In y = m x + c , make c as the subject and write the formula.

The given formula is y = m x + c . We have to make c as the subject of the formula. We know that the subject of a formula is the variable that is expressed in terms of the other variables involved in the formula. Thus, we have, y = m x + c ⇒ c = y - m x Therefore, the required auxiliary formula with c as the subject is c = y - m x .

Find the missing numbers a , b and c in the following table. Changing kilometres into miles. Number of kilometres 5 10 15 20 25 30 Number of miles 8 16 24 a b c

We shall frame a formula for changing kilometres into miles. Let the number in kilometres be k and the number of miles be m . When k = 5 , we have, m = 8 . So, k : m = 5 : 8 . When k = 10 , we have, m = 16 . So, k : m = 10 : 16 = 10 2 : 16 2 = 5 : 8 . When k = 15 , we have, m = 24 . So, k : m = 15 : 24 = 15 3 : 24 3 = 5 : 8 . Thus, we observe that the ratio of k and m is always 5 : 8 . Hence, the formula for changing kilometres into miles can be taken as k : m = 5 : 8 ⇒ k m = 5 8 . We shall express this formula with m as the subject. We know that the subject of a formula is the variable that is expressed in terms of the other variables involved in the formula. Thus, we have, k m = 5 8 ⇒ 5 × m = k × 8 ⇒ m = 8 5 × k . Now, when k = 20 , we get, m = 8 5 × 20 = 32 . When k = 25 , we get, m = 8 5 × 25 = 40 . When k = 30 , we get, m = 8 5 × 30 = 48 . Therefore, a = 32 , b = 40 and c = 48 .

The following table gives the number of sides and the number of diagonals of a polygon. Number of sides n 3 4 5 6 7 8 Number of diagonals d 0 2 5 9 14 20 Write a formula to find d in terms of n .

The given table is Number of sides n 3 4 5 6 7 8 Number of diagonals d 0 2 5 9 14 20 Let the formula to find d in terms of n be d = x n 2 + y n + z -----(i), where x , y and z are constants. From the table, we observe, when n = 3 , d = 0 . From (i), we get, 0 = x × 3 2 + y × 3 + z ⇒ 0 = 9 x + 3 y + z -----(ii) Also, we observe, when n = 4 , d = 2 Again, from (i), we get, 2 = x × ( 4 ) 2 + y × 4 + z ⇒ 2 = 16 x + 4 y + z -----(iii) Again, we observe, when n = 5 , d = 5 So, from (i), we obtain, 5 = x × ( 5 ) 2 + y × 5 + z ⇒ 5 = 25 x + 5 y + z -----(iv) Subtracting (ii) from (iii), we obtain, 2 = 7 x + y -----(v) Subtracting (iii) from (iv), we obtain, 3 = 9 x + y -----(vi) Now, subtracting (v) from (vi), we obtain, 2 x = 1 ⇒ x = 1 2 -----(vii) Putting the value of x from (vii) in (v), we obtain, 2 = 7 × 1 2 = y ⇒ y = 2 - 7 2 = 4 - 7 2 = - 3 2 -----(viii) Putting the value of x from (vii) and the value of y from (viii) in (ii), we obtain, 0 = 9 × 1 2 + 3 × - 3 2 + z ⇒ 0 = 9 2 - 9 2 + z ⇒ z = 0 Now, putting the values of x , y and z in (i), we obtain, d = 1 2 × n 2 + - 3 2 n + 0 ⇒ d = n 2 2 - 3 n 2 ⇒ d = n n - 3 2 Therefore, the required formula to find d in terms of n is d = n ( n - 3 ) 2 .

If y - y 1 y 2 - y 1 = x - x 1 x 2 - x 1 , then express ' y ' in terms of x , x 1 , y 1 , x 2 and y 2 .

The given formula is y - y 1 y 2 - y 1 = x - x 1 x 2 - x 1 . We have to express ' y ' in terms of x , x 1 , y 1 , x 2 and y 2 . We know that the subject of a formula is the variable that is expressed in terms of the other variables involved in the formula. Thus, we have, y - y 1 y 2 - y 1 = x - x 1 x 2 - x 1 ⇒ y - y 1 x 2 - x 1 = y 2 - y 1 x - x 1 ⇒ y - y 1 = y 2 - y 1 x - x 1 x 2 - x 1 ⇒ y - y 1 = y 2 - y 1 x - x 1 x 2 - x 1 ⇒ y = y 2 - y 1 x - x 1 x 2 - x 1 + y 1 Therefore, the required formula with y as the subject is y = y 2 - y 1 x - x 1 x 2 - x 1 + y 1 .

MEDIUM

8th Foundation

IMPORTANT

Earn 100

If $x^{2} + y^{2} = r^{2}$ , then find the formula with $x$ as the subject.

Important Questions on Formulae

EASY

8th Foundation

IMPORTANT

Pearson IIT Foundation Mathematics Class 8>Chapter 16 - Formulae>PRACTICE QUESTIONS CLASSROOM WING>Q 40

y = m x + c

, make

c

as the subject and write the formula.

HARD

8th Foundation

IMPORTANT

Pearson IIT Foundation Mathematics Class 8>Chapter 16 - Formulae>PRACTICE QUESTIONS CLASSROOM WING>Q 41

Find the missing numbers $a, b$ and $c$ in the following table.
Changing kilometres into miles.

Number of kilometres	$5$	$10$	$15$	$20$	$25$	$30$
Number of miles	$8$	$16$	$24$	$a$	$b$	$c$

HARD

8th Foundation

IMPORTANT

Pearson IIT Foundation Mathematics Class 8>Chapter 16 - Formulae>PRACTICE QUESTIONS CLASSROOM WING>Q 41

Find the missing numbers $a, b$ and $c$ in the following table.

Change Centigrade $({}^{\circ}C)$ into Fahrenheit $({}^{\circ}F)$ where centigrade scale is divided into $100$ equal parts and Fahrenheit scale is divided into $180$ equal parts.

Temperature in $° C$	$- 5$	$0$	$5$	$10$	$15$	$20$
Temperature in $° F$	$23$	$32$	$41$	$a$	$b$	$c$

HARD

8th Foundation

IMPORTANT

Pearson IIT Foundation Mathematics Class 8>Chapter 16 - Formulae>PRACTICE QUESTIONS CLASSROOM WING>Q 42

The following figure has a network of rectangles. Two rows and three columns.

Question Image

How many rectangles are there in the figure?

HARD

8th Foundation

IMPORTANT

Pearson IIT Foundation Mathematics Class 8>Chapter 16 - Formulae>PRACTICE QUESTIONS CLASSROOM WING>Q 42

The following figure has a network of rectangles.

Question Image

If there are $x$ rectangles in each row and $y$ rectangles in each column, how many rectangles will be there in the network, in terms of $x$ and $y$ .

HARD

8th Foundation

IMPORTANT

Pearson IIT Foundation Mathematics Class 8>Chapter 16 - Formulae>PRACTICE QUESTIONS CLASSROOM WING>Q 43

The following table gives the number of sides and the number of diagonals of a polygon.

Number of sides $(n)$	$3$	$4$	$5$	$6$	$7$	$8$
Number of diagonals $(d)$	$0$	$2$	$5$	$9$	$14$	$20$

Write a formula to find $d$ in terms of $n$ .

MEDIUM

8th Foundation

IMPORTANT

Pearson IIT Foundation Mathematics Class 8>Chapter 16 - Formulae>PRACTICE QUESTIONS CLASSROOM WING>Q 44

\frac{y - y_{1}}{y_{2} - y_{1}} = \frac{x - x_{1}}{x_{2} - x_{1}}

, then express

' y'

in terms of

x, x_{1}, y_{1}, x_{2}

and

y_{2}

MEDIUM

8th Foundation

IMPORTANT

Pearson IIT Foundation Mathematics Class 8>Chapter 16 - Formulae>PRACTICE QUESTIONS CLASSROOM WING>Q 45

The diagonal of a rectangle is

10

units. The formula to find the diagonal is

d = \sqrt{l^{2} + b^{2}}

, where

l

and

b

are length and breadth, respectively. If the value of

(10 + b) (10 - b)

l^{k}

, then

k =

_____.

If x2+y2=r2, then find the formula with x as the subject.

Important Questions on Formulae

Learn and Prepare for any exam you want !

If $x^{2} + y^{2} = r^{2}$ , then find the formula with $x$ as the subject.