rocedwrp
2020-11-23
Answered

a cube-shaped cat hideaway is 8ft cubed. On 3 sides there is a 1 ft opening. What is the area in fractions of the surface area that is not an opening?

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Margot Mill

Answered 2020-11-24
Author has **106** answers

You are given that the volume of the cube-shaped hideaway is 8 ft^{3}.The volume of a cube is

The surface area of a cube is

If each opening has a length and width of 1 ft, then each opening has an area of

The surface area of the cube that is not openings is then

The fraction of the surface area that is not an opening is then:

surface area that is not openings/total surface area

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Write the equations in cylindrical coordinates.

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A quadratic function f is given

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a) Express f in transformation form

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Can the triangles below be proven similar by the SAS Similarity Postulate?

Yes, the SAS Similarity Postulate can be used because 2 sets of corresponding sides are proportional, and the included angles by these sides are congruent.

Yes, the SAS Similarity Postulate can be used because 2 sets of corresponding sides are congruent, and the included angles by these sides are congruent.

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Yes, the SAS Similarity Postulate can be used because 2 sets of corresponding sides are proportional, and the included angles by these sides are congruent.

Yes, the SAS Similarity Postulate can be used because 2 sets of corresponding sides are congruent, and the included angles by these sides are congruent.

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I have a multivariable function that I have defined the cost function and its gradient with respect to the variable vector. Let's call the cost function $f(\overrightarrow{x})$, and variable vector $\overrightarrow{x}$. I have been using nonlinear conjugate gradient descenet method for minimization. Algorithm is as follows:

$k=0\phantom{\rule{0ex}{0ex}}x=0\phantom{\rule{0ex}{0ex}}{g}_{0}={\mathrm{\nabla}}_{\overrightarrow{x}}f({x}_{0})\phantom{\rule{0ex}{0ex}}\mathrm{\Delta}{x}_{0}=-{g}_{0}$

${x}_{k+1}\leftarrow {x}_{k}+t\mathrm{\Delta}{x}_{k}\phantom{\rule{0ex}{0ex}}{g}_{k+1}\leftarrow \mathrm{\nabla}f({x}_{k+1})\phantom{\rule{0ex}{0ex}}\mathrm{\Delta}{x}_{k+1}\leftarrow -{g}_{k+1}+\gamma \mathrm{\Delta}{x}_{k}$

I know that I need to update formula so the solution "ascends" instead of descension. How can I update the algorithm? Also I wonder how the wolfe condition changes for maximization problems. Thank you and have a nice day.

$k=0\phantom{\rule{0ex}{0ex}}x=0\phantom{\rule{0ex}{0ex}}{g}_{0}={\mathrm{\nabla}}_{\overrightarrow{x}}f({x}_{0})\phantom{\rule{0ex}{0ex}}\mathrm{\Delta}{x}_{0}=-{g}_{0}$

${x}_{k+1}\leftarrow {x}_{k}+t\mathrm{\Delta}{x}_{k}\phantom{\rule{0ex}{0ex}}{g}_{k+1}\leftarrow \mathrm{\nabla}f({x}_{k+1})\phantom{\rule{0ex}{0ex}}\mathrm{\Delta}{x}_{k+1}\leftarrow -{g}_{k+1}+\gamma \mathrm{\Delta}{x}_{k}$

I know that I need to update formula so the solution "ascends" instead of descension. How can I update the algorithm? Also I wonder how the wolfe condition changes for maximization problems. Thank you and have a nice day.

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