Question

Solve the following equations on joint and combined variation.
1. y varies jointly as x and z. If y = 5 when x = 3 and z = 4, find y when x = 6 and z = 8.

2. y varies jointly as x and z. If y = 12 when x = 4 and z = 3, find y when x = 9 and z = 8.

3. y varies directly as x and inversely as z. If y = 5 when x = 3 and z = 4, find y when x = 6 and z = 8.

4.y varies directly as x^2 and inversely as z. If y = 12 when x = 2 and z = 7, find y when x = 3 and z = 9.

5. A varies jointly as b and h. If A = 16 when b = 2 and h = 8, find A when b = 8 and h = 16.

6. y varies jointly as x and the square root of z . If y = 6 when x = 3 and z = 9, find y when x = 4 and z = 36.

7. y varies jointly as the cube root of x and the square of z . If y = 3 when x = 8 and z = 4, find y correct to 3 significant figures, when x = 27 and z = 6.

8. y varies directly as x and inversely as z. If y = 10 when x = 9 and z = 12, find y correct to two decimal places, when x = 16 and z = 10.

9.x varies jointly as y^3 and square root of z . If x = 7 when y = 2 and z = 4, find x correct to 2 decimal places, when y = 3 and z = 9.

10. x varies jointly as y^3 and inversely as the square root of z . If x = 7 when y = 2 and z = 4, find x when y = 3 and z = 9.

Answer 1

$\frac{40}{3}$Solution:

1. y=kxz (where k is a constant number)

5=k×3×4

k=$\frac{5}{12}$

then, y=$\frac{5}{12}$×6×8

         y=20

2. y=kxz (where k is a constant number)

12=k×4×3

k=1

then, y=1×9×8

         y=72

3. y=k×$\frac{x}{z}$ (where k is a constant number)

5=k×$\frac{3}{4}$

k=$\frac{20}{3}$

then, y=$\frac{20}{3}$×$\frac{6}{8}$

        y=5

4. y=k×$\frac{x^{2} }{z}$  (where k is a constant number)

12=k×$\frac{4}{7}$

k=21

then, y=21×$\frac{9}{9}$

        y=21

5. A=kbh  (where k is a constant number)

16=k×2×8

k=1

then, A=1×8×16

         A=128

6. y=kx$\sqrt{z}$  (where k is a constant number)

6=k×3×3

k=$\frac{2}{3}$

then, y=$\frac{2}{3}$×4×6

        y=16

7. y=k$\sqrt[3]{x}$$z^{2}$   (where k is a constant number)

3=k×2×16

k=$\frac{3}{32}$

then, y=$\frac{3}{32}$××3×36

        y=$\frac{324}{32}$

8. y=k$\frac{x}{z}$  (where k is a constant number)

10=k$\frac{9}{12}$

k=$\frac{40}{3}$

then, y=  $\frac{40}{3}$×$\frac{16}{10}$

         y=$\frac{64}{3}$

9. x=k$y^{3}\sqrt{z}$   (where k is a constant number)

7=k×8×2

k=$\frac{7}{16}$

then, x=$\frac{7}{16}$×27×3

        x=2.21

10. x=k$\frac{y^{3} }{\sqrt{z} }$   (where k is a constant number)

7=k$\frac{8}{2}$

k=$\frac{14}{8}$

then, x=$\frac{14}{8}$×$\frac{27}{3}$

         x=$\frac{63}{4}$

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