9.1 Inverse & Joint Variation By: L. Keali’i Alicea.
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Transcript of 9.1 Inverse & Joint Variation By: L. Keali’i Alicea.
9.1 Inverse & Joint 9.1 Inverse & Joint VariationVariation
By: L. Keali’i AliceaBy: L. Keali’i Alicea
Just a reminder from chapter 2Just a reminder from chapter 2
Direct Variation
Use y=kx.
Means “y varies directlyvaries directly with x.”
k is called the constant of variationconstant of variation.
New stuff!New stuff!
Inverse VariationInverse Variation
“y varies inverselyvaries inversely with x.”
k is the constant of variationconstant of variation.
x
ky
Ex: tell whether x & y show direct variation, Ex: tell whether x & y show direct variation, inverse variation, or neither.inverse variation, or neither.
a. xy=5
b. x+y = 7
c. 5.1
yx
Hint: Solve the equation for y and take notice of
the relationship.
xy
5
Inverse Variation
Neither
xy 5.1
Direct Variation
Ex: The variables x & y vary inversely. Use Ex: The variables x & y vary inversely. Use the given values to write an equation relating the given values to write an equation relating
x and y. Then find y when x =4. x and y. Then find y when x =4. • x=2, y=4
k=8• Find y when x= 4.
y= 2
x
kyuse :
24
k
x
ky
xy
8
4
8y
Ex: The variables x & y vary inversely. Use Ex: The variables x & y vary inversely. Use the given values to write an equation relating the given values to write an equation relating
x and y. Then find y when x =4. x and y. Then find y when x =4. • x=16, y= 1/4
k=(1/4)16= 4• Find y when x= 4.
y= 1
x
kyuse :
164/1
k
x
ky
xy
4
4
4y
Joint VariationJoint Variation
• When a quantity varies directly as the product of 2 or more other quantities.
• For example: if z varies jointly with x & y, then z=kxy.
• Ex: if y varies inversely with the square of x, then y=k/x2.
• Ex: if z varies directly with y and inversely with x, then z=ky/x.
Examples: Write an equation.Examples: Write an equation.
• y varies directly with x and inversely with z2.
• y varies inversely with x3.
• y varies directly with x2 and inversely with z.
• z varies jointly with x2 and y.
• y varies inversely with x and z.
2z
kxy
3x
ky
z
kxy
2
ykxz 2
xz
ky
The variable z varies jointly with x and y. Use the The variable z varies jointly with x and y. Use the given values to write an equation relating x, y, and given values to write an equation relating x, y, and
z. Then find z when x= -3 and y= 4.z. Then find z when x= -3 and y= 4.
• x= 1, y=2, z=6We use:z = kxyWe put in the values for z, x, and y to solve for k.6= k(1)(2) Then solve for k.k= 6/2 = 3z = 3xyWe then put in the values for x and y and solve for
z.
z= 3(-3)(4)= -36
AssignmentAssignment
9.1 B (2-12 even, 13-18)