expressing a quantity as a function of another quantity
DESCRIPTION
Expressing a quantity as a function of another quantity. Do Now: Express the area, A, of a circle as a function of its circumference. i.e. Write an Area formula in terms of C. Write the radius in terms of the circumference and then substitute that radius into the Area equation. x. x. - PowerPoint PPT PresentationTRANSCRIPT
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AIM: APPLICATIONS OF FUNCTIONS? HW P. 27 #74, 76, 77, Functions Worksheet #1-3
Expressing a quantity as a function of another quantity.
Do Now: Express the area, A, of a circle as a function of its circumference.
i.e. Write an Area formula in terms of C.2A r 2C r
2
Cr
2
2
CA
2
2
CA C
2
2 22
CA C
2
24
CA C
2
4
CA C
Write the radius in terms of the circumference and then substitute that radius into the Area equation.
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AIM: APPLICATIONS OF FUNCTIONS? HW P. 27 #74, 76, 77, Functions Worksheet #1-3
Expressing a quantity as a function of another quantity.
Equal squares are cut from the corners of a rectangular piece of cardboard 5 ft wide and 7 ft long. The sides are then folded up to form a box with no top.
1. Express the volume of the box as a function of the width of the squares that are cut out.
2. What is the domain of this function?
5
7
x
x
5 2 7 2V x x x 5 2 7 2 0
0 2.5
x x x
x
7 2
5 2
V L W H
L x
W x
H x
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AIM: APPLICATIONS OF FUNCTIONS? HW P. 27 #74, 76, 77, Functions Worksheet #1-3
Expressing a quantity as a function of another quantity.
A square is 24 cm on each side. Equal squares are then cut from each corner and folded up to make a box with no top.
1. Express the volume of the box as a function of the width of the squares that are cut out.
2. What is the domain of this function?
24
24
x
x
224 2 24 2
24 2
V x x x
V x x
224 2 0
0 12
x x x
x
24 2
24 2
V L W H
L x
W x
H x
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AIM: APPLICATIONS OF FUNCTIONS? HW P. 27 #74, 76, 77, Functions Worksheet #1-3
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AIM: APPLICATIONS OF FUNCTIONS? HW P. 27 #74, 76, 77, Functions Worksheet #1-3
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AIM: APPLICATIONS OF FUNCTIONS? HW P. 27 #74, 76, 77, Functions Worksheet #1-3
Function Worksheet #1-3
1. A farmer uses 80 ft. of fencing to make four sides of a rectangular pen. Express the area of the pen as a function of the length of the pen. What is the domain of this-function?
2. A woman is designing a rectangular garden that will have an area of 400 sq.ft. She needs to know how much fencing would be required for various dimensions of the garden: Let P(w) denote the perimeter of the garden if its width is w feet. Give a formula for the function P. What is it domain?
3. Express the area of a rectangle inscribed in a circle of radius 10 as a function of its width.
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AIM: APPLICATIONS OF FUNCTIONS? HW P. 27 #74, 76, 77, Functions Worksheet #1-3
The function has positive x and y-values within this domain
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AIM: APPLICATIONS OF FUNCTIONS? HW P. 27 #74, 76, 77, Functions Worksheet #1-3
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AIM: APPLICATIONS OF FUNCTIONS? HW P. 27 #74, 76, 77, Functions Worksheet #1-3