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1. The sum of two positive numbers is 200. What is the maximum possible value for their product? 2. What is the area of the largest rectangle in the first quadrant that can fit with one edge on the r-axis, one edge on the y-axis and touching the line y 2-z at one point? 3. Show that the point between two posts of fixed lengths A and B which minimizes the distance a + B has the property that = -

1. The sum of two positive numbers is 200. What is the maximum possible value for their product? 2. What is the area of the largest rectangle in the first quadrant that can fit with one edge on the r-axis, one edge on the y-axis and touching the line y 2-z at one point? 3. Show that the point between two posts of fixed lengths A and B which minimizes the distance a + B has the property that = -

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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need help with 2and 3 not number 1 !!!

1. The sum of two positive numbers is 200. What is the maximum possible value for their product? 2. What is the area of the largest rectangle in the first quadrant that can fit with one edge on the r-axis, one edge on the y-axis and touching the line y 2-z at one point? 3. Show that the point between two posts of fixed lengths A and B which minimizes the distance a + B has the property that = -
Transcribed Image Text:1. The sum of two positive numbers is 200. What is the maximum possible value for their product? 2. What is the area of the largest rectangle in the first quadrant that can fit with one edge on the r-axis, one edge on the y-axis and touching the line y 2-z at one point? 3. Show that the point between two posts of fixed lengths A and B which minimizes the distance a + B has the property that = -
Expert Solution
Step 1

Let x and y be the length of sides of rectangle along x-axis and y-axis respectively. Then , the vertex (x,y) of the rectangle line on the line 

Calculus homework question answer, step 1, image 1

Area of rectangle is

Calculus homework question answer, step 1, image 2

Step 2

Differentiating with respect to x, we get

Calculus homework question answer, step 2, image 1

Now, we solve dA/dx=0 for x

Calculus homework question answer, step 2, image 2

For this value of x

Calculus homework question answer, step 2, image 3

Therefore, area of rectangle is maximum for x=1

Calculus homework question answer, step 2, image 4

Therefore, area of largest rectangle is

Calculus homework question answer, step 2, image 5

 

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