Purchase Solution

# Area of Rectangle under a Parabola and Sectors in an Arc

Not what you're looking for?

Proving the area of a shaded rectangle under a parabola and then differentiating the expression.
Minimizing the perimeter of sectors in an arc.

Please see the attached file for the fully formatted problems.

##### Solution Summary

The area of a rectangle under a parabola is calculated and the perimeter of a sector in an arc is minimized.

##### Solution Preview

because parabola eqn. is given as:
y = 3 - x^2
Rectangle length is 2x and is symmetric about y axis, it means, the intersection points of parabola and rectangle are:
(x, 3-x^2) and (-x, 3-x^2)
therefore the area of shaded part:
A = area of the rectangle = length * width
width = ...

Solution provided by:
###### Education
• MSc , Pune University, India
• PhD (IP), Pune University, India
###### Recent Feedback
• " In question 2, you incorrectly add in the \$3.00 dividend that was just paid to determine the value of the stock price using the dividend discount model. In question 4 response, it should have also been recognized that dividend discount models are not useful if any of the parameters used in the model are inaccurate. "
• "feedback: fail to recognize the operating cash flow will not begin until the end of year 3."
• "Great thanks"
• "Perfect solution..thank you"

##### Free BrainMass Quizzes

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.