2.9 Notes.notebook
February 27, 2013
Feb 27­9:32 AM
2.9: COMBINED AND JOINT VARIATION
Feb 26­2:24 PM
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2.9 Notes.notebook
February 27, 2013
COMBINATION
JOINT
FORMULA
“Y VARIES “Y VARIES _______________AS _______________AS THIS IS READ AS… ______ ______ AND_____________
AND_______”
______ AS ______”
Feb 26­2:24 PM
1. The volume of a gas varies directly as its temperature measured in degrees Kelvin and inversely as its pressure. When the temperature of a certain gas is 1250 and its pressure is 47.625 cm of mercury, its volume is 600 cm3.
A)
Find the constant of variation.
B)
Write an equation that models the situation.
C) What would be the volume of this gas to the nearest cubic centimeter, if its temperature were 2000 pressure were 72.2 cm of mercury?
Feb 27­9:50 AM
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2.9 Notes.notebook
February 27, 2013
2. The wind force F on a sail varies jointly as the area A of the sail and the square of the wind speed W. The force on a sail with area 500 ft2 is 100 pounds when the wind speed is 20 mph.
A) Find the constant of variation.
B) Write an equation that models the situation.
C) What would the force be with a 30 mph wind?
Feb 27­9:50 AM
TRANSLATION:
A. y varies directly with x and inversely with y squared.
B. y varies jointly as x cubed and y.
C. The volume of a cone varies jointly with the height of the cone and the radius of the
cone squared.
D. The maximum weight a board can hold varies directly with the width of the board and
inversely with the distance between the supports.
Feb 26­2:24 PM
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2.9 Notes.notebook
February 27, 2013
E. w varies directly with the square of x and inversely as y. When x = 5 and y = 2, w = 23.75. Find w when x =­3 and y = ­6.
Feb 26­2:24 PM
F. The kinetic energy of an object varies jointly as its mass and the square of its velocity. The kinetic energy of an object with mass 12 kg moving at 8m/x is 384 joules. Find the kinetic energy of an object with mass 8kg moving at 12m/s.
Feb 26­2:25 PM
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2.9 Notes.notebook
February 27, 2013
G. c varies directly as the square of a and inversely as b. c = 5 and a = 5 and b = 10. Find c when a = 3 and b = 4.
Feb 26­2:25 PM
3. A baseball pitcher’s Earned Run Average (ERA) varies directly as the number of earned
runs allowed and inversely as the number of innings pitched. In a recent year, a pitcher had
an ERA of 2.56, having given up 72 runs in 253 innings pitched. What would the pitchers ERA
be if he had given up 80 runs in 300 innings?
Feb 26­2:26 PM
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2.9 Notes.notebook
February 27, 2013
H. z varies directly as the square of x and inversely as y. When x = 3 and y = 5, z = 4.5. Find z when x = ­2 and y = ­1.5
Feb 26­2:25 PM
Go For It!
1. Write the variation formula for : R varies
directly as the square of P, directly as L, and
inversely as the square root of A.
Feb 26­2:25 PM
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2.9 Notes.notebook
February 27, 2013
2. z varies jointly as the square root of x and the cube of y. When
x = 5 and y = 2, z = 4. Find z when x = 25 and y = ­5.
Feb 26­2:26 PM
4. The wind force F on a vertical surface varies jointly as the area A of the
surface and the square of the wind speed. The force is 340 Newtons on a
vertical surface area of 1 m2 when the wind blows at 18m/sec. Find the force
exerted by the wind of 35m/sec on a vertical surface of 2m2.
Feb 26­2:26 PM
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