# Math Help - Need Some Help with Inverse and Direct Variation

1. ## Need Some Help with Inverse and Direct Variation

Hey guys haven’t been here in a while but have a few questions , I realize you all giving me the answers plainly wouldn’t really help me but if you could take me step by step into solving them if you can that would be help

1. Y varies directly as x and y is 2 when x is 3 calculate

A) Y when X is 9

B) X when y = 18

Copy and Complete the following table so that y is directly proportionate to x squared

x - 0 , BLANK , 3 , 4 , 5 , Blank

y- Blank , 12 , 27, blank , 75 , 192

p is inversely proportionate to the square root of y . If p = 1.2 when y = 100, calculate
A) The value of p when y = 4
B) the value of y when p = 3

(27/8)-2/3
Solve the following questions

3 2x = 243

Any assistance you give is quite esteemed… Thanks all

2. ## Re: Need Some Help with Inverse and Direct Variation

Originally Posted by bahamamath
Hey guys haven’t been here in a while but have a few questions , I realize you all giving me the answers plainly wouldn’t really help me but if you could take me step by step into solving them if you can that would be help

1. Y varies directly as x and y is 2 when x is 3 calculate

y = kx ... sub in your given values for x and y , then solve for k, the constant of proportionality. use your equation to answer A) and B)

A) Y when X is 9

B) X when y = 18

Copy and Complete the following table so that y is directly proportionate to x squared

y = kx2 ... same drill as before

x - 0 , BLANK , 3 , 4 , 5 , Blank

y- Blank , 12 , 27, blank , 75 , 192

p is inversely proportionate to the square root of y . If p = 1.2 when y = 100, calculate

$\color{red}{p = \frac{k}{\sqrt{y}}}$ ... same drill again

A) The value of p when y = 4
B) the value of y when p = 3

(27/8)-2/3 = (8/27)2/3 ... cube root of 8/27, then square the result

Solve the following questions

3 2x = 243

note that 243 = 35
...

3. ## Re: Need Some Help with Inverse and Direct Variation

Hello, bahamamath!

Here are the first two . . .

$1.\;y\text{ varies directly as }x,\text{ and }y=2\text{ when }x = 3.$

$\text{Calculate:}$

$A)\;y\text{ when }x = 9.$

$y\text{ varies directly as }x\quad\Rightarrow\quad y \:=\:kx$

$y = 2\text{ when }x = 3 \quad\Rightarrow\quad 2 \:=\:k(3) \qyad\Rightarrow\quad k \:=\:\tfrac{2}{3}$

. . $\text{Hence: }\:y \:=\:\tfrac{2}{3}x$

$\text{When }x = 9,\text{ we have: }\:y \:=\:\tfrac{2}{3}(9) \quad\Rightarrow\quad y \:=\:6$

$B)\;x\text{ when }y = 18.$

$\text{When }y = 18,\text{ we have: }\:18 \:=\:\tfrac{2}{3}x \quad\Rightarrow\quad x \:=\:27$

$\text{Copy and complete the following table so that }y\text{ is directly proportionate to }x^2.$

. . $\begin{array}{|c||c|c|c|c|c|c|} \hline x & 0 & - & 3 & 4 & 5 & - \\ \hline y & - &12 & 27& - & 75 & 192 \\ \hline \end{array}$

$y\text{ is directly proportionate to }x^2 \quad\Rightarrow\quad y \:=\:kx^2$

$\text{When }x = 3,\:y = 27\!:\;\;27 \:=\:k(3^2) \quad\Rightarrow\quad k \:=\:3$

. . $\text{Hence: }\:y \:=\:3x^2$

$\text{When }x=0\!:\;y \,=\,3(0^2) \quad\Rightarrow\quad y \,=\,0$

$\text{When }y = 12\!:\;12 \,=\,3x^2 \quad\Rightarrow\quad x^2 \,=\,4 \quad\Rightarrow\quad x \,=\,2$

$\text{When }x = 4\!:\;y \,=\,3(4^2) \quad\Rightarrow\quad y \,=\,48$

$\text{When }y = 192\!:\;192 \,=\,3x^2 \quad\Rightarrow\quad x^2 \,=\,64 \quad\Rightarrow\quad x \,=\,8$

The completed table:

. . $\begin{array}{|c||c|c|c|c|c|c|}\hline x & 0 & 2 & 3 & 4 & 5 & 8 \\ \hline y & 0 &12 & 27& 48 & 75 & 192 \\ \hline\end{array}$

Too slow . . . again!
.