Formulas: Perimeter of a rectangle: P = 2l + 2w Area of a rectangle : A = lw Perimeter of a square : P = 4s Area of a square: A = s 2 Circumference of.

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Presentation transcript:

Formulas: Perimeter of a rectangle: P = 2l + 2w Area of a rectangle : A = lw Perimeter of a square : P = 4s Area of a square: A = s 2 Circumference of a circle: C = 2πr Area of a circle : A = πr2

John wants to plant a rectangular garden on his farm. He needs to enclose the garden with a fence. If John has 420 linear feet of fence boards, find the dimensions of the garden that will produce the largest area. Find the area of the garden. Garden Perimeter 420 = 2l + 2w 2l = 420 – 2w L = w Area A = lw A = (210 – w)w Graph the equation for area of the garden and find the maximum point. X would be the width of the garden and y would be the maximum area.

A farmer with 2000 meters of fencing wants to enclose a rectangular plot that borders on a straight highway. If the farmer does not fence the side along the highway. What is the largest area that can be enclosed. Land Area A = lw A = (2000 –2 w)w Graph the equation for area of the garden and find the maximum point. X would be the width of the garden and y would be the maximum area. Highway w w w

The marketing department at Widgets Inc. found that, when certain widgets are sold at a price of p dollars per unit, the number x of widgets sold is given by the demand equation x = 1500 – 30p Copyright © 2013 Pearson Education, Inc. All rights reserved

The marketing department at Widgets Inc. found that, when certain widgets are sold at a price of p dollars per unit, the number x of widgets sold is given by the demand equation x = 1500 – 30p (e)How many units are sold at this price? (f)Graph R. (g)What price should Widgets Inc. charge to collect at least $12,000 in revenue? So the company should charge between $10 and $40 to earn at least $12,000 in revenue. Copyright © 2013 Pearson Education, Inc. All rights reserved Put y = 12,000 in your calculator and see where they intersect.

A farmer has 1600 yards of fence to enclose a rectangular field. What are the dimensions of the rectangle that encloses the most area? The farmer should make the rectangle 400 yards by 400 yards to enclose the most area. Copyright © 2013 Pearson Education, Inc. All rights reserved

(a) Find the maximum height of the projectile. Copyright © 2013 Pearson Education, Inc. All rights reserved Type into calculator and find the maximum

(b) How far from the base of the cliff will the projectile strike the water? Solution cannot be negative so the projectile will hit the water about 5458 feet from the base of the cliff. These are the zeros

Copyright © 2013 Pearson Education, Inc. All rights reserved

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