AA Sectionn 1-6
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Transcript of AA Sectionn 1-6
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Section 1-6Rewriting Formulas
![Page 2: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/2.jpg)
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4za. Find x when y = 2
and z = 3b. Find z when y = 2
and x = 3
![Page 3: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/3.jpg)
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
![Page 4: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/4.jpg)
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
![Page 5: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/5.jpg)
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
![Page 6: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/6.jpg)
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w+1 +1
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
![Page 7: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/7.jpg)
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
114 = 6w
+1 +1
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
![Page 8: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/8.jpg)
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
114 = 6w
+1 +1
6 6
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
![Page 9: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/9.jpg)
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
114 = 6w
+1 +1
6 6
w = 19
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
![Page 10: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/10.jpg)
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
114 = 6w
+1 +1
6 6
w = 19
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
2 = 3x + 4(3)
![Page 11: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/11.jpg)
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
114 = 6w
+1 +1
6 6
w = 19
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
2 = 3x + 4(3)2 = 3x + 12
![Page 12: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/12.jpg)
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
114 = 6w
+1 +1
6 6
w = 19
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
2 = 3x + 4(3)2 = 3x + 12
-10 = 3x
![Page 13: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/13.jpg)
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
114 = 6w
+1 +1
6 6
w = 19
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
2 = 3x + 4(3)2 = 3x + 12
-10 = 3x
x = − 10
3
![Page 14: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/14.jpg)
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
114 = 6w
+1 +1
6 6
w = 19
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
2 = 3x + 4(3)2 = 3x + 12
-10 = 3x
x = − 10
3
2 = 3(3) + 4z
![Page 15: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/15.jpg)
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
114 = 6w
+1 +1
6 6
w = 19
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
2 = 3x + 4(3)2 = 3x + 12
-10 = 3x
x = − 10
3
2 = 3(3) + 4z2 = 9 + 4z
![Page 16: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/16.jpg)
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
114 = 6w
+1 +1
6 6
w = 19
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
2 = 3x + 4(3)2 = 3x + 12
-10 = 3x
x = − 10
3
2 = 3(3) + 4z2 = 9 + 4z
-7 = 4z
![Page 17: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/17.jpg)
Warm-up1. Suppose . f(w) = 3 − (4 − 6w) Find w when f(w) = 113.
2. y = 3x + 4z
113 = 3 − (4 − 6w)
113 = 3 − 4 + 6w
113 = −1+ 6w
114 = 6w
+1 +1
6 6
w = 19
a. Find x when y = 2 and z = 3
b. Find z when y = 2 and x = 3
2 = 3x + 4(3)2 = 3x + 12
-10 = 3x
x = − 10
3
2 = 3(3) + 4z2 = 9 + 4z
-7 = 4z
z = − 7
4
![Page 18: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/18.jpg)
Question
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Question
Suppose we kept working with the problem in #2. Is there a way to make the problem easier to work with if we
kept getting different values for x and y?
![Page 20: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/20.jpg)
Solved for a variable:
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Solved for a variable: Applying the rules of mathematics to a problem to isolate a certain variable
![Page 22: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/22.jpg)
Solved for a variable: Applying the rules of mathematics to a problem to isolate a certain variable
“in terms of”:
![Page 23: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/23.jpg)
Solved for a variable: Applying the rules of mathematics to a problem to isolate a certain variable
“in terms of”: When an equation is solved for a variable, the equation is written “in terms of” the remaining variables
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Example 1a. Solve for h in terms of b and A.
b =
2A
h
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Example 1a. Solve for h in terms of b and A.
b =
2A
h
h(b) = h
2A
h
⎛⎝⎜
⎞⎠⎟
![Page 26: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/26.jpg)
Example 1a. Solve for h in terms of b and A.
b =
2A
h
h(b) = h
2A
h
⎛⎝⎜
⎞⎠⎟
bh = 2A
![Page 27: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/27.jpg)
Example 1a. Solve for h in terms of b and A.
b =
2A
h
h(b) = h
2A
h
⎛⎝⎜
⎞⎠⎟
bh = 2A
bh
b=
2A
b
![Page 28: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/28.jpg)
Example 1a. Solve for h in terms of b and A.
b =
2A
h
h(b) = h
2A
h
⎛⎝⎜
⎞⎠⎟
bh = 2A
bh
b=
2A
b
h =
2A
b
![Page 29: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/29.jpg)
Example 1b. Solve for A in terms of b and h.
b =
2A
h
![Page 30: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/30.jpg)
Example 1b. Solve for A in terms of b and h.
b =
2A
h
h(b) = h
2A
h
⎛⎝⎜
⎞⎠⎟
![Page 31: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/31.jpg)
Example 1b. Solve for A in terms of b and h.
b =
2A
h
h(b) = h
2A
h
⎛⎝⎜
⎞⎠⎟
bh = 2A
![Page 32: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/32.jpg)
Example 1b. Solve for A in terms of b and h.
b =
2A
h
h(b) = h
2A
h
⎛⎝⎜
⎞⎠⎟
bh = 2A
bh
2=
2A
2
![Page 33: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/33.jpg)
Example 1b. Solve for A in terms of b and h.
b =
2A
h
h(b) = h
2A
h
⎛⎝⎜
⎞⎠⎟
bh = 2A
bh
2=
2A
2
A = 1
2bh
![Page 34: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/34.jpg)
Example 2Solve C = 2πr for r.
![Page 35: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/35.jpg)
Example 2Solve C = 2πr for r.
C
2π=
2π r
2π
![Page 36: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/36.jpg)
Example 2Solve C = 2πr for r.
C
2π=
2π r
2π
r =
C
2π
![Page 37: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/37.jpg)
Example 3Solve the formula for .
v0
h = − 1
2gt2 − v
0t + h
0
![Page 38: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/38.jpg)
Example 3Solve the formula for .
v0
h = − 1
2gt2 − v
0t + h
0
+ 1
2gt2
![Page 39: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/39.jpg)
Example 3Solve the formula for .
v0
h = − 1
2gt2 − v
0t + h
0
+ 1
2gt2
−h
0
![Page 40: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/40.jpg)
Example 3Solve the formula for .
v0
h = − 1
2gt2 − v
0t + h
0
+ 1
2gt2
−h
0 + 1
2gt2 − h
0
![Page 41: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/41.jpg)
Example 3Solve the formula for .
v0
h = − 1
2gt2 − v
0t + h
0
+ 1
2gt2
−h
0 + 1
2gt2 − h
0
![Page 42: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/42.jpg)
Example 3Solve the formula for .
v0
h = − 1
2gt2 − v
0t + h
0
+ 1
2gt2
−h
0 + 1
2gt2 − h
0
12
gt2 − h0+ h = −v
0t
![Page 43: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/43.jpg)
Example 3Solve the formula for .
v0
h = − 1
2gt2 − v
0t + h
0
+ 1
2gt2
−h
0 + 1
2gt2 − h
0
12
gt2 − h0+ h = −v
0t
12
gt2 − h0+ h
−t=−v
0t
−t
![Page 44: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/44.jpg)
Example 3Solve the formula for .
v0
h = − 1
2gt2 − v
0t + h
0
+ 1
2gt2
−h
0 + 1
2gt2 − h
0
12
gt2 − h0+ h = −v
0t
12
gt2 − h0+ h
−t=−v
0t
−t
v
0= −
12
gt2 − h0+ h
t
![Page 45: AA Sectionn 1-6](https://reader034.fdocuments.net/reader034/viewer/2022052601/558e47491a28ab46268b4720/html5/thumbnails/45.jpg)
Homework
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Homework
p. 38 #1 - 20