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Paha777 [63]
3 years ago
7

Past experience shows that they need twice as many vans as small trucks. how many of each type of vehicle can they​ buy?

Mathematics
1 answer:
deff fn [24]3 years ago
5 0
Two of each. one for the small vechile while two for the bigger car
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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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IgorLugansk [536]

Answer:

part A :BODMAS ( Bracket of Division Multiplication Addition Subtraction )

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Step-by-step explanation:

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