- 1. Warm Up The length of the edge of a cube is 10 inches. How
does the volume of a cube with edges 3 times as long compare to the
volume of the smaller cube?
2. Warm UpThe length of the edge of a cube is 10inches. How does
the volume of a cubewith edges 3 times as long compare to thevolume
of the smaller cube?The volume of the large one is 27,000 cubic
incheswhile the smaller one is 1,000 cubic inches 3. Warm UpThe
length of the edge of a cube is 10inches. How does the volume of a
cubewith edges 3 times as long compare to thevolume of the smaller
cube?The volume of the large one is 27,000 cubic incheswhile the
smaller one is 1,000 cubic inches So, the volume will be 27 times
as large. 4. 2.3 FundamentalTheorem ofVariation & 2.9 Combined
andJoint Variation 5. THE ESSENTIAL QUESTION How do we solve
variations? What is the Fundamental Theorem of Variation? 6. The
Fundamental Theorem of Variation 7. The Fundamental Theorem of
VariationIf y varies directly as xn (y = kxn), and xis multiplied
by c, then y is multiplied bycn. 8. The Fundamental Theorem of
VariationIf y varies directly as xn (y = kxn), and xis multiplied
by c, then y is multiplied bycn. If y varies inversely as xn (y =
k/xn), and xis multiplied by a nonzero constant c, theny is divided
by cn. 9. Suppose that the value of x is doubling, how is y
changing if: 10. Suppose that the value of x is doubling, how is y
changing if: 3 1. If y varies directly as x , then ______ 11.
Suppose that the value of x is doubling, how is y changing if:3 1.
If y varies directly as x , then ______y is multiplied by 8, from
23 12. Suppose that the value of x is doubling, how is y changing
if:3 1. If y varies directly as x , then ______y is multiplied by
8, from 23 2. If y varies directly as x4 , then ______ 13. Suppose
that the value of x is doubling, how is y changing if:3 1. If y
varies directly as x , then ______y is multiplied by 8, from 23 2.
If y varies directly as x4 , then ______y is multiplied by 16, from
24 14. Suppose that the value of x is doubling, how is y changing
if:3 1. If y varies directly as x , then ______y is multiplied by
8, from 23 2. If y varies directly as x4 , then ______y is
multiplied by 16, from 242 3. If y varies inversely as x , then
________ 15. Suppose that the value of x is doubling, how is y
changing if:3 1. If y varies directly as x , then ______y is
multiplied by 8, from 23 2. If y varies directly as x4 , then
______y is multiplied by 16, from 242 3. If y varies inversely as x
, then ________ y is divided by 4, from 22 16. 4. The formula I =
k/D2 tells that the intensity of light varies inversely as the
square of the distance from the light source. What effect does
doubling the distance have on the intensity of the light? 17. 4.
The formula I = k/D2 tells that the intensity of light varies
inversely as the square of the distance from the light source. What
effect does doubling the distance have on the intensity of the
light? We have an inverse variation so our answer is divided by cn
. 18. 4. The formula I = k/D2 tells that the intensity of light
varies inversely as the square of the distance from the light
source. What effect does doubling the distance have on the
intensity of the light? We have an inverse variation so our answer
is divided by cn . In the formula D is squared, so our n value is
2, since we are doubling, our c value is 2. 19. 4. The formula I =
k/D2 tells that the intensity of light varies inversely as the
square of the distance from the light source. What effect does
doubling the distance have on the intensity of the light? We have
an inverse variation so our answer is divided by cn . In the
formula D is squared, so our n value is 2, since we are doubling,
our c value is 2. So we would divide by 4, which is the same as
multiplying by 1/4, so the light is 1/4 the intensity. 20. Combined
& Joint Variation 21. Combined & Joint VariationCombined
variation - when direct and inversevariations occur together 22.
Combined & Joint VariationCombined variation - when direct and
inversevariations occur together 23. Combined & Joint
VariationCombined variation - when direct and inversevariations
occur together Joint variation - when one quantity variesdirectly
as the product of two or moreindependent variables 24. Combined
& Joint VariationCombined variation - when direct and
inversevariations occur together Joint variation - when one
quantity variesdirectly as the product of two or moreindependent
variables 25. Combined & Joint VariationCombined variation -
when direct and inversevariations occur together Joint variation -
when one quantity variesdirectly as the product of two or
moreindependent variables 26. Combined & Joint
VariationCombined variation - when direct and inversevariations
occur together kx for example -y=zJoint variation - when one
quantity variesdirectly as the product of two or more independent
variables 27. Combined & Joint VariationCombined variation -
when direct and inversevariations occur together kx for example
-y=zJoint variation - when one quantity variesdirectly as the
product of two or more independent variablesfor example - A = kbh
28. 5. A baseball pitchers earned run average (ERA) varies directly
as the number of earned runs allowed and inversely as the number of
innings pitched. Write a general equation to modelthis situation.
29. 5. A baseball pitchers earned run average (ERA) varies directly
as the number of earned runs allowed and inversely as the number of
innings pitched. Write a general equation to modelthis situation.
Let e = ERA, R = # of earned runs and I = # of innings. 30. 5. A
baseball pitchers earned run average (ERA) varies directly as the
number of earned runs allowed and inversely as the number of
innings pitched. Write a general equation to modelthis situation.
Let e = ERA, R = # of earned runs and I = # of innings.kR E= I 31.
5. A baseball pitchers earned run average (ERA) varies directlyas
the number of earned runs allowed and inversely as thenumber of
innings pitched. Write a general equation to model this situation.
Let e = ERA, R = # of earned runs and I = # of innings.kR E= I 6.
In a recent year, a pitcher had an ERA of 2.56, having given up 72
earned runs in 253 innings. How many earned runs would the pitcher
have given up if he had pitched 300 innings, assuming that his ERA
remained the same? 32. 5. A baseball pitchers earned run average
(ERA) varies directlyas the number of earned runs allowed and
inversely as thenumber of innings pitched. Write a general equation
to model this situation. Let e = ERA, R = # of earned runs and I =
# of innings.kR E= I 6. In a recent year, a pitcher had an ERA of
2.56, having given up 72 earned runs in 253 innings. How many
earned runs would the pitcher have given up if he had pitched 300
innings, assuming that his ERA remained the same?kRE=I 33. 5. A
baseball pitchers earned run average (ERA) varies directlyas the
number of earned runs allowed and inversely as thenumber of innings
pitched. Write a general equation to model this situation. Let e =
ERA, R = # of earned runs and I = # of innings.kR E= I 6. In a
recent year, a pitcher had an ERA of 2.56, having given up 72
earned runs in 253 innings. How many earned runs would the pitcher
have given up if he had pitched 300 innings, assuming that his ERA
remained the same?kR72kE=2.56 =I253 34. 5. A baseball pitchers
earned run average (ERA) varies directlyas the number of earned
runs allowed and inversely as thenumber of innings pitched. Write a
general equation to model this situation. Let e = ERA, R = # of
earned runs and I = # of innings.kR E= I 6. In a recent year, a
pitcher had an ERA of 2.56, having given up 72 earned runs in 253
innings. How many earned runs would the pitcher have given up if he
had pitched 300 innings, assuming that his ERA remained the
same?kR72k 72kE=2.56 = 253 2.56 = 253I253 253 35. 5. A baseball
pitchers earned run average (ERA) varies directlyas the number of
earned runs allowed and inversely as thenumber of innings pitched.
Write a general equation to model this situation. Let e = ERA, R =
# of earned runs and I = # of innings.kR E= I 6. In a recent year,
a pitcher had an ERA of 2.56, having given up 72 earned runs in 253
innings. How many earned runs would the pitcher have given up if he
had pitched 300 innings, assuming that his ERA remained the
same?kR72k 72kE=2.56 = 253 2.56 = 253 647.68 = 72kI253 253 36. 5. A
baseball pitchers earned run average (ERA) varies directlyas the
number of earned runs allowed and inversely as thenumber of innings
pitched. Write a general equation to model this situation. Let e =
ERA, R = # of earned runs and I = # of innings.kR E= I 6. In a
recent year, a pitcher had an ERA of 2.56, having given up 72
earned runs in 253 innings. How many earned runs would the pitcher
have given up if he had pitched 300 innings, assuming that his ERA
remained the same?kR72k 72kE=2.56 = 253 2.56 = 253 647.68 = 72kk
9I253 253 37. 5. A baseball pitchers earned run average (ERA)
varies directlyas the number of earned runs allowed and inversely
as thenumber of innings pitched. Write a general equation to model
this situation. Let e = ERA, R = # of earned runs and I = # of
innings.kR E= I 6. In a recent year, a pitcher had an ERA of 2.56,
having given up 72 earned runs in 253 innings. How many earned runs
would the pitcher have given up if he had pitched 300 innings,
assuming that his ERA remained the same?kR72k 72kE=2.56 = 253 2.56
= 253 647.68 = 72kk 9I253 2539R2.56 = 300 38. 5. A baseball
pitchers earned run average (ERA) varies directlyas the number of
earned runs allowed and inversely as thenumber of innings pitched.
Write a general equation to model this situation. Let e = ERA, R =
# of earned runs and I = # of innings.kR E= I 6. In a recent year,
a pitcher had an ERA of 2.56, having given up 72 earned runs in 253
innings. How many earned runs would the pitcher have given up if he
had pitched 300 innings, assuming that his ERA remained the
same?kR72k 72kE=2.56 = 253 2.56 = 253 647.68 = 72kk 9I253 2539R
9R2.56 = 300 2.56 = 300 300 300 39. 5. A baseball pitchers earned
run average (ERA) varies directlyas the number of earned runs
allowed and inversely as thenumber of innings pitched. Write a
general equation to model this situation. Let e = ERA, R = # of
earned runs and I = # of innings.kR E= I 6. In a recent year, a
pitcher had an ERA of 2.56, having given up 72 earned runs in 253
innings. How many earned runs would the pitcher have given up if he
had pitched 300 innings, assuming that his ERA remained the
same?kR72k 72kE=2.56 = 253 2.56 = 253 647.68 = 72kk 9I253 2539R
9R2.56 = 300 300 2.56 = 300300 R 85 runs 40. 7. The power in an
electrical circuit varies jointly as the square of the current and
the resistance. Write a formula to show this relationship. 41. 7.
The power in an electrical circuit varies jointly as the square of
the current and the resistance. Write a formula to show this
relationship. Let p = power, c = current and r = resistance. 42. 7.
The power in an electrical circuit varies jointly as the square of
the current and the resistance. Write a formula to show this
relationship. Let p = power, c = current and r = resistance.Then P
= kc2r 43. 7. The power in an electrical circuit varies jointly as
the square of the current and the resistance. Write a formula to
show this relationship. Let p = power, c = current and r =
resistance.Then P = kc2r b. The power in a certain circuit is 1500
watts when the current is 15 amps and the resistance is 10 ohms.
Find the power in that circuit when the current is 20 amps and the
resistance is 21 ohms. 44. 7. The power in an electrical circuit
varies jointly as the square of the current and the resistance.
Write a formula to show this relationship. Let p = power, c =
current and r = resistance.Then P = kc2r b. The power in a certain
circuit is 1500 watts when the current is 15 amps and the
resistance is 10 ohms. Find the power in that circuit when the
current is 20 amps and the resistance is 21 ohms. HINT: Find k rst.
45. 7. The power in an electrical circuit varies jointly as the
square of the current and the resistance. Write a formula to show
this relationship. Let p = power, c = current and r =
resistance.Then P = kc2r b. The power in a certain circuit is 1500
watts when the current is 15 amps and the resistance is 10 ohms.
Find the power in that circuit when the current is 20 amps and the
resistance is 21 ohms. HINT: Find k rst. so... 1500 = k(15)2(10)
46. 7. The power in an electrical circuit varies jointly as the
square of the current and the resistance. Write a formula to show
this relationship. Let p = power, c = current and r =
resistance.Then P = kc2r b. The power in a certain circuit is 1500
watts when the current is 15 amps and the resistance is 10 ohms.
Find the power in that circuit when the current is 20 amps and the
resistance is 21 ohms. HINT: Find k rst. so... 1500 =
k(15)2(10)1500 = k(2250) 47. 7. The power in an electrical circuit
varies jointly as the square of the current and the resistance.
Write a formula to show this relationship. Let p = power, c =
current and r = resistance.Then P = kc2r b. The power in a certain
circuit is 1500 watts when the current is 15 amps and the
resistance is 10 ohms. Find the power in that circuit when the
current is 20 amps and the resistance is 21 ohms. HINT: Find k rst.
so... 1500 = k(15)2(10)1500 = k(2250)2/3 = k 48. 7. The power in an
electrical circuit varies jointly as the square of the current and
the resistance. Write a formula to show this relationship. Let p =
power, c = current and r = resistance.Then P = kc2r b. The power in
a certain circuit is 1500 watts when the current is 15 amps and the
resistance is 10 ohms. Find the power in that circuit when the
current is 20 amps and the resistance is 21 ohms. HINT: Find k
rst.NOW: Find the power. so... 1500 = k(15)2(10)1500 = k(2250)2/3 =
k 49. 7. The power in an electrical circuit varies jointly as the
square of the current and the resistance. Write a formula to show
this relationship. Let p = power, c = current and r =
resistance.Then P = kc2r b. The power in a certain circuit is 1500
watts when the current is 15 amps and the resistance is 10 ohms.
Find the power in that circuit when the current is 20 amps and the
resistance is 21 ohms. HINT: Find k rst.NOW: Find the power. so...
1500 = k(15)2(10) P = (2/3)c2r1500 = k(2250)2/3 = k 50. 7. The
power in an electrical circuit varies jointly as the square of the
current and the resistance. Write a formula to show this
relationship. Let p = power, c = current and r = resistance.Then P
= kc2r b. The power in a certain circuit is 1500 watts when the
current is 15 amps and the resistance is 10 ohms. Find the power in
that circuit when the current is 20 amps and the resistance is 21
ohms. HINT: Find k rst.NOW: Find the power. so... 1500 = k(15)2(10)
P = (2/3)c2r1500 = k(2250) P = (2/3)(20)2(21)2/3 = k 51. 7. The
power in an electrical circuit varies jointly as the square of the
current and the resistance. Write a formula to show this
relationship. Let p = power, c = current and r = resistance.Then P
= kc2r b. The power in a certain circuit is 1500 watts when the
current is 15 amps and the resistance is 10 ohms. Find the power in
that circuit when the current is 20 amps and the resistance is 21
ohms. HINT: Find k rst.NOW: Find the power. so... 1500 = k(15)2(10)
P = (2/3)c2r1500 = k(2250) P = (2/3)(20)2(21)2/3 = kP = 5600 watts
52. Homework worksheet 2.3A/2.9A
