1. Warm Up Set up equations for each. 1. y varies directly with the square root of x 2. p varies inversely with the cube of m 3. g is proportional to the square of c

2. Review Direct Variation Inverse Variation

3. Joint Variation If a quantity is equal to a constant (k), times the product of two other quantities, then we say that the first quantity varies jointly as the other two. If a quantity is equal to a constant (k), times the product of two other quantities, then we say that the first quantity varies jointly as the other two. Example: x varies jointly as y and z Example: x varies jointly as y and z k is the constant of variation k is the constant of variation After solving for k: After solving for k:

4. Set up the equation with K P varies inversely as R and directly as the square root of W P varies inversely as R and directly as the square root of W g varies directly as 2x+1 and directly as y

5. Video/Examples 1. R varies jointly as the square of s and the square of t. R=12 when s=1 and t=2. Find r when s=3 and t=4 2. x is directly proportional to y and inversely proportional to the cube of z. x=3 when y=3 and z=2. Find x when y=2 and z=5 3. The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P. A measuring device is calibrated to give V=300 in 3 when T=250 degrees and P=10 lb/in 2. What is the volume on this device when the temperature is 370 degrees and the pressure is 20 lb/in 2 ? 4. 3 tailors are sewing 15 clothes in 5 days. How long would it take for 5 tailors to sew 20 clothes? 5. 9 workers, working 8 hours a day, complete a piece of work in 52 days. How long will it take for 13 workers to complete the same job by working 6 hours a day

6. Classwork/Homework 1. If y varies directly as x and inversely as z, and if y=10 when x=8 and z=5, find the joint variation equation. Then find y when x=6 and z=2.5 2. y varies directly as the square of x and inversely as the square root of z. When x=8 and z=25, y=16. Find y when x=5 and z=9 3. If y 2 varies directly as x–1 and inversely as x+d and if x=2, d=4 for y=1, then find x when y=2 and d=1. 4. If x varies directly as y 2 and inversely as p, and if x=2 for y=3 and p=1, then find y when x=4 and p=5. 5. If 2 students can type 210 pages in 3 days, how many students will be needed to type 700 pages in 2 days? 6. P varies directly as V and inversely as the square root of R. Given that P=180 when R=25 and V=9, find P when V=6 and R=36. 7. The height h of a cone varies directly as its volume v and inversely as the square of its radius r. Write a formula for the height of the cone.