Question

What is the mean proportional between the fourth proportionals of (0.03, 5, 0.006) and (0.81, 29.4, 5.4)?

Answer 1

Answer:

14

Step-by-step explanation:

fourth proportional of (0.03,5,0.006) is 1

fourth proportional of (0.81,29.4,5.4) is 196

mean proprtional of 1& 196 is √1*196= 14

**done**

Answer 2

To find: The mean proportional between the fourth proportionals of $(0.03, 5, 0.006)$ and $(0.81, 29.4; 5.4)$ ?

Solution:

Assume that the fourth proportional of $(0.03, 5, 0.006)$ is x and fourth proportional of $(0.81, 294,5.4)$ is y .

Find the value of x.

Know that,  

Product of extreme $=$product of means .

$\[ \Rightarrow 0.03 \times x = 5 \times 0.006\]$

Divide both sides by $0.03$.

$\[\begin{array}{l} \Rightarrow x = 5 \times 0.2\\ \Rightarrow x = 1\end{array}\]$

Find the value of y.

Product of extreme $=$product of means .

$\[\begin{array}{l}0.81 \times y = 29.4 \times 5\\ \Rightarrow y = \frac{{29.4 \times 5}}{{0.81}}\\ \Rightarrow y = 196\end{array}\]$

 Know that,

Mean proportional of $\[a:b = \sqrt {\left( {a \times b} \right)} \]$

Therefore,

Mean proportional of x and y is,

$\[\begin{array}{l} \Rightarrow xy = \sqrt {x \times y} \\ \Rightarrow xy = \sqrt {1 \times 196} \\ \Rightarrow xy = \sqrt {196} \\ \Rightarrow xy = 14\end{array}\]$

Hence, the mean proportional between the fourth proportional of the given ratio is 14.