Char Basic!
P varies jointly as q and r. Illustrate my mathematical sentence.
a. r=kPq
b. P=kqr
c. k=Pqr
d. q=kPr
b. P=kqr
a varies jointly as b and c. If a=60 when b=5 and c=3, Find the constant of variation k.
a. 4k=a/bc
k=60/(5)(3)
k=60/15
k=4
Therefore, k=4 is the constant of variation.
a. 4
Q varies jointly as r and s. If Q=2.4 when r=0.6 and s=0.8, find Q when r=1.6 and s=.01.
a. 0.06
b. 0.08
c. 0.10
d. 0.09
Q=krs
Solve for k:
k=Q / rs
k=2.4 / (0.6)(0.8)
k=2.4 / 0.48
k=5
then solve for Q:
Q=krs
Q=(5)(1.6)(.01)
Q=0.08
b. 0.08
The heat H produced by an electric lamp varies jointly as the resistance R and the square of the current i.
a. R=kHi
b. i=kHR
c. H=kRi
d. H=k/Ri
c. H=kRi
z varies jointly as x and y. If z=150 when x=3 and y=5. Find the constant of variation k.
a. 8b. 9
c. 11
d. 10
k=z / xy
k=150 / (3)(5)
k=150 / 15
k=10
Therefore, k=10 is the constant of variation.
d. 10
Z varies jointly as x and y. If Z=60 when x=3 and y=4, find y when Z=80 and x=2.
a. 8
b. 5
c. 7
d. 6
Z=kxy
Solve for k:
k=Z / xy
k=60 / (3)(4)
k=60 / 12
k=5
Then solve for y:
y=Z / kx
y=80 / (5)(2)
y=80 / 10
y=8
a. 8
I am the quotient of a variable and the product of two or more variables. What am I?
a. Direct Variation
b. Joint Variation
c. Constant
d. Variation
c. Constant
P varies jointly as Q and R. If P=108 when Q=9 and R=3. Find the constant of variation k.
a. 1
b. 2
c. 3
d. 4
k=P/QR
k=108 / (9)(3)
k=108 / 27
k=4
Therefore, k=4 is the constant of variation.
d. 4
w varies jointly as x, y, and z. If w=18 when x=2, y=6, and z=5. Find w when x=5, y=12 and z=3.
a. 52
b. 54
c. 56
d. 58
Solve for k:
k=w / xyz
k=18 / (2)(6)(5)
k=18 / 60
k=3/10
Solve for w:
w=kxyz
w=(3/10)(5)(12)(3)
w=(3/10)(180)
w=540/10
w=54
b. 54