A 10-m ladder is leaning against a building. The bottom of theladder is 5-m from the building. How high is the top of theladder?

on2t1inf8b
2022-07-27
Answered

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juicilysv

Answered 2022-07-28
Author has **17** answers

The building and the ground form a right triangle.We can use the pythaorean theorum to solve.The ladder forms the hypoteneuse.

${5}^{2}+{h}^{2}={10}^{2}\phantom{\rule{0ex}{0ex}}25+{h}^{2}=100\phantom{\rule{0ex}{0ex}}{h}^{2}=75h=\sqrt{75}h=5\sqrt{3}\approx 8.66m$

${5}^{2}+{h}^{2}={10}^{2}\phantom{\rule{0ex}{0ex}}25+{h}^{2}=100\phantom{\rule{0ex}{0ex}}{h}^{2}=75h=\sqrt{75}h=5\sqrt{3}\approx 8.66m$

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Ultimate goal is to find the maximum of

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given ${a}^{T}x=b$, where $P$ is a symmetric positive definite matrix.

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where $a$,$a,x\in {\mathbb{R}}^{n}$, $b$ is a number. Can I solve $x$ in terms of $a$,$b$?

Ultimate goal is to find the maximum of

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given ${a}^{T}x=b$, where $P$ is a symmetric positive definite matrix.

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Greatest distance one point can have from a vertice of a square given following conditions

A point P lies in the same plane as a given square of side 1.Let the vertices of the square,taken counterclockwise,be A,B,C, and D.Also,let the distances from P to A,B, and C, respectively, be u,v and w.

What is the greatest distance that P can be from D if ${u}^{2}+{v}^{2}={w}^{2}$?

Some thoughts I had:

1) Given a pair of vertices I could construct an ellipse with P as a point on the ellipse.

2) From the equality ${u}^{2}+{v}^{2}={w}^{2}$. I think that I have to consider the case where the angle between u and v is ${90}^{\circ}$. In this case I would have $w=1$ and $PD<2$.

That being said,I still fail to come at a concrete solution of the problem,it might be that none of my thoughts are right...

A point P lies in the same plane as a given square of side 1.Let the vertices of the square,taken counterclockwise,be A,B,C, and D.Also,let the distances from P to A,B, and C, respectively, be u,v and w.

What is the greatest distance that P can be from D if ${u}^{2}+{v}^{2}={w}^{2}$?

Some thoughts I had:

1) Given a pair of vertices I could construct an ellipse with P as a point on the ellipse.

2) From the equality ${u}^{2}+{v}^{2}={w}^{2}$. I think that I have to consider the case where the angle between u and v is ${90}^{\circ}$. In this case I would have $w=1$ and $PD<2$.

That being said,I still fail to come at a concrete solution of the problem,it might be that none of my thoughts are right...

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