Joint Variation, in Depth
Read this topicExplanations 2
- (Video) Joint Variation by ThinkwellVids Here's a video by ThinkwellVids explaining joint variation. He gives the following problem: "The area aaa of a triangle varies jointly a…
By Alex Federspiel, Jonathan Heller
- **Joint Variation ** \\ Joint variation is a type of variable where one variable depends on two or more variables. \\ If zzz varies jointly in proportion to xxx and yyy, the joi…
By Eunji Kwon
Problems 20
- Suppose yyy jointly varies with ttt and sss. When t=4t=4t=4 and s=6s=6s=6, y=192y=192y=192. What is kkk, the constant of variation?
- Suppose xxx varies directly with ggg and the square root of hhh. If x=48x=48x=48 when g=4g=4g=4 and h=9h=9h=9, what is kkk?
- Suppose zzz varies inversely with xxx and yyy. When z=4z=4z=4, x=3x=3x=3 and y=2y=2y=2, what is kkk, the constant of variation?
- Suppose hhh varies with directly with aaa and inversely with the cube of bbb. What does this relation look like?
- jjj varies inversely with hhh, and directly with the square of lll. What does this relationship look like?
- You know zzz varies jointly with xxx and yyy. If x=3x=3x=3 and y=4y=4y=4 when z=72z=72z=72 find zzz when x=5x=5x=5 and y=10y=10y=10.
- You know zzz varies inversely with the product xxx and yyy. If x=13x=\frac13x=31 and y=27y=27y=27 when z=118z=\frac1{18}z=181 find zzz when x=5x=5x=5 and y=10y=10y=10.
- What is the value of www when x=10x = 10x=10, y=8y = 8y=8, and z=5z = 5z=5?
- Let yyy vary jointly with x2x^2x2 and z\sqrt{z}z. If y=15y=15y=15 when x=2x=2x=2 and z=25z=25z=25, what is yyy when x=3x=3x=3 and z=16z=16z=16?
- Let yyy vary inversely with xxx and zzz. If y=5y=5y=5 then x=4x=4x=4 and z=3z=3z=3, what is yyy when x=5x=5x=5 and z=8z=8z=8?
- Let yyy vary directly with xxx and inversely with zzz. If y=−5y=-5y=−5 when x=10x=10x=10 and z=6z=6z=6, what is yyy when x=8x=8x=8 and z=34z=\frac34z=43?
- Ley yyy vary inversely with xxx and directly with zzz. If y=3y=3y=3 when x=−5x=-5x=−5 and z=1z=1z=1, what is yyy when x=−2x=-2x=−2 and z=−4z=-4z=−4?
- Let yyy vary jointly with xxx and zzz. If y=12y=\frac12y=21 when x=13x=\frac13x=31 and z=11z=11z=11, what is yyy when x=43x=\frac43x=34 and z=9z=9z=9?
- Let yyy vary inversely with the product of xxx and the square of zzz. What does this relationship look like?
- The area of a rectangle, a=l⋅wa=l\cdot wa=l⋅w, is considered to be joint variation. What is the constant of variation, kkk, in this formula?
- Which of the following equations show joint variation?
- The volume of a pyramid, vvv, varies jointly with the area of it's base, bbb, and the height, hhh. If the volume of a pyramid is 15 units315\text{ units}^315 units3 when the bas…
- Let yyy vary inversely with xxx and directly with the square of zzz. If y=1y=1y=1 when x=15x=15x=15 and z=3z=3z=3, what is yyy when x=20x=20x=20 and z=4z=4z=4?
- Let yyy vary directly with the square of xxx and the square of zzz. If y=2y=2y=2 when x=3x=3x=3 and z=4z=4z=4, what is yyy when x=1x=1x=1 and z=2z=2z=2?
- Let yyy vary directly with the square of xxx, and with zzz. If y=6y=6y=6 when x=3x=3x=3 and z=4z=4z=4, what is the constant of variation, kkk?