Answer:

he value of zz is \frac{18}{5}

5

18

.

Step-by-step explanation:

Variation is one of the topics that is discussed in high school mathematics. Variation is the relationship between two variables. Varies Directly means that the two variables are in the same direction. Thus, the two variables are increasing or decreasing together. Varies Inversely means that the two variables go in the opposite direction. Furthermore, one variable increases, and the other one decreases.

Type of Variation

1. Varies Directly

2. Varies Inversely

A variable, yy , varies directly as xx implies that there exists a kk such that y=kxy=kx .

A variable, yy , varies inversely as xx implies that there exists a kk such that y=\frac{k}{x}y=

x

k

.

A variable, zz , varies jointly as xx and yy means that there exists a kk such that z=kxyz=kxy .

Find zz , when x=6x=6 and y=9y=9 .

Steps in Solving

1. Substitute the values of z=3z=3 , x=3x=3 , and y=15y=15 into the equation z=kxyz=kxy , then solve for \begin{gathered}k.\\\end{gathered}

k.

2. Substitute the values of x=6x=6 , y=9y=9 , and the value of kk from Step 1 into the equation z=kxyz=kxy .

Solution:

\begin{gathered}\begin{aligned}z&=kxy\\3&=k(3)(15)\\3&=45k\\\frac{3}{45}&=\frac{45k}{45}\\\frac{3}{45}&=k\\\frac{1}{15}&=k\end{aligned}\end{gathered}

z

3

3

45

3

45

3

15

1

=kxy

=k(3)(15)

=45k

=

45

45k

=k

=k

\begin{gathered}\begin{aligned}z&=kxy\\z&=\frac{1}{15}(6)(9)\\z&=\frac{54}{15}\\z&=\frac{18}{5}\end{aligned}\end{gathered}

z

z

z

z

=kxy

=

15

1

(6)(9)

=

15

54

=

5

18

Thus, the value of zz is \frac{18}{5}

5

18

, when x=6x=6 and y=9y=9