Inverse Variations and Square Root

INVERSE VARIATION

Multiple Select

The renovation of a room will take 6 days to complete if 4 people are working. State the change on

(i) the time needed to complete the renovation if the number of people working is halved.

(ii) the number of people working if the time needed to complete the renovation is decreased by 50%

• (i) the time needed is doubled

• (i) the time needed is halved

• (ii) the number of people working is decreased by 50%

• (ii) the unmber of people working is increased by 50%

Multiple Choice

The table below shows the values of x and y. Determine whether y varies inversely as x.

x : 3 4 9 15

y : 9 12 27 35

• xy is a constant, therefore y varies inversely as x

• xy is not a constant, therefore y does not vary inversely as x.

Multiple Choice

The table below shows the relationship between the height, H cm, and the radius, R cm, of a cylinder. Determine whether H varies inversely as

$$R^2$$  
R :   2    4      5       6
H : 18  4.5   2.88    2

• $$R^2H$$  is a constant, therefore H varies inversely as  $$R^2$$  

• $$R^2H$$  is not a constant, therefore H does not varies inversely as  $$R^2$$  

Multiple Choice

p varies inversely as the square of q and p = 0.05 when q = 4. Express p in terms of q.

(Hint: find k, write in equation form)

• $$p\ =\ \frac{4}{5q^2}$$

• $$p\ =\ 320q^2$$

• $$p\ =\ \frac{1}{5q^2}$$

Multiple Choice

$$y\ varies\ inversely\ as\ \sqrt{x}$$   and y = 5 when x = 2.56. Express y in terms of x.
(Hint: find the value of k)

• $$y=\ \frac{64}{5\sqrt{x}}$$  

• $$y=\frac{8}{\sqrt{x}}$$  

• $$y=8\sqrt{x}$$  

Multiple Select

It is given that y varies inversely as the square root of x and y = 15 when x = 0.64.

(i) Express y in terms of x.

(ii) Find the value of x when y = 0.8.

• $$y=\frac{12}{\sqrt{x}}$$

• $$y=\frac{48}{5\sqrt{x}}$$

• $$x=225$$

• $$x=15$$

Multiple Select

$$D\ varies\ inversely\ as\ E^2$$ and D = 25 when E = 0.8.
 (i) Express D in terms of E.
(ii) Find the positive value of E when D=0.64

• $$D=\frac{16}{E^2}$$  

• $$D=\frac{20}{E^2}$$  

• E = 5

• E = 25

Multiple Select

The radius, r cm, of a cylinder of fixed volume varies inversely as the square root of its height,h cm. It is given that the radius of a cylinder is 2 cm when its height is 49 cm.

(i) Express r in terms of h.

(ii) Find the value of h when r = 3.5.

• $$r=\frac{98}{\sqrt{h}}$$

• $$r=\frac{14}{\sqrt{h}}$$

• h = 16

• h = 28