Explanation The theoretical statement can be converted into a mathematical statement by assuming some variable for the unknowns in the statement and by applying suitable algebraic method, the value of the unknown in the statement can be obtained. Calculation: Given, In the right triangle OPA O A = x (Base of the triangle) P A = y (Height of the triangle) Now, the area of the right triangle OAP is given by, A = 1 2 × base × height A = 1 2 × x × y A = 1 2 x y Now, from the given equation x + y = 1 . Add − x on both sides, x + y + ( − x ) = 1 + ( − x ) y + x − x = 1 − x y = 1 − x Substitute y = 1 − x in A . A = 1 2 x ( 1 − x ) A = x 2 ( 1 − x ) By the distributive property of multiplication, A = x 2 ( 1 ) − x ( x 2 ) A = x 2 − x 2 2 A = − x 2 2 + x 2 Hence, the function of the area is given by, A ( x ) = − x 2 2 + x 2 Comparing with the equation of quadratic function f ( x ) = a x 2 + b x + c . We have, a = − 1 2 , b = 1 2 and c = 0 The coefficient of the x 2 term of the obtained expression for the area A ( x ) is negative

Bundle: Webassign Printed Access Card For Gustafson/hughes' College Algebra, Single-term + Student Solutions Manual For Gustafson/hughes? College Algebra, 12th

12th Edition

ISBN: 9781337605304

Author: R. David Gustafson; Jeff Hughes

Publisher: Cengage Learning

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Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 4.1, Problem 100E

To determine

To find:

The co-ordinates of P.

Expert Solution & Answer

Chapter 4 Solutions

Bundle: Webassign Printed Access Card For Gustafson/hughes' College Algebra, Single-term + Student Solutions Manual For Gustafson/hughes? College Algebra, 12th

Ch. 4.1 - Find the vertex of the graph of the quadratic...Ch. 4.1 - Prob. 2SC Ch. 4.1 - Prob. 3SC Ch. 4.1 - Prob. 4SC Ch. 4.1 - Find the largest area possible if the association...Ch. 4.1 - A company that makes and sells baseball caps has...Ch. 4.1 - Fill in the blanks. A quadratic function is...Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E

Knowledge Booster

The co-ordinates of P .

Solution Summary: The author explains that the theoretical statement can be converted into a mathematical statement by assuming some variable for the unknowns in the statement and applying suitable algebraic method.

To find:

The co-ordinates of P.

Chapter 4 Solutions

The co-ordinates of P .

Solution Summary: The author explains that the theoretical statement can be converted into a mathematical statement by assuming some variable for the unknowns in the statement and applying suitable algebraic method.

To find: The co-ordinates of P.

Chapter 4 Solutions

To find:

The co-ordinates of P.