Worksheet on Mean Proportional

Practice the questions given in the worksheet on mean proportional

1. Find the mean proportional of the following sets of positive numbers:

(i) x\(^{3}\)y, xy\(^{3}\)

(ii) (x - y)\(^{2}\), (x + y)\(^{3}\)


2. Find the mean proportional of the following:

(i) 9, 16

(ii) 4\(\frac{4}{7}\), 3\(\frac{1}{2}\)

(iii) (a + b)(a - b)\(^{3}\), (a + b)\(^{3}\)(a - b)

(iv) \(\frac{x^{2}}{4ab}\), \(\frac{a}{by^{2}}\)


3. Find the mean proportional between

(i) 5 and 45

(ii) 0.04 and 0.0036

(iii) 0.25 and 6.25

 

4. Find the third proportional of the following:

(i) 0.5, 0.25

(ii) a\(^{2}\)b, ab\(^{2}\)

(iii) \(\frac{x}{y}\) + \(\frac{y}{x}\), \(\frac{x}{y}\)

 

5. (i) If the mean proportional of a and c is b then prove that a, c, a\(^{2}\) + b\(^{2}\) and b\(^{2}\) + c\(^{2}\) are proportional.

(ii) If b is the mean proportional of a and c, prove that the mean proportional of a\(^{2}\) + b\(^{2}\) and b\(^{2}\) + c\(^{2}\) is ab + bc.

(iii) If b is the mean proportional of a and c, prove that

\[\left ( \frac{ab + bc + ca}{a + b + c} \right )^{3} = abc\]

 

Answers for the worksheet on mean proportional are given below.


Answers


1. (i) x\(^{2}\)y\(^{2}\)

(ii) x\(^{2}\) - y\(^{2}\)


2. (i) 12

(ii) 4

(iii) \((a^{2} - b^{2})^{2}\)

(iv) \(\frac{x}{2by}\)


3. (i) 15

(ii) 0.012

(iii) 1.25


4. (i) 0.125

(ii) b\(^{3}\)

(iii) \(\frac{x^{3}}{y(x^{2} + y^{2})}\)

 








10th Grade Math

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