REARRANGING FORMULAS WORKSHEET

(1)  Make y the subject of :

2x + 5y = 10

(2)  Solve for x :

3x + a = d

(3)  Solve for x :

5x + 2y = d

(4)  Make a the subject of F = ma

(5)  Make d the subject of V  =  ldh

(6)  Make h the subject of A  =  bh/2

(7)  Rearrange this formula into the form y = mx + c.

Hence, state the value of :

a) the slope m

b) the y-intercept c.

(8)  Make t the subject of s  =  (1/2) gt², where t > 0.

(9)  Make x the subject of y  =  (3x+2)/(x-1)

(10)  Make y the subject of M  =  4/(x²+y²)

(11) 

A = 180(n - 2)/n

The formula above shows the relationship between A, the measure of each angle of a regular polygon, and n, the number of sides of a regular polygon

Which of the following expresses the number of sides in terms of the measure of an angle?

a) n = (A - 180)/360     b)  n = (A/360) - 2

c) n = 180A - (1/2)        d)  n = 360/(180 - A) 

12)  If p, q, r, and s are four different positive numbers such that

p = r/(s - r) and q = r/s

What is q in terms of s ?

a)  1 + (1/p)     b) 1 - (1/p)    c) 1/(1 + p)     d) p/(1+p) 

13)  

Mosteller's formula A =  √hw/60

Current's formula A = (4 + w)/30

The formulas are used in medicine to estimate the body surface area A, in square meters, of infants and children whose weight w ranges between 3 and 30 kilograms and whose height h is measured in centimeters.

a)  Based on Current's formula, what is w in terms of A 

b)  If Mosteller's and Current's formula give the same estimate for A, which of the following expression is equivalent to √hw

a)  (4 + w)/2    b)  (4 + w)/1800   c) 2(4 + w) 

d) (4 + w)²/2

14) The formula below is often used by the project managers to compute E, the estimated time to complete a job. Where O is the shortest completion time, P is the longest completion time and M is the most likely completion time.

E = (O + 4M + P)/6

Which of the following correctly gives P in terms of E, O and M ?

a)  P = 6E - O - 4M      b)  P = -6E + O + 4M

c)  P = (O + 4M + E)/6     d)  P = (O + 4M - E)/6

(1)  Solution :

Solving the equation for y, we get

5y  =  10-2x

Divide by 5 on both sides, we get

y  =  (10-2x)/5

y  =  2 - (2x/5)

(2)  Solution :

3x  =  d-a

x  =  (d-a)/3

(3)  Solution :

5x  =  d-2y

x  =  (d-2y)/5

(4)  Solution :

F = ma

a  =  F/m

(5)  Solution :

V  =  ldh

d  =  V/lh

(6)  Solution :

A  =  bh/2

h  =  2A/b

(7)  Solution :

y  =  mx + c

(a) Solve the formula for m :

mx  =  y - c

m  =  (y-c)/x

(b)  Solving for c :

c  =  y-mx

(8)  Solution :

s  =  (1/2) gt²

2s  =  gt²

t²  =  2s/g

t  =  √(2s/g)

(9)  Solution :

y  =  (3x+2)/(x-1)

y(x-1)  =  3x+2

xy-y  =  3x+2

xy-3x  =  2+y

x(y-3)  =  2+y

x  =  (2+y)/(y-3)

(10)  Solution :

M  =  4/(x²+y²)

x²+y²  =  4/M

y²  =  (4/M) - x²

y  =  √[(4/M) - x²]

(11) Solution :

A = 180(n - 2)/n

Here we have to solve for n,

An = 180(n - 2)

An = 180n - 360

Adding 360 on both sides,

360 = 180 n - A n

360 = n(180 - A)

Dividing by 180 - A on both sides,

360 / (180 - A) = n

So, option d is correct.

12) Solution :

p = r/(s - r) and q = r/s

Solving for r from the above information, we get

r = p(s - r) -----(1)

r = qs ------(2)

p(s - r) = qs

ps - pr = qs

Dividing by s on both sides

ps/s - pr/s = q

p - p(r/s) = q

Applying the value of r/s = q, we get

p - pq = q

p = q + pq

p = q(1 + p)

q = p/(1 + p)

13) Solution :

So, option d is correct.

Mosteller's formula A =  √hw/60  ----(1)

Current's formula A = (4 + w)/30 ---(2)

a) For this, we have to solve for w in terms of A.

Multiplying by 30 on both sides

30A = 4 + w

Subtracting 4 on both sides

w = 30A - 4

b) 

Mosteller's formula A =  √hw/60  ----(1)

Current's formula A = (4 + w)/30 ---(2)

(1) = (2)

 √hw/60 = (4 + w)/30

 √hw = 60 [(4 + w)/30]

 √hw = 2 (4 + w)

14) Solution :

E = (O + 4M + P)/6

Here we have to solve for P, we get

6E = O + 4M + P

Subtracting O and 4M on both sides.

6E - O - 4M = P

So, P = 6E - O - 4M

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