbers, including 2.
Ann [662]2 years ago
6 0

Answer:

the answer is 61

Step-by-step explanation:

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What are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotenuse is 15 units long?
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The legs of a triangle with a hypotenuse that measures 15 units long have lengths that are equal to 15 times the sine or cosine of the given angle.
                      leg 1 = (15 units) x (cos 19) = 14.18 units
                      leg 2 = (15 units) x (sin 19) = 4.88 units
The lengths of the legs are 14.18 units and 4.88 units. 
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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)
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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
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=18\pi\left(1-\dfrac1{\sqrt2}\right)
=9(2-\sqrt2)\pi
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2 years ago
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