Write an equation for the following: y varies directly with x and z. Find K when x=2, y=12 and z=5.

1 answer:

6 0

$\qquad \qquad \textit{direct joint variation} \\\\ \textit{\underline{y} varies directly with \underline{x} and \underline{z}}~\hspace{8.5em} \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}xz~\hfill } \\\\ \textit{\underline{y} varies directly with \underline{x}, }w^2\textit{ and }z^5~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}xw^2z^5~\hfill } \\\\[-0.35em] ~\dotfill$

$y = kxz\qquad \textit{we know that} \begin{cases} x=2\\ y=12\\ z=5 \end{cases}\implies 12=k(2)(5) \\\\\\ \cfrac{12}{(2)(5)}=k\implies \cfrac{6}{5}=k~\hspace{10em}\boxed{y=\cfrac{6}{5}xz}$

You might be interested in

Find the midpoint of the line seg<br> (-4, -2) and (3, 3)

Serggg [28]

Answer:

Step-by-step explanation:

(-4 + 3)/2= -1/2

(-2 + 3)/2= 1/2

(-1/2, 1/2) the midpoint

6 0

2 years ago

Solve the volume of the box! Help ASAP also you get extra points <3.

olga2289 [7]

Answer:

22½ in³ or 22.5 in³

Step-by-step explanation:

V=bwh

V=5(3)(1.5)

V=15(1.5)

V=22.5

8 0

2 years ago

Need help with both of these please!! ASAP

Alik [6]

x = 1

Answer:

$m\angle XVW = 100\degree$

Step-by-step explanation:

In the first figure, FP is the bisector of $\angle DFE$

$\therefore m\angle 1 = m\angle 2\\\therefore 44x + 1 = 46x - 1\\\therefore 1 + 1 = 46x - 44x\\\therefore 2 = 2x\\\therefore \frac{2}{2} = x \\\huge \red {\boxed {\therefore x = 1}}$

In the second figure, VP is the bisector of $\angle XVW$

$\therefore m\angle 1 = m\angle 2\\\therefore 12x + 2 = 11x +6\\\therefore 12x - 11x = 6 - 2\\\therefore x = 4\\\because m\angle XVW = m\angle1 + m\angle 2\\\therefore m\angle XVW = 12x + 2 + 11x +6\\\therefore m\angle XVW = 23x + 8\\\therefore m\angle XVW = 23\times 4+ 8\\\therefore m\angle XVW = 92+ 8\\\huge \purple {\boxed {\therefore m\angle XVW = 100\degree}} \\$