Given a rectangular card that is 5 inches long and 3 inches wide, what does it mean for another rectangular card to have the same shape?

Albarellak
2021-08-15
Answered

Given a rectangular card that is 5 inches long and 3 inches wide, what does it mean for another rectangular card to have the same shape?

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smallq9

Answered 2021-08-16
Author has **106** answers

For 2 rectangular to have the same shape is for them to have the same proportions between sides. Suggest x & a are two different rectangulars

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We have a function:

$f(x,y,z)=x\mathrm{cos}(\omega \phantom{\rule{mediummathspace}{0ex}}t+y+{\varphi}_{1})+z\mathrm{cos}(\omega \phantom{\rule{mediummathspace}{0ex}}t+y+{\varphi}_{2}).$

I want to solve the following maximization problems:

$\underset{x,y,z}{max}\underset{t}{max}f(x,y,z)\phantom{\rule{2em}{0ex}}\text{or}\phantom{\rule{2em}{0ex}}\underset{x,y,z}{max}{\int}_{<T>}f(x,y,z)dt.$

Surely, $x$ and $z$ are nonnegative, and $y$ is in $[0,2\pi )$.

Can someone give me hints for solving the problem, or let me know some references to solve this types of problem?

$f(x,y,z)=x\mathrm{cos}(\omega \phantom{\rule{mediummathspace}{0ex}}t+y+{\varphi}_{1})+z\mathrm{cos}(\omega \phantom{\rule{mediummathspace}{0ex}}t+y+{\varphi}_{2}).$

I want to solve the following maximization problems:

$\underset{x,y,z}{max}\underset{t}{max}f(x,y,z)\phantom{\rule{2em}{0ex}}\text{or}\phantom{\rule{2em}{0ex}}\underset{x,y,z}{max}{\int}_{<T>}f(x,y,z)dt.$

Surely, $x$ and $z$ are nonnegative, and $y$ is in $[0,2\pi )$.

Can someone give me hints for solving the problem, or let me know some references to solve this types of problem?

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Given:

The given triangles are:

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Elliptical cylinder surface area | Analytic geometry

I have to find the equation of a Cylindrical surface area. This area has the generating lines parallel to the axis z. The directrix is an ellipse on the floor Oxy with center C(1;3;0) and vertices A(1;-1;0), B(-1;3;0).

I tried to make a system with:

- $a=2$ // As the distance from the center and the B vertex is 2

- changed X and Y values with those of the vertex A first

- and then with those of the vertex B.

I now have a system of 3 equations with variables a and b, but they're squared only, as they're supposed to be in an ellipse.

I tried to solve it but it doesn't look good as the solution has parameters xand y not squared as well.

Solution: $4{x}^{2}+{y}^{2}-x-6y-3=0$

I have to find the equation of a Cylindrical surface area. This area has the generating lines parallel to the axis z. The directrix is an ellipse on the floor Oxy with center C(1;3;0) and vertices A(1;-1;0), B(-1;3;0).

I tried to make a system with:

- $a=2$ // As the distance from the center and the B vertex is 2

- changed X and Y values with those of the vertex A first

- and then with those of the vertex B.

I now have a system of 3 equations with variables a and b, but they're squared only, as they're supposed to be in an ellipse.

I tried to solve it but it doesn't look good as the solution has parameters xand y not squared as well.

Solution: $4{x}^{2}+{y}^{2}-x-6y-3=0$