variation joint and direct

Question

How would you describe the difference between direct variation and joint variation in words? Use examples to help illustrate

Answer 1

direct variation is y=kx

inverse variation is y=x/k

joint variation is y=kxz

another version of direct variation

for direct, the output is a mutliple of the input

for inverse the output times the input is a constant

joint variation is a multiple of the inputs

graphically, direct variation is a straight line through the origin

grpahically, inverse variation is a rectangular hyperbola with the axes as asymptotes

you need 3 dimensions to graph joint variation

the more hours you work the more you get paid is an example of direct variation

if you have an hourly wage of $10 and you work zero hours, you get paid zero dollars

work 10 hours you get paid $100 for the week. work 20 hours you get paid $200

$10 is k in the formula y=kx. y is your pay check. x is your hours worked

graph your weekly salary against hours worked for the week and it's a striaght line through the origin (0,0) with slope = 10. salary on the y axis, hours worked on the x axis

Period and Frequency are inversely related P=1/F, PF = a constant = 1

if your interest on savings is compounded quarterly, the frequency= 4 times per year

the period of compounding is 1/4 of a year. 4 x 1/4 = 1.

the speed of rotation of a planet in th solar system varies inversely with the length of its day.

S=1/L. If the speed approaches infinity, the day lasts nearly zero time. if the rotation speed slows down, the day lasts longer.

your pay check may depend on hours worked plus commissions for sales. the check amount varies jointly with hours and sales