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Gnesinka [82]
9 months ago
14

So if 3 paper clips equal 9 cm how many paper clips equal 15cm?

Mathematics
1 answer:
Dmitry_Shevchenko [17]9 months ago
3 0

Given,

The number of paper clips used for 9 cm paper is 3.

Consider, the number of paper clips used for 15 cm paper,

By proportionality,

\begin{gathered} \frac{3}{9}=\frac{x}{15} \\ 3\times15=9\times x \\ \frac{45}{9}=x \\ x=5 \end{gathered}

Hence, the number of paper clips used for 15 cm of paper is equal to 5.

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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
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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

z=2

With\lambda =- 2

x=-2(-2)=4

y=-2

z=-2

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

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Answer:

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Step-by-step explanation:

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the answer is b

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