Given:

ABDC is a rectangle.

Yulia
2021-07-11
Answered

To determine:The measure of angle 6.

Given:

ABDC is a rectangle.

$m\mathrm{\angle}1=38$

Given:

ABDC is a rectangle.

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gotovub

Answered 2021-07-12
Author has **98** answers

Calculation:

The diagonals of a rectangle are congruent and also bisect each other.

So, triangle AEC is an isosceles triangle.

According to Isosceles Triangle Theorem,

Also, according to the definition of a rectangle,

Using Alternate Interior Angles Theorem.

By Transitive Property of Congruence.

So,

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To explain: The way to know that each pair of triangle is congruent.

Given:

The given figure is as follows.

Given:

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asked 2022-06-24

I am trying to solve functional maximization problems. They are typically of the following form (where support of $\theta $ is [0,1]):

$\int [v(\theta ,x(\theta ))+u(\theta ,x(\theta ))-{u}_{1}(\theta ,x(\theta ))(\frac{1-F(\theta )}{f(\theta )})]f(\theta )d\theta$

Now one way that was proposed to me was of point-wise maximization. That is you fix a $\theta $ and then solve:

$argma{x}_{x(\theta )}v(\theta ,x(\theta ))+u(\theta ,x(\theta ))-{u}_{1}(\theta ,x(\theta ))(\frac{1-F(\theta )}{f(\theta )})$

Solving this problem would give me a number $x$ for each $\theta $ and I will recover a function $x(\theta )$ that will maximize the original objective function.

I have two questions related to this:

1) Does such point-wise maximization always work?

2) What happens if rather than doing point-wise maximization I try and take the derivative of the objective function with respect to x(θ) and equating the first order condition to 0? Is this a legitimate way of solving the problem? Can someone show exactly what such a derivative would look like and how to compute it?

$\int [v(\theta ,x(\theta ))+u(\theta ,x(\theta ))-{u}_{1}(\theta ,x(\theta ))(\frac{1-F(\theta )}{f(\theta )})]f(\theta )d\theta$

Now one way that was proposed to me was of point-wise maximization. That is you fix a $\theta $ and then solve:

$argma{x}_{x(\theta )}v(\theta ,x(\theta ))+u(\theta ,x(\theta ))-{u}_{1}(\theta ,x(\theta ))(\frac{1-F(\theta )}{f(\theta )})$

Solving this problem would give me a number $x$ for each $\theta $ and I will recover a function $x(\theta )$ that will maximize the original objective function.

I have two questions related to this:

1) Does such point-wise maximization always work?

2) What happens if rather than doing point-wise maximization I try and take the derivative of the objective function with respect to x(θ) and equating the first order condition to 0? Is this a legitimate way of solving the problem? Can someone show exactly what such a derivative would look like and how to compute it?