Mathematics: Find the volume of the tetrahedron with the given vertices. (2, 0, 0), (0, 4, 0), (0, 0, 4), (2, 4, 4)

Find the volume of the tetrahedron with the given

Ответ:

hardwick744

10.02.2022

Mathematics

The volume of the tetrahedron is

$\frac{-32}{3}$

Step-by-step explanation:

To find the volume of a tetrahedron with vertices (2, 0, 0), (0, 4, 0), (0, 0, 4), (2, 4, 4).

We know by definition that the volume of a tetrahedron with vertices $(x_{1}, y_{1}, z_{1}), (x_{2}, y_{2}, z_{2}), (x_{3}, y_{3}, z_{3})$ is

$\frac{1}{6}\begin{vmatrix}2 & 0 & 0 & 1\\0 & 4 & 0 & 1\\0 & 0 & 4 & 1\\2 & 4 & 4 & 1\end{vmatrix}$

From here we have:

$\frac{1}{6}\begin{vmatrix}x_1 & y_1 & z_1 & 1\\x_2 & y_2 & y_2 & 1\\x_3 & y_3 & z_3 & 1\\x_4 & y_4 & y_4 & 1\end{vmatrix}$

Finding the determinant of that matrix we have:

$\frac{1}{6} (-64)$ = $\frac{-32}{3}$

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Ответ:

ntrann22

26.10.2022

Mathematics

Based on the graph alone, we don´t have enough information to calculate nominal and deflator GDP.

Explanation:

First, we have to know what those types of GDP are to learn the rationale behind the mathematical equation.

Nominal GDP is a GDP in a given year before accounting for that year's inflation. When you apply the inflation to the nominal GDP, it becomes the real GDP.

GDP deflator is the inflation variable that we will apply to the nominal GDP to find the real GDP.

The formula is in attach.

Does anyone know how to find nominal gdp and gdp deflator from real gdp? Based on this graph.

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Find the volume of the tetrahedron with the given vertices. (2, 0, 0), (0, 4, 0), (0, 0, 4), (2, 4, 4)

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