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2 years ago

Which statements are true the ordered pair (1, 2) and the system of equations?

Mathematics

1 answer:

galina1969 [7]2 years ago

4 0

Answer:

when (1.2) is substituted into the second equation the equation is true

Step-by-step explanation:

further you substitute x and the then solve

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The equation giving a family of ellipsoids is u = (x^2)/(a^2) + (y^2)/(b^2) + (z^2)/(c^2) . Find the unit vector normal to each

Fynjy0 [20]

Answer:

$\hat{n}\ =\ \ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

Step-by-step explanation:

Given equation of ellipsoids,

$u\ =\ \dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}$

The vector normal to the given equation of ellipsoid will be given by

$\vec{n}\ =\textrm{gradient of u}$

$=\bigtriangledown u$

$=\ (\dfrac{\partial{}}{\partial{x}}\hat{i}+ \dfrac{\partial{}}{\partial{y}}\hat{j}+ \dfrac{\partial{}}{\partial{z}}\hat{k})(\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2})$

$=\ \dfrac{\partial{(\dfrac{x^2}{a^2})}}{\partial{x}}\hat{i}+\dfrac{\partial{(\dfrac{y^2}{b^2})}}{\partial{y}}\hat{j}+\dfrac{\partial{(\dfrac{z^2}{c^2})}}{\partial{z}}\hat{k}$

$=\ \dfrac{2x}{a^2}\hat{i}+\ \dfrac{2y}{b^2}\hat{j}+\ \dfrac{2z}{c^2}\hat{k}$

Hence, the unit normal vector can be given by,

$\hat{n}\ =\ \dfrac{\vec{n}}{\left|\vec{n}\right|}$

$=\ \dfrac{\dfrac{2x}{a^2}\hat{i}+\ \dfrac{2y}{b^2}\hat{j}+\ \dfrac{2z}{c^2}\hat{k}}{\sqrt{(\dfrac{2x}{a^2})^2+(\dfrac{2y}{b^2})^2+(\dfrac{2z}{c^2})^2}}$

$=\ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

Hence, the unit vector normal to each point of the given ellipsoid surface is

$\hat{n}\ =\ \ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

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3 years ago

A medium pizza at Pizzaz Pizza

blondinia [14]

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Step-by-step explanation:

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3 years ago

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Identify the variable expression that is not a polynomial

andre [41]

B because of the y to the zero? Anyone wanna back me up?

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3 years ago

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Which matrix is equal to ( -6 -6.5 1.7 2 -8.5 19.3 )

DochEvi [55]

The matrix that is equal to the considered matrix [-6,-6.5,1.7; 2, -8..5, 19.3 ] is given by: Option D: [-6,-6.5,1.7; 2, -8..5, 19.3 ]

<h3>When are two matrices called being equal?</h3>

Two matrices are equal if and only if their shapes are same, and they've got the same elements for each corresponding row and column positions.

The missing options are specified in the image attached below.

The considered matrix is:

$\left[\begin{array}{ccc}-6&-6.5&1.7\\2&-8.5&19.3\end{array}\right]$

It has 2 rows and 3 columns.

Evaluating each of the options:

Option A and B are wrong as they've got 3 rows and 2 columns, which makes their shape not matching with the shape of the considered matrix.

Option C although has got 2 rows and 3 colums, but its elements are not matching with corresponding elements of the considered matrix.

Option D has 2 rows and 3 colums and its each element matches with the corresponding element of the considered matrix. (ie, for example, element common in first row and first column in option D is -6, and so as for the considered matrix, and similarly, all correspoding elements for each row and column is same in both matrices.)

Thus, the matrix that is equal to the considered matrix [-6,-6.5,1.7; 2, -8..5, 19.3 ] is given by: Option D: [-6,-6.5,1.7; 2, -8..5, 19.3 ]

Learn more about matrices here:

brainly.com/question/13430728

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2 years ago

Point K is the midpoint of ¹segment JL<br>JK = 2x+4<br>JL=12

Eddi Din [679]

Step-by-step explanation:

$2(2x + 4) = 12 \\ 4x + 8 = 12 \\ 4x = 4 \\ x = 1$

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3 years ago