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2 years ago

The area of a rectangle is 42 square feet.

Mathematics

1 answer:

Alchen [17]2 years ago

3 0

Answer:

26 ft and 46 ft.

Step-by-step explanation:

The prime factors of 42 are 2 * 3 * 7.

Possible lengths and widths are:

L = 7, W = 6 giving a perimeter of 2*7 + 2*6 = 26 ft.

L = 14 , W = 3 giving perimeter = 34 ft.

L = 21, W = 2 giving perimeter = 46 ft.

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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

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)

7 0

3 years ago

9+19 - 12 + 12 + 12323 - 39

Alexxandr [17]

Answer : 12312

Step-by-step explanation : According to BODMAS, Addition (+) comes first

Hence -- 9 + 19 + 12 + 12323 = 12363

12363 - 12 - 39 = 12363 - 51

= 12312

5 0

2 years ago

Factor the expression. 3x + 21

Delicious77 [7]

Answer: 3 ( x + 7 )

Step-by-step explanation:

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2 years ago

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True or false? Do the following set of ordered pairs represent a function {(8,1),(0,-1),(9,4),(-6,-7),(8,9)}

Anika [276]

Hi there!

Unfortunately, the set of ordered pairs does NOT represent a function! This is because there are two of the same x values. In a function, there is one input for every output. In this case, there are two of the same inputs. However, there can be two of the same outputs.
Just to clarify - Not a function

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!

6 0

3 years ago

Estimate and solve 3,836 ÷ 63 = ________. (2 points) 60 r 9 58 r 56 60 r 56 58 r 9

7nadin3 [17]

Answer:

60 r 56

Step-by-step explanation:

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2 years ago