Alexandra Richardson
2022-07-23
Answered

How do you find the area of the largest isosceles triangle having a perimeter of 18 meters?

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grocbyntza

Answered 2022-07-24
Author has **25** answers

Using the wikipwdia notation:

f(x,y)-function that you want to maximize (area of the triangle)

g(x,y)- function that is your "bond" (perimeter) written in equation form g(x,y)=0

$L(x,y,\lambda )=f(x,y)-\lambda \cdot g(x,y)$

Maximaze $L(x,y,\lambda )$:

1. $\frac{\partial L}{\partial x}=0$

2. $\frac{\partial L}{\partial y}=0$

3. $\frac{\partial L}{\partial \lambda}=0$

express $x,y\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}\lambda$ end put it in the 3. equation

f(x,y)-function that you want to maximize (area of the triangle)

g(x,y)- function that is your "bond" (perimeter) written in equation form g(x,y)=0

$L(x,y,\lambda )=f(x,y)-\lambda \cdot g(x,y)$

Maximaze $L(x,y,\lambda )$:

1. $\frac{\partial L}{\partial x}=0$

2. $\frac{\partial L}{\partial y}=0$

3. $\frac{\partial L}{\partial \lambda}=0$

express $x,y\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}\lambda$ end put it in the 3. equation

asked 2021-01-13

How do Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem relate to the Fundamental Theorem of Calculus for ordi-nary single integral?

asked 2021-09-21

Use a Numerical approach (i,e., a table of values)
to approximate $\underset{x\to 0}{lim}\frac{{e}^{2}x-1}{x},$
Provide support for your analysis (slow the table and
explain your resoning).

asked 2021-12-02

Select one:

True

False

asked 2022-07-02

This might be trivial but I am struggling to justify the following simplification.from:

$h({x}^{\ast}+d)-h({x}^{\ast})\ge \sum _{j\text{\u29f8}\in G}{\mathrm{\nabla}}_{j}f({x}^{\ast})\ast {d}_{j}+\gamma \sum _{j\text{\u29f8}\in G}|{d}_{j}|$

to:

$h({x}^{\ast}+d)-h({x}^{\ast})\ge -\underset{j\text{\u29f8}\in G}{max}|{\mathrm{\nabla}}_{j}f({x}^{\ast})|\sum _{j\text{\u29f8}\in G}|{d}_{j}|+\gamma \sum _{j\text{\u29f8}\in G}|{d}_{j}|$

Specifically, why is there a negative in front of the maximization?

Note:

I can get behind the fact that

$\sum _{j\text{\u29f8}\in G}{\mathrm{\nabla}}_{j}f({x}^{\ast})\ast {d}_{j}\ge \underset{j\text{\u29f8}\in G}{max}|{\mathrm{\nabla}}_{j}f({x}^{\ast})|\sum _{j\text{\u29f8}\in G}|{d}_{j}|$

provided the jacobian is nonnegative element-wise. But then why add the negative sign?

$h({x}^{\ast}+d)-h({x}^{\ast})\ge \sum _{j\text{\u29f8}\in G}{\mathrm{\nabla}}_{j}f({x}^{\ast})\ast {d}_{j}+\gamma \sum _{j\text{\u29f8}\in G}|{d}_{j}|$

to:

$h({x}^{\ast}+d)-h({x}^{\ast})\ge -\underset{j\text{\u29f8}\in G}{max}|{\mathrm{\nabla}}_{j}f({x}^{\ast})|\sum _{j\text{\u29f8}\in G}|{d}_{j}|+\gamma \sum _{j\text{\u29f8}\in G}|{d}_{j}|$

Specifically, why is there a negative in front of the maximization?

Note:

I can get behind the fact that

$\sum _{j\text{\u29f8}\in G}{\mathrm{\nabla}}_{j}f({x}^{\ast})\ast {d}_{j}\ge \underset{j\text{\u29f8}\in G}{max}|{\mathrm{\nabla}}_{j}f({x}^{\ast})|\sum _{j\text{\u29f8}\in G}|{d}_{j}|$

provided the jacobian is nonnegative element-wise. But then why add the negative sign?

asked 2021-11-14

Let $f\left(x\right)={x}^{3}-6{x}^{2}-15x+23$

a) Perform a full sign analysis on$f\left(x\right):$ find its zeroes, and determine its sign on each interval.

b) Use the information in (2) to determine intervals of concave up / concave down for f.

c) Find the coordinates (x, y) of the inflection point(s) of f.

d) Find the absolute maximum and minimum values of f on the interval$[0,\text{}7]$ . Justify your answer with appropriate calculus work.

a) Perform a full sign analysis on

b) Use the information in (2) to determine intervals of concave up / concave down for f.

c) Find the coordinates (x, y) of the inflection point(s) of f.

d) Find the absolute maximum and minimum values of f on the interval

asked 2021-09-08

Define variables, write systems of equations, write coefficient matrix, the B matrix and the solution matrix, x

asked 2021-09-05

Exercise No. 10 (D.E. with coefficient linear in two variables)

Find the general / solution of the following D.E.

4.