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Lubov Fominskaja [6]
3 years ago
14

The prime factorization of 396 is _____ .

Mathematics
1 answer:
Elena L [17]3 years ago
4 0

Answer:

396 : 2 * 2 * 3 * 3 * 11

Step-by-step explanation:

using long division of prime factors, you will end up with the following:

396 : 2 * 2 * 3 * 3 * 11

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Find a point on the ellipsoid x2+y2+4z2=36x2+y2+4z2=36 where the tangent plane is perpendicular to the line with parametric equa
Anvisha [2.4K]

Answer:

A point on the ellipsoid is (-4,2,2) or (4,-2,-2)

Step-by-step explanation:

Given equation of ellipsoid f(x,y,z) :x^2+y^2+4z^2=36

Parametric equations:

x=-4t-1

y=2t+1

z=8t+3

Finding the gradient of function

\nabla f(x,y,z)=\\\nabla f(x,y,z)=

So, The directions vectors=(-4,2,8)

Now the line is perpendicular to plane when direction vector is parallel to the normal vector of line

\nablaf(x,y,z)=(2x,2y,8z)=\lambda(-4,2,8)

So, 2x=-4\lambda

\Rightarrow x=-2\lambda

2y=2\lambda\\\Rightarrow y=\lambda\\8z=8\lambda\\\Rightarrow z=\lambda

Substitute the value of x , y and z in the ellipsoid equation

(2\lambda)^2+(\lambda)^2+4(\lambda)^2=36\\9(\lambda)^2=36\\\lambda^2=4\\\lambda=\pm 2

With \lambda = 2

x=-2(2)=-4

y=2

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With\lambda =- 2

x=-2(-2)=4

y=-2

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3 years ago
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Given:

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What method would you use to solve -4x2 - 5x + 5=0
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